Type:	Package
Title:	Tools for Model Specification in the Latent Variable Framework
Version:	2.0.3
Date:	2024-02-22
URL:	https://github.com/bozenne/lavaSearch2
BugReports:	https://github.com/bozenne/lavaSearch2/issues
Description:	Tools for model specification in the latent variable framework (add-on to the 'lava' package). The package contains three main functionalities: Wald tests/F-tests with improved control of the type 1 error in small samples, adjustment for multiple comparisons when searching for local dependencies, and adjustment for multiple comparisons when doing inference for multiple latent variable models.
License:	GPL-3
Encoding:	UTF-8
Depends:	R (≥ 2.10), ggplot2, lava (≥ 1.6.4)
Imports:	abind, doParallel, MASS, Matrix, methods, multcomp, mvtnorm, nlme, parallel, Rcpp, reshape2, sandwich, stats, utils
Suggests:	clubSandwich, data.table, foreach, emmeans, lme4, lmerTest, numDeriv, pbapply, pbkrtest, R.rsp, riskRegression, survival, testthat
LinkingTo:	Rcpp, RcppArmadillo
VignetteBuilder:	R.rsp
NeedsCompilation:	yes
RoxygenNote:	7.2.3
Packaged:	2024-02-22 11:18:47 UTC; hpl802
Author:	Brice Ozenne [aut, cre]
Maintainer:	Brice Ozenne <brice.mh.ozenne@gmail.com>
Repository:	CRAN
Date/Publication:	2024-02-23 09:10:02 UTC

Tools for Model Specification in the Latent Variable Framework

Description

The package contains three main functionalities:

• compare2, summary2: Wald tests/robust Wald tests/F-tests/robust F-tests with improved control of the type 1 error in small samples.

• glht2: adjustment for multiple comparisons when doing inference for multiple latent variable models.

• modelsearch2: searching for local dependencies with adjustment for multiple comparisons.

It contains other useful functions such as:

• calibrateType1: simulation study of the type 1 error of Wald tests.

• createContrast: user-friendly function generating a contrast matrix.

• getVarCov2: reconstruct the conditional variance covariance matrix.

• iidJack: extract the jackknife iid decomposition.

Details

The latent variable models (LVM) considered in this package can be written
as a measurement model:

Y_i = \nu + \eta_i \Lambda + X_i K + \epsilon_i

and a structural model:

\eta_i = \alpha + \eta_i B + X_i \Gamma + \zeta_i

where \Sigma is the variance covariance matrix of the residuals \epsilon,
and \Psi is the variance covariance matrix of the residuals \zeta.

The corresponding conditional mean is:

\mu_i(\theta) = E[Y_i|X_i] = \nu + (\alpha + X_i \Gamma) (1-B)^{-1} \Lambda + X_i K

\Omega(\theta) = Var[Y_i|X_i] = \Lambda^{t} (1-B)^{-t} \Psi (1-B)^{-1} \Lambda + \Sigma

The package aims to provides tool for testing linear hypotheses on the model coefficients \nu, \Lambda, K, \Sigma, \alpha, B, \Gamma, \Psi. Searching for local dependency enable to test whether the proposed model is too simplistic and if so to identify which additional coefficients should be added to the model.

Limitations

'lavaSearch2' has been design for Gaussian latent variable models. This means that it may not work / give valid results:

• in presence of censored or binary outcomes.

• with stratified models (i.e. object of class multigroup).

Compute the First Derivative of the Expected Information Matrix

Description

Compute the first derivative of the expected information matrix.

Usage

.dInformation2(
  dmu,
  dOmega,
  d2mu,
  d2Omega,
  OmegaM1,
  missing.pattern,
  unique.pattern,
  name.pattern,
  grid.3varD1,
  grid.2meanD1.1varD1,
  grid.2meanD2.1meanD1,
  grid.2varD2.1varD1,
  name.param,
  leverage,
  n.cluster,
  weights
)

Details

calc_dinformation will perform the computation individually when the argument index.Omega is not null.

Add a New Link Between Two Variables in a LVM

Description

Generic interface to add links to lvm objects.

Usage

addLink(object, ...)

## S3 method for class 'lvm'
addLink(
  object,
  var1,
  var2,
  covariance,
  all.vars = lava::vars(object),
  warnings = FALSE,
  ...
)

## S3 method for class 'lvm.reduced'
addLink(object, ...)

Arguments

Details

The argument all.vars is useful for lvm.reduce object where the command vars(object) does not return all variables. The command vars(object, xlp = TRUE) must be used instead.

Arguments var1 and var2 are passed to initVarlink.

Examples

library(lava)
set.seed(10)

m <- lvm()
regression(m) <- c(y1,y2,y3)~u
regression(m) <- u~x1+x2
latent(m) <- ~u
m2 <- m

addLink(m, x1 ~ y1, covariance = FALSE)
addLink(m, y1 ~ x1, covariance = FALSE)
coef(addLink(m, y1 ~ y2, covariance = TRUE))

addLink(m2, "x1", "y1", covariance = FALSE)
addLink(m2, "y1", "x1", covariance = FALSE)
newM <- addLink(m, "y1", "y2", covariance = TRUE)
coef(newM)

2D-display of the Domain Used to Compute the Integral

Description

2D-display of the domain used to compute the integral.

Usage

## S3 method for class 'intDensTri'
autoplot(object, coord.plot = c("x", "y1"), plot = TRUE, ...)

Arguments

Value

A ggplot object.

See Also

intDensTri

Graphical Display of the Bias or Type 1 Error

Description

Graphical display of the bias or type 1 error for the output of calibrateType1.

Usage

## S3 method for class 'calibrateType1'
autoplot(
  object,
  type = "bias",
  plot = TRUE,
  color.threshold = "red",
  type.bias = "absolute",
  alpha = 0.05,
  nrow.legend = NULL,
  name2label = NULL,
  color = NULL,
  keep.method = NULL,
  ...
)

Arguments

Details

Method names:

• p.Ztest

• p.Satt

• p.KR

• p.robustZtest

• p.robustSatt

• p.robustKR

Value

An list containing:

• plot: a ggplot object.

• data: the dataset used to generate the ggplot object.

Display the Value of a Coefficient across the Steps.

Description

Display the value of a coefficient across the steps.

Usage

## S3 method for class 'modelsearch2'
autoplot(
  object,
  param,
  ci = TRUE,
  step = 0:nStep(object),
  conf.level = 0.95,
  plot = TRUE,
  add.0 = TRUE,
  ...
)

Arguments

Value

A list containing

• plot: a ggplot object.

• data: the data used to generate the ggplot object.

Examples

## Not run: 
mSim <- lvm(Y~G+X1+X2+X3+X4+X5)
addvar(mSim) <- ~Z1+Z2

set.seed(10)
df.data <- lava::sim(mSim, 1e2)

mBase <- lvm(Y~G)
addvar(mBase) <- ~X1+X2+X3+X4+X5+Z1+Z2
e.lvm <- estimate(mBase, data = df.data)
res <- modelsearch2(e.lvm, method.p.adjust = "holm", alpha = 0.05)
autoplot(res, param = "Y~G")
autoplot(res, param = c("Y","Y~G"))

## End(Not run)

Adjust the p.values Using the Quantiles of the Max Statistic

Description

Adjust the p.values using the quantiles of the max statistic.

Usage

calcDistMaxIntegral(
  statistic,
  iid,
  df,
  iid.previous = NULL,
  quantile.previous = NULL,
  quantile.compute = lava.options()$search.calc.quantile.int,
  alpha,
  cpus = 1,
  cl = NULL,
  trace
)

calcDistMaxBootstrap(
  statistic,
  iid,
  iid.previous = NULL,
  quantile.previous = NULL,
  method,
  alpha,
  cpus = 1,
  cl = NULL,
  n.sim,
  trace,
  n.repmax = 100
)

Arguments

Value

A list containing

• p.adjust: the adjusted p-values.

• z: the rejection threshold.

• Sigma: the correlation matrix between the test statistic.

• correctedLevel: the alpha level corrected for conditioning on previous tests.

Examples

library(mvtnorm)

set.seed(10)
n <- 100
p <- 4
link <- letters[1:p]
n.sim <- 1e3 # number of bootstrap simulations 

#### test - not conditional ####
X.iid <- rmvnorm(n, mean = rep(0,p), sigma = diag(1,p))
colnames(X.iid) <- link
statistic <- setNames(1:p,link)


r1 <- calcDistMaxIntegral(statistic = statistic, iid = X.iid, 
            trace = FALSE, alpha = 0.05, df = 1e6) 

r3 <- calcDistMaxBootstrap(statistic = statistic, iid = X.iid,
            method = "residual",
            trace = FALSE, alpha = 0.05, n.sim = n.sim)

r4 <- calcDistMaxBootstrap(statistic = statistic, iid = X.iid,
            method = "wild",
            trace = FALSE, alpha = 0.05, n.sim = n.sim)

rbind(integration = c(r1$p.adjust, quantile = r1$z),
      bootResidual = c(r3$p.adjust, quantile = r3$z),
      bootWild    = c(r4$p.adjust, quantile = r4$z))

#### test - conditional ####
## Not run: 
Z.iid <- rmvnorm(n, mean = rep(0,p+1), sigma = diag(1,p+1))
seqQuantile <- qmvnorm(p = 0.95, delta = rep(0,p+1), sigma = diag(1,p+1), 
                    tail = "both.tails")$quantile

r1c <- calcDistMaxIntegral(statistic = statistic, iid = X.iid,
            iid.previous = Z.iid, quantile.previous =  seqQuantile, 
            trace = FALSE, alpha = 0.05, df = NULL)

r3c <- calcDistMaxBootstrap(statistic = statistic, iid = X.iid,
            iid.previous = Z.iid, quantile.previous =  seqQuantile, method = "residual",
            trace = FALSE, alpha = 0.05, n.sim = n.sim)

r4c <- calcDistMaxBootstrap(statistic = statistic, iid = X.iid,
            iid.previous = Z.iid, quantile.previous =  seqQuantile, method = "wild",
            trace = FALSE, alpha = 0.05, n.sim = n.sim)

rbind(integration = c(r1c$p.adjust, quantile = r1c$z),
      bootResidual = c(r3c$p.adjust, quantile = r3c$z),
      bootWild    = c(r4c$p.adjust, quantile = r4c$z))

## End(Not run)

Compute the Type 1 Error After Selection [EXPERIMENTAL]

Description

Compute the type 1 error after selection [EXPERIMENTAL].

Usage

calcType1postSelection(
  level,
  mu,
  Sigma,
  quantile.previous,
  distribution,
  df,
  n = 10,
  correct = TRUE,
  ...
)

Arguments

Details

The number of tests at the current step (i.e. after selection) is assumed to be one less than the number of tests at the previous step (i.e. before selection).

Arguments mu and Sigma must contain the moments for the vector of test statistics before and after selection (in that order).

Value

[numeric] the type 1 error.

Author(s)

Brice Ozenne

Examples

library(mvtnorm)
n <- 350

#### only 2 tests
Sigma <- rbind(c(1,0,0),c(0,1,1),c(0,1,1))
z2 <- qmvnorm(0.95, mean = rep(0,2), sigma = Sigma[1:2,1:2], tail = "both.tails")$quantile

## no selection since strong effect
mu <- c(10,0,0)
calcType1postSelection(0.95, quantile.previous = z2, distribution = "gaussian",
                        mu = mu, Sigma = Sigma, correct = TRUE)

## strong selection
## Not run: 
mu <- c(0,0,0)
levelC <- calcType1postSelection(0.95, quantile.previous = z2, distribution = "gaussian",
                        mu = mu, Sigma = Sigma)
print(levelC) # more liberal than without selection
calcType1postSelection(levelC, quantile.previous = z2, distribution = "gaussian",
                        mu = mu, Sigma = Sigma, correct = FALSE)

## End(Not run)

#### 3 tests
Sigma <- diag(1,5,5)
Sigma[4,2] <- 1
Sigma[2,4] <- 1
Sigma[5,3] <- 1
Sigma[3,5] <- 1

z2 <- qmvnorm(0.95, mean = mu[1:3], sigma = Sigma[1:3,1:3], tails = "both.tails")$quantile

## no selection since strong effect
## Not run: 
mu <- c(10,0,0,0,0)
calcType1postSelection(0.95, quantile.previous = z2, distribution = "gaussian",
                        mu = mu, Sigma = Sigma, correct = TRUE)

## strong selection
mu <- c(0,0,0,0,0)
levelC <- calcType1postSelection(0.95, quantile.previous = z2,
                        mu = mu, Sigma = Sigma, distribution = "gaussian")
calcType1postSelection(levelC, quantile.previous = z2, distribution = "gaussian",
                        mu = mu, Sigma = Sigma, correct = FALSE)

## End(Not run)

Simulation Study Assessing Bias and Type 1 Error

Description

Perform a simulation study over one or several sample size to assess the bias of the estimate and the type 1 error of the Wald test and robust Wald test

Usage

calibrateType1(object, param, n.rep, ...)

## S3 method for class 'lvm'
calibrateType1(
  object,
  param,
  n.rep,
  n,
  correction = TRUE,
  warmup = NULL,
  null = NULL,
  F.test = FALSE,
  cluster = NULL,
  generative.object = NULL,
  generative.coef = NULL,
  true.coef = NULL,
  n.true = 1e+06,
  round.true = 2,
  bootstrap = FALSE,
  n.bootstrap = 1000,
  checkType1 = FALSE,
  checkType2 = FALSE,
  dir.save = NULL,
  label.file = NULL,
  seed = NULL,
  cpus = 1,
  trace = 2,
  ...
)

## S3 method for class 'lvmfit'
calibrateType1(
  object,
  param,
  n.rep,
  correction = TRUE,
  F.test = FALSE,
  bootstrap = FALSE,
  n.bootstrap = 1000,
  seed = NULL,
  trace = 2,
  cpus = 1,
  ...
)

Arguments

Value

An object of class calibrateType1.

Author(s)

Brice Ozenne

See Also

link{autoplot.calibrateType1} for a graphical display of the bias or of the type 1 error.

Examples

## Not run: 
#### simulate data ####
m.Sim <- lvm(c(Y1[mu1:sigma]~1*eta,
               Y2[mu2:sigma]~1*eta,
               Y3[mu3:sigma]~1*eta,
               eta~beta1*Group+beta2*Gender))
latent(m.Sim) <- ~eta
categorical(m.Sim, labels = c("M","F")) <- ~Gender

d <- lava::sim(m.Sim, 1e2)

#### calibrate type 1 error on the estimated model ####
m <- lvm(Y1~eta,
         Y2~eta,
         Y3~eta,
         eta~Group+Gender)
e <- lava::estimate(m, data = d)
res <- calibrateType1(e, param = "eta~Group", n.rep = 100)
res <- calibrateType1(e, param = c("eta~Group","Y1~eta"), F.test = TRUE, n.rep = 100)
res <- calibrateType1(e, param = "eta~Group", n.rep = 100, cpus = 4)
summary(res)

## End(Not run)

Check that Validity of the Dataset

Description

Check whether the dataset can be used to fit the lvm object.

Usage

checkData(object, data, trace)

## S3 method for class 'lvm'
checkData(object, data, trace = TRUE)

Arguments

Value

Invisible TRUE or FALSE.

Examples

m <- lvm()
regression(m) <- c(y1,y2,y3)~u
regression(m) <- u~x
latent(m) <- ~u

d <- lava::sim(m,1e2)

try(checkData(m, data = d)) # return an error

checkData(m, data = d[,-4])

try(checkData(m, data = d[,-(3:4)])) # return an error

Simplify a lvm object

Description

Remove variables with no link.

Usage

clean(x, ...)

## S3 method for class 'lvm'
clean(x, rm.exo = TRUE, rm.endo = TRUE, rm.latent = TRUE, ...)

Arguments

Examples

m <- lvm()
m <- regression(m, x=paste0("x",1:5),y="y1")
m <- regression(m, x=paste0("x",1:5),y="y2")
covariance(m) <- y1~y2

cancel(m) <- y1 ~ x1
cancel(m) <- y2 ~ x1
clean(m)

m <- lvm(y1 ~ eta + x1, y2 ~ eta, y3 ~ eta + x2)
latent(m) <- ~eta
clean(m)
m
cancel(m) <- y1 ~ eta
cancel(m) <- y2 ~ eta
cancel(m) <- y3 ~ eta
clean(m)

Model Coefficients With Small Sample Correction

Description

Extract the coefficients from a latent variable model. Similar to lava::compare but with small sample correction.

Usage

coef2(object, as.lava, ...)

## S3 method for class 'lvmfit'
coef2(object, as.lava = TRUE, ssc = lava.options()$ssc, ...)

Arguments

Details

When argument object is a lvmfit object, the method first calls estimate2 and then extract the model coefficients.

Value

A numeric vector named with the names of the coefficients.

See Also

estimate2 to obtain lvmfit2 objects.

Examples

#### simulate data ####
set.seed(10)
dW <- sampleRepeated(10, format = "wide")
set.seed(10)
dL <- sampleRepeated(10, format = "long")
dL$time2 <- paste0("visit",dL$time)

#### latent variable models ####
e.lvm <- estimate(lvm(c(Y1,Y2,Y3) ~ 1*eta + X1, eta ~ Z1), data = dW)
coef(e.lvm)
coef2(e.lvm)
coef2(e.lvm, as.lava = FALSE)

Extract the Coefficient by Type

Description

Extract specific types of coefficient from a lvm object: covariance coefficient(s) (coefCov), extra parameter(s) (coefExtra), position in the list of models for each coefficient (coefIndexModel), intercept coefficient(s) (coefIntercept), coefficient(s) that are used as reference (coefRef), regression coefficient(s) (coefReg), variance coefficient(s) (coefVar).

Usage

coefCov(object, value, keep.var, ...)

## S3 method for class 'lvm'
coefCov(object, value = FALSE, keep.var = FALSE, ...)

## S3 method for class 'lvmfit'
coefCov(object, value = FALSE, keep.var = FALSE, ...)

## S3 method for class 'multigroup'
coefCov(object, value = FALSE, keep.var = FALSE, ...)

coefExtra(object, value, ...)

## S3 method for class 'lvm'
coefExtra(object, value = FALSE, ...)

## S3 method for class 'lvmfit'
coefExtra(object, value = FALSE, ...)

## S3 method for class 'multigroup'
coefExtra(object, value = FALSE, ...)

coefIndexModel(object, ...)

## S3 method for class 'lvm'
coefIndexModel(object, ...)

## S3 method for class 'lvmfit'
coefIndexModel(object, ...)

## S3 method for class 'multigroup'
coefIndexModel(object, ...)

## S3 method for class 'multigroupfit'
coefIndexModel(object, ...)

coefIntercept(object, value, ...)

## S3 method for class 'lvm'
coefIntercept(object, value = FALSE, ...)

## S3 method for class 'lvmfit'
coefIntercept(object, value = FALSE, ...)

## S3 method for class 'multigroup'
coefIntercept(object, value = FALSE, ...)

coefRef(object, value, ...)

## S3 method for class 'lvmfit'
coefRef(object, value = FALSE, ...)

coefReg(object, value, ...)

## S3 method for class 'lvm'
coefReg(object, value = FALSE, ...)

## S3 method for class 'lvmfit'
coefReg(object, value = FALSE, ...)

## S3 method for class 'multigroup'
coefReg(object, value = FALSE, ...)

coefVar(object, value, ...)

## S3 method for class 'lvm'
coefVar(object, value = FALSE, ...)

## S3 method for class 'lvmfit'
coefVar(object, value = FALSE, ...)

## S3 method for class 'multigroup'
coefVar(object, value = FALSE, ...)

Arguments

Value

A vector containing the names of the positions of the coefficients.

Examples

#### regression ####
m <- lvm(Y~X1+X2)
e <- estimate(m, lava::sim(m, 1e2))

coefCov(m)
coefCov(m, value = TRUE)

coefCov(m, keep.var = TRUE)
coefCov(m, value = TRUE, keep.var = TRUE)

coefIndexModel(m)
coefIndexModel(e)

coefIntercept(m)
coefIntercept(m, value = TRUE)

coefReg(m)
coefReg(m, value = TRUE)

#### LVM ####
m <- lvm()
regression(m) <- c(y1,y2,y3)~u
regression(m) <- u~x1+x2
latent(m) <- ~u
covariance(m) <- y1~y2

m.Sim <- m
categorical(m.Sim, labels = c("a","b","c")) <- ~x2
e <- estimate(m, lava::sim(m.Sim, 1e2))

coefCov(m)
coefCov(m, value = TRUE) 

coefCov(m, keep.var = TRUE)
coefCov(m, value = TRUE, keep.var = TRUE)

coefExtra(m)

coefIndexModel(m)
coefIndexModel(e)

## additional categorical variable 
categorical(m, labels = as.character(1:3)) <- "X1"

coefExtra(m)
coefExtra(m, value = TRUE)

## additional categorical variable
categorical(m, labels = as.character(1:3)) <- "x1"

coefIntercept(m)
coefIntercept(m, value = TRUE)
coefIntercept(e)

coefReg(e, value = TRUE)

#### multigroup ####
m <- lvm(Y~X1+X2)
eG <- estimate(list(m,m), list(lava::sim(m, 1e2), lava::sim(m, 1e2)))

coefIndexModel(eG)

Extract the Type of Each Coefficient

Description

Extract the type of each coefficient of a lvm object.

Usage

coefType(object, as.lava, ...)

## S3 method for class 'lvm'
coefType(object, as.lava = TRUE, data = NULL, ...)

## S3 method for class 'lvmfit'
coefType(object, as.lava = TRUE, ...)

## S3 method for class 'multigroup'
coefType(object, as.lava = TRUE, ...)

Arguments

Details

A lvm can be written as a measurement model:

Y_i = \nu + \Lambda \eta_i + K X_i + \epsilon_i

and a structural model:

\eta_i = \alpha + B \eta_i + \Gamma X_i + \zeta_i

where \Psi is the variance covariance matrix of the residuals \zeta
and \Sigma is the variance covariance matrix of the residuals \epsilon.

coefType either returns the Latin/Greek letter corresponding to the coefficients or it groups them:

• intercept: \nu and \alpha.

• regression: \Lambda, K, B, and \Gamma.

• covariance: extra-diagonal terms of \Sigma and \Psi.

• variance: diagonal of \Sigma and \Psi.

A link denotes a relationship between two variables. The coefficient are used to represent the strength of the association between two variable, i.e. the strength of a link. A coefficient may corresponds to the strength of one or several link.

Value

coefType returns a data.frame when as.lava=FALSE:

• name: name of the link

• Y: outcome variable

• X: regression variable in the design matrix (could be a transformation of the original variables, e.g. dichotomization).

• data: original variable

• type: type of link

• value: if TRUE, the value of the link is set and not estimated.

• marginal: if TRUE, the value of the link does not impact the estimation.

• detail: a more detailed description of the type of link (see the details section)

• lava: name of the coefficient in lava

When as.lava=TRUE, coefType returns a named vector containing the type of each coefficient.

Examples

#### regression ####
m <- lvm(Y~X1+X2)
e <- estimate(m, lava::sim(m, 1e2))

coefType(m)
coefType(e)

#### LVM ####
m <- lvm()
regression(m) <- c(y1,y2,y3)~u
regression(m) <- u~x1+x2
latent(m) <- ~u
covariance(m) <- y1~y2

m.Sim <- m
categorical(m.Sim, labels = c("a","b","c")) <- ~x2
e <- estimate(m, lava::sim(m.Sim, 1e2))

coefType(m)
coefType(e)

## additional categorical variables 
categorical(m, labels = as.character(1:3)) <- "X1"

coefType(m, as.lava = FALSE)

#### LVM with constrains ####
m <- lvm(c(Y1~0+1*eta1,Y2~0+1*eta1,Y3~0+1*eta1,
          Z1~0+1*eta2,Z2~0+1*eta2,Z3~0+1*eta2))
latent(m) <- ~eta1 + eta2
e <- estimate(m, lava::sim(m,1e2))

coefType(m)
coefType(e)

#### multigroup ####
m <- lvm(Y~X1+X2)
eG <- estimate(list(m,m), list(lava::sim(m, 1e2), lava::sim(m, 1e2)))
coefType(eG)

Form all Unique Combinations Between two Vectors

Description

Form all unique combinations between two vectors (removing symmetric combinations).

Usage

.combination(..., levels = FALSE)

Arguments

Value

A matrix, each row being a different combination.

Examples

.combination <- lavaSearch2:::.combination

.combination(1,1)
.combination(1:2,1:2)
.combination(c(1:2,1:2),1:2)

.combination(alpha = 1:2, beta = 3:4)
.combination(alpha = 1:2, beta = 3:4, gamma = 1:4)
.combination(alpha = 1:3, beta = 1:3, gamma = 1:3)

Combine formula

Description

Combine formula by outcome

Usage

combineFormula(ls.formula, as.formula = TRUE, as.unique = FALSE)

Arguments

Examples

combineFormula(list(Y~X1,Y~X3+X5,Y1~X2))
lava.options(symbols = c("~",","))
combineFormula(list("Y~X1","Y~X3+X5","Y1~X2"))
lava.options(symbols = c("<-","<->"))
combineFormula(list("Y<-X1","Y<-X3+X5","Y1<-X2"))

combineFormula(list(Y~X1,Y~X3+X1,Y1~X2))
combineFormula(list(Y~X1,Y~X3+X1,Y1~X2), as.formula = FALSE)
combineFormula(list(Y~X1,Y~X3+X1,Y1~X2), as.unique = TRUE)

lava.options(symbols = c("~","~~"))
combineFormula(list("Y~X1","Y~X3","Y1~X2"))

Test Linear Hypotheses With Small Sample Correction

Description

Test Linear Hypotheses using Wald statistics in a latent variable model. Similar to lava::compare but with small sample correction.

Usage

compare2(
  object,
  linfct,
  rhs,
  robust,
  cluster,
  as.lava,
  F.test,
  conf.level,
  ...
)

## S3 method for class 'lvmfit'
compare2(
  object,
  linfct = NULL,
  rhs = NULL,
  robust = FALSE,
  cluster = NULL,
  as.lava = TRUE,
  F.test = TRUE,
  conf.level = 0.95,
  ssc = lava.options()$ssc,
  df = lava.options()$df,
  ...
)

## S3 method for class 'lvmfit2'
compare2(
  object,
  linfct = NULL,
  rhs = NULL,
  robust = FALSE,
  cluster = NULL,
  as.lava = TRUE,
  F.test = TRUE,
  conf.level = 0.95,
  ...
)

## S3 method for class 'lvmfit2'
compare(
  object,
  linfct = NULL,
  rhs = NULL,
  robust = FALSE,
  cluster = NULL,
  as.lava = TRUE,
  F.test = TRUE,
  conf.level = 0.95,
  ...
)

Arguments

Details

The linfct argument and rhs specify the set of linear hypotheses to be tested. They can be written:

linfct * \theta = rhs

where \theta is the vector of the model coefficients.
The par argument must contain expression(s) involving the model coefficients. For example "beta = 0" or c("-5*beta + alpha = 3","-alpha") are valid expressions if alpha and beta belong to the set of model coefficients. A contrast matrix and the right hand side will be generated inside the function.

When directly specified, the contrast matrix must contain as many columns as there are coefficients in the model (mean and variance coefficients). Each hypothesis correspond to a row in the contrast matrix.

The rhs vector should contain as many elements as there are row in the contrast matrix.

Value

If as.lava=TRUE an object of class htest. Otherwise a data.frame object.

See Also

createContrast to create contrast matrices.
estimate2 to obtain lvmfit2 objects.

Examples

#### simulate data ####
set.seed(10)
mSim <- lvm(Y~0.1*X1+0.2*X2)
categorical(mSim, labels = c("a","b","c")) <- ~X1
transform(mSim, Id~Y) <- function(x){1:NROW(x)}
df.data <- lava::sim(mSim, 1e2)

#### with lvm ####
m <- lvm(Y~X1+X2)
e.lvm <- estimate(m, df.data)

compare2(e.lvm, linfct = c("Y~X1b","Y~X1c","Y~X2"))
compare2(e.lvm, linfct = c("Y~X1b","Y~X1c","Y~X2"), robust = TRUE)

Confidence Intervals With Small Sample Correction

Description

Extract confidence intervals of the coefficients from a latent variable model. Similar to lava::confint but with small sample correction.

Extract estimate, standard error, confidence intervals and p-values associated to each coefficient of a latent variable model. Similar to lava::confint but with small sample correction.

Usage

confint2(object, robust, cluster, transform, as.lava, conf.level, ...)

## S3 method for class 'lvmfit'
confint2(
  object,
  robust = FALSE,
  cluster = NULL,
  transform = NULL,
  as.lava = TRUE,
  conf.level = 0.95,
  ssc = lava.options()$ssc,
  df = lava.options()$df,
  ...
)

model.tables2(object, robust, cluster, transform, as.lava, conf.level, ...)

Arguments

Details

When argument object is a lvmfit object, the method first calls estimate2 and then extract the confidence intervals.

When argument object is a lvmfit object, the method first calls estimate2 and then extract the confidence intervals.

Value

A data.frame with a row per coefficient.

A data.frame with a row per coefficient.

Examples

#### simulate data ####
set.seed(10)
dW <- sampleRepeated(10, format = "wide")
set.seed(10)
dL <- sampleRepeated(10, format = "long")
dL$time2 <- paste0("visit",dL$time)

#### latent variable models ####
e.lvm <- estimate(lvm(c(Y1,Y2,Y3) ~ 1*eta + X1, eta ~ Z1), data = dW)
confint(e.lvm)
confint2(e.lvm)
confint2(e.lvm, as.lava = FALSE)

Create Rownames for a Contrast Matrix

Description

Create rownames for a contrast matrix using the coefficients and the names of the coefficients. The rownames will be [value * name] == null, e.g. [beta + 4*alpha] = 0.

Usage

.contrast2name(contrast, null = NULL, sep = c("[", "]"))

Arguments

Details

When argument NULL is null then the rownames will not be put into brackets and the right hand side will not be added to the name.

Value

a character vector.

formula character conversion

Description

Conversion of formula into character string or vice versa

Usage

formula2character(f, type = "formula")

Arguments

Examples

formula2character(Y1~X1+X2)
formula2character(Y1~X1+X2, type = "symbols")

Create Contrast matrix

Description

Returns a contrast matrix corresponding an object. The contrast matrix will contains the hypotheses in rows and the model coefficients in columns.

Usage

createContrast(object, ...)

## S3 method for class 'character'
createContrast(object, ...)

## S3 method for class 'lvmfit'
createContrast(object, linfct, ...)

## S3 method for class 'lvmfit2'
createContrast(object, linfct, ...)

## S3 method for class 'list'
createContrast(object, linfct = NULL, ...)

## S3 method for class 'mmm'
createContrast(object, linfct = NULL, ...)

Arguments

Details

One can initialize an empty contrast matrix setting the argumentlinfct to character(0).

Value

A list containing

• contrast [matrix] a contrast matrix corresponding to the left hand side of the linear hypotheses.

• null [vector] the right hand side of the linear hypotheses.

• Q [integer] the rank of the contrast matrix.

• ls.contrast [list, optional] the contrast matrix corresponding to each submodel. Only present when the argument object is a list of models.

Examples

## Simulate data
mSim <- lvm(X ~ Age + Treatment,
            Y ~ Gender + Treatment,
            c(Z1,Z2,Z3) ~ eta, eta ~ treatment,
            Age[40:5]~1)
latent(mSim) <- ~eta
categorical(mSim, labels = c("placebo","SSRI")) <- ~Treatment
categorical(mSim, labels = c("male","female")) <- ~Gender
n <- 1e2
set.seed(10)
df.data <- lava::sim(mSim,n)

## Estimate separate models
lmX <- lava::estimate(lvm(X ~ -1 + Age + Treatment), data = df.data)
lmY <- lava::estimate(lvm(Y ~ -1 + Gender + Treatment), data = df.data)
lvmZ <- lava::estimate(lvm(c(Z1,Z2,Z3) ~ -1 + 1*eta, eta ~ -1 + Treatment), 
                 data = df.data)

## Contrast matrix for a given model
createContrast(lmX, linfct = "X~Age")
createContrast(lmX, linfct = c("X~Age=0","X~Age+5*X~TreatmentSSRI=0"))
createContrast(lmX, linfct = c("X~Age=0","X~Age+5*X~TreatmentSSRI=0"), sep = NULL)
createContrast(lmX, linfct = character(0))

## Contrast matrix for the join model
ls.lvm <- list(X = lmX, Y = lmY, Z = lvmZ)
createContrast(ls.lvm, linfct = "TreatmentSSRI=0")
createContrast(ls.lvm, linfct = "TreatmentSSRI=0", rowname.rhs = FALSE)
createContrast(ls.lvm, linfct = character(0))

## Contrast for multigroup models
m <- lava::lvm(Y~Age+Treatment)
e <- lava::estimate(list(m,m), data = split(df.data, df.data$Gender))
print(coef(e))
createContrast(e, linfct = "Y~TreatmentSSRI@1 - Y~TreatmentSSRI@2 = 0")
createContrast(e, linfct = "Y~TreatmentSSRI@2 - Y~TreatmentSSRI@1 = 0")

Create a Mesh for the Integration

Description

Create a mesh for the integration.

Usage

createGrid(n, xmin, xmax, d.y, d.z, zmax, fine, double)

Arguments

Details

This create a mesh for integrating over a triangular surface using rectangles. The domain is define by constrains on three types of variables:

• the x variable: [unidimensional] that varies freely between [-xmax,-xmin] U [xmin,xmax].

• the y variables: [dimension d.y] constrained to be lower in absolute value than the x variable. In 2D this corresponds to 2 triangles, and in higher dimension to cones/hypercones.

• the z variables: [dimension d.z] constrained to vary between [-zmax,zmax].

The intersection of these three conditions define the domain.

The mesh is obtained slicing the triangles using rectangles.

Value

A list containing:

• grid: a data.frame where each line corresponds to a point.

• seqNames.min: a character giving the name of the x,y variables (min).

• seqNames.max: a character giving the name of the x,y variables (max).

Examples

createGrid <- lavaSearch2:::createGrid

## no z 
gridInt_2d <- createGrid(5, d.y = 1, xmin = 0, xmax = 4, 
                         d.z = 0, fine = FALSE, double = FALSE)
gridExt_2d <- createGrid(5, d.y = 1, xmin = 0, xmax = 4, 
                         d.z = 0, fine = FALSE, double = TRUE)

gridInt_4d <- createGrid(5, d.y = 3, xmin = 0, xmax = 4, 
                         d.z = 0, fine = FALSE, double = FALSE)
gridExt_4d <- createGrid(5, d.y = 3, xmin = 0, xmax = 4, 
                         d.z = 0, fine = FALSE, double = TRUE)

gridInt_2d <- createGrid(5, d.y = 1, xmin = 0, xmax = 4, 
                         d.z = 0, fine = TRUE, double = FALSE)

##  z
gridIntZ1_2d <- createGrid(5, d.y = 1, xmin = 0, xmax = 4, 
                           d.z = 1, zmax = 2, fine = FALSE, double = FALSE)
gridExtZ1_2d <- createGrid(5, d.y = 1, xmin = 0, xmax = 4, 
                           d.z = 1, zmax = 2, fine = FALSE, double = TRUE)
 
gridIntZ2_4d <- createGrid(5, d.y = 3, xmin = 0, xmax = 4, 
                           d.z = 2, zmax = 2, fine = FALSE, double = FALSE)
gridExtZ2_4d <- createGrid(5, d.y = 3, xmin = 0, xmax = 4, 
                           d.z = 2, zmax = 2, fine = FALSE, double = TRUE)

Identify Categorical Links in LVM

Description

Identify categorical links in latent variable models.

Usage

defineCategoricalLink(object, link, data)

## S3 method for class 'lvm'
defineCategoricalLink(object, link = NULL, data = NULL)

Arguments

Value

a data.frame with a description of each link in rows.
The column factitious identify the links that will be replaced with other links (e.g. "Y1~X1" becomes "Y1~X1b" and "Y1~X1c").

Examples

## Not run: 
defineCategoricalLink <- lavaSearch2:::defineCategoricalLink
defineCategoricalLink.lvm <- lavaSearch2:::defineCategoricalLink.lvm

## linear model
m <- lvm(Y1~X1+X2,Y2~X1+X3)
categorical(m, K = 3) <- "X1"
try(defineCategoricalLink(m)) # error

categorical(m, K = 3, labels = 1:3) <- "X1"
defineCategoricalLink(m)
defineCategoricalLink(m, "Y~X1")
defineCategoricalLink(m, "X1:0|1")
defineCategoricalLink(m, "X1:1|2")
defineCategoricalLink(m, c("X1:0|1", "X1:1|2"))
defineCategoricalLink(m, c("Y~X1","Y~X2"))
defineCategoricalLink(m, c("Y~X2","Y~X1"))

## latent variable model
m <- lvm()
regression(m) <- c(y1,y2,y3)~u
regression(m) <- u~x1+x2
latent(m) <- ~u
covariance(m) <- y1~y2
categorical(m, labels = as.character(1:3)) <- "X1"

defineCategoricalLink(m)

## End(Not run)

Degree of Freedom for the Chi-Square Test

Description

Computation of the degrees of freedom of the chi-squared distribution relative to the model-based variance

Usage

dfSigma(contrast, score, vcov, rvcov, dVcov, dRvcov, keep.param, type)

Arguments

References

Wei Pan and Melanie M. Wall, Small-sample adjustments in using the sandwich variance estiamtor in generalized estimating equations. Statistics in medicine (2002) 21:1429-1441.

Effects Through Pathways With Small Sample Correction

Description

Test whether a path in the latent variable model correspond to a null effect. Similar to lava::effects but with small sample correction (if any). So far it only work for a single path related two variable composed of one or two edges.

Usage

effects2(object, linfct, robust, cluster, conf.level, ...)

## S3 method for class 'lvmfit'
effects2(
  object,
  linfct,
  robust = FALSE,
  cluster = NULL,
  conf.level = 0.95,
  to = NULL,
  from = NULL,
  df = lava.options()$df,
  ssc = lava.options()$ssc,
  ...
)

## S3 method for class 'lvmfit2'
effects2(
  object,
  linfct,
  robust = FALSE,
  cluster = NULL,
  conf.level = 0.95,
  to = NULL,
  from = NULL,
  ...
)

## S3 method for class 'lvmfit2'
effects(
  object,
  linfct,
  robust = FALSE,
  cluster = NULL,
  conf.level = 0.95,
  to = NULL,
  from = NULL,
  ...
)

Arguments

Details

When argument object is a lvmfit object, the method first calls estimate2 and then extract the confidence intervals.

Value

A data.frame with a row per path.

Satterthwaite Correction and Small Sample Correction

Description

Correct the bias of the ML estimate of the variance and compute the first derivative of the information matrix.

Compute bias corrected residuals variance covariance matrix and information matrix. Also provides the leverage values and corrected sample size when adjust.n is set to TRUE.

Usage

estimate2(
  object,
  param,
  data,
  ssc,
  df,
  derivative,
  hessian,
  dVcov.robust,
  iter.max,
  tol.max,
  trace,
  ...
)

## S3 method for class 'lvm'
estimate2(
  object,
  param = NULL,
  data = NULL,
  ssc = lava.options()$ssc,
  df = lava.options()$df,
  derivative = "analytic",
  hessian = FALSE,
  dVcov.robust = FALSE,
  iter.max = 100,
  tol.max = 1e-06,
  trace = 0,
  ...
)

## S3 method for class 'lvmfit'
estimate2(
  object,
  param = NULL,
  data = NULL,
  ssc = lava.options()$ssc,
  df = lava.options()$df,
  derivative = "analytic",
  hessian = FALSE,
  dVcov.robust = FALSE,
  iter.max = 100,
  tol.max = 1e-06,
  trace = 0,
  ...
)

## S3 method for class 'list'
estimate2(object, ...)

## S3 method for class 'mmm'
estimate2(object, ...)

.sscResiduals(object, ssc, algorithm = "2")

Arguments

Details

The argument value is equivalent to the argument bias.correct of the function summary2.

Examples

#### simulate data ####
set.seed(10)
dW <- sampleRepeated(10, format = "wide")

#### latent variable model ####
m.lvm <- lvm(Y1~X1+X2+Z1)

e2.lvm <- estimate2(m.lvm, data = dW)
summary2(e2.lvm)

Find Object in the Parent Environments

Description

Search an object in the parent environments. For internal use.

Usage

evalInParentEnv(name)

Arguments

Extract Data From a Latent Variable Model

Description

Extract data from a latent variable model.

Usage

extractData(object, design.matrix, as.data.frame, envir, rm.na)

## S3 method for class 'lvmfit'
extractData(
  object,
  design.matrix = FALSE,
  as.data.frame = TRUE,
  envir = environment(),
  rm.na = TRUE
)

Arguments

Value

a dataset.

Examples

#### simulate data ####
set.seed(10)
n <- 101

Y1 <- rnorm(n, mean = 0)
Y2 <- rnorm(n, mean = 0.3)
Id <- findInterval(runif(n), seq(0.1,1,0.1))
data.df <- rbind(data.frame(Y=Y1,G="1",Id = Id),
           data.frame(Y=Y2,G="2",Id = Id)       
           )

#### latent variable model ####
library(lava)
e.lvm <- estimate(lvm(Y ~ G), data = data.df)
extractData(e.lvm)
extractData(e.lvm, design.matrix = TRUE)

Find all New Links Between Variables

Description

Find all new links between variables (adapted from lava::modelsearch).

Usage

findNewLink(object, ...)

## S3 method for class 'lvm'
findNewLink(
  object,
  data = NULL,
  type = "both",
  exclude.var = NULL,
  rm.latent_latent = FALSE,
  rm.endo_endo = FALSE,
  rm.latent_endo = FALSE,
  output = "names",
  ...
)

Arguments

Value

A list containing:

• M.links: a matrix with two columns indicating (by name or position) the exogenous and endogenous variable corresponding to each link.

• links: the name of the additional possible links

• directional: a logical vector indicating for each link whether the link is unidirectional (TRUE, i.e. regression link) or bidirectional (FALSE, i.e. covariance link).

Examples

library(lava)

m <- lvm()
regression(m) <- c(y1,y2,y3)~u
categorical(m,labels=c("M","F","MF")) <- ~X1
findNewLink(m, rm.endo = FALSE)
findNewLink(m, rm.endo = TRUE)
findNewLink(m, exclude.var = "X1")

regression(m) <- u~x1+x2
latent(m) <- ~u

findNewLink(m, rm.endo = FALSE)
findNewLink(m, rm.endo = TRUE)
findNewLink(m, rm.endo = TRUE, output = "index")
findNewLink(m, type = "covariance")
findNewLink(m, type = "regression")

Estimate LVM With Weights

Description

Estimate LVM with weights.

Usage

gaussian_weight.estimate.hook(x, data, estimator, ...)

gaussian_weight_method.lvm

gaussian_weight_logLik.lvm(object, type = "cond", p, data, weights, ...)

gaussian_weight_objective.lvm(x, ...)

gaussian_weight_score.lvm(
  x,
  data,
  p,
  S,
  n,
  mu = NULL,
  weights = NULL,
  debug = FALSE,
  reindex = FALSE,
  mean = TRUE,
  constrain = TRUE,
  indiv = FALSE,
  ...
)

gaussian_weight_gradient.lvm(...)

gaussian_weight_hessian.lvm(x, p, n, weights = NULL, ...)

Arguments

Format

An object of class character of length 1.

Examples

#### linear regression with weights ####

## data
df <- data.frame(Y = c(1,2,2,1,2),
                 X = c(1,1,2,2,2),
                 missing = c(0,0,0,0,1),
                 weights = c(1,1,2,1,NA))

## using lm
e.lm.GS <- lm(Y~X, data = df)
e.lm.test <- lm(Y~X, data = df[df$missing==0,], weights = df[df$missing==0,"weights"])

## using lvm
m <- lvm(Y~X)
e.GS <- estimate(m, df)
## e.lava.test <- estimate(m, df[df$missing==0,], weights = df[df$missing==0,"weights"])
## warnings!!
e.test <- estimate(m, data = df[df$missing==0,],
                   weights = df[df$missing==0,"weights"],
                   estimator = "gaussian_weight")

Identify the Endogenous Variables

Description

Identify the endogenous variables, i.e., returns a vector with length the number of observations, whose values are the index of the repetitions.

Usage

.getIndexOmega(object, data, ...)

## S3 method for class 'lvm'
.getIndexOmega(object, data, ...)

## S3 method for class 'lvmfit'
.getIndexOmega(object, data, ...)

Arguments

Examples

## Not run: 
#### simulate data ####
set.seed(10)
dW <- sampleRepeated(10, format = "wide")
set.seed(10)
dL <- sampleRepeated(10, format = "long")
dL$time2 <- paste0("visit",dL$time)

#### lvm model ####
e.lvm <- estimate(lvm(c(Y1,Y2,Y3) ~ 1*eta + X1, eta ~ Z1), data = dW)
## lavaSearch2:::.getIndexOmega(e.lvm, data = dW)

## End(Not run)

Extract the Links that Have Been Found by the modelsearch2.

Description

Extract the links that have been found relevant by modelsearch2.

Usage

getNewLink(object, step)

## S3 method for class 'modelsearch2'
getNewLink(object, step = 1:nStep(object))

Arguments

Value

A character vector.

Examples

## Not run: 
mSim <- lvm(Y~G+X1+X2)
addvar(mSim) <- ~Z1+Z2+Z3+Z4+Z5+Z6

set.seed(10)
df.data <- lava::sim(mSim, 1e2)

mBase <- lvm(Y~G)
addvar(mBase) <- ~X1+X2+Z1+Z2+Z3+Z4+Z5+Z6
e.lvm <- estimate(mBase, data = df.data)
res <- modelsearch2(e.lvm, method.p.adjust = "holm")
getNewLink(res)

## End(Not run)

Extract the Model that Has Been Retains by the modelsearch2.

Description

Extract the model that has been retained by modelsearch2.

Usage

getNewModel(object, step)

## S3 method for class 'modelsearch2'
getNewModel(object, step = nStep(object))

Arguments

Value

A lvmfit object.

Examples

## Not run: 
mSim <- lvm(Y~G+X1+X2)
addvar(mSim) <- ~Z1+Z2+Z3+Z4+Z5+Z6

set.seed(10)
df.data <- lava::sim(mSim, 1e2)

mBase <- lvm(Y~G)
addvar(mBase) <- ~X1+X2+Z1+Z2+Z3+Z4+Z5+Z6
e.lvm <- estimate(mBase, data = df.data)
res <- modelsearch2(e.lvm, method.p.adjust = "holm")
getNewModel(res)

## End(Not run)

Extract one Step From the Sequential Procedure

Description

Extract one step from the sequential procedure.

Usage

getStep(object, step, slot)

## S3 method for class 'modelsearch2'
getStep(object, step = nStep(object), slot = NULL)

Arguments

Examples

## Not run: 
mSim <- lvm(Y~G+X1+X2)
addvar(mSim) <- ~Z1+Z2+Z3+Z4+Z5+Z6
df.data <- lava::sim(mSim, 1e2)

mBase <- lvm(Y~G)
addvar(mBase) <- ~X1+X2+Z1+Z2+Z3+Z4+Z5+Z6
e.lvm <- estimate(mBase, data = df.data)
res <- modelsearch2(e.lvm, method.p.adjust = "holm")

getStep(res)
getStep(res, slot = "sequenceTest")
getStep(res, step = 1)

## End(Not run)

Residual Variance-Covariance Matrix With Small Sample Correction.

Description

Reconstruct the residual variance-covariance matrix from a latent variable model. It is similar to nlme::getVarCov but with small sample correction.

Usage

getVarCov2(object, ...)

## S3 method for class 'lvmfit'
getVarCov2(object, ssc = lava.options()$ssc, ...)

## S3 method for class 'lvmfit2'
getVarCov2(object, ...)

Arguments

Details

When argument object is a lvmfit object, the method first calls estimate2 and then extract the residuals.

Value

A matrix with as many rows and column as the number of endogenous variables

Examples

#### simulate data ####
set.seed(10)
n <- 101

Y1 <- rnorm(n, mean = 0)
Y2 <- rnorm(n, mean = 0.3)
Id <- findInterval(runif(n), seq(0.1,1,0.1))
data.df <- rbind(data.frame(Y=Y1,G="1",Id = Id),
           data.frame(Y=Y2,G="2",Id = Id)
           )

#### latent variable models ####
library(lava)
e.lvm <- estimate(lvm(Y ~ G), data = data.df)
getVarCov2(e.lvm)

General Linear Hypothesis Testing With Small Sample Correction

Description

Test linear hypotheses on coefficients from a latent variable models with small sample corrections.

Usage

glht2(object, ...)

## S3 method for class 'lvmfit'
glht2(
  object,
  linfct,
  rhs = NULL,
  robust = FALSE,
  cluster = NULL,
  ssc = lava.options()$ssc,
  df = lava.options()$df,
  ...
)

## S3 method for class 'lvmfit2'
glht2(object, linfct, rhs = NULL, robust = FALSE, cluster = NULL, ...)

## S3 method for class 'mmm'
glht2(object, linfct, rhs = 0, robust = FALSE, cluster = NULL, ...)

## S3 method for class 'lvmfit2'
glht(model, linfct, rhs = NULL, robust = FALSE, cluster = NULL, ...)

Arguments

Details

Whenever the argument linfct is not a matrix, it is passed to the function createContrast to generate the contrast matrix and, if not specified, rhs.

Since only one degree of freedom can be specify in a glht object and it must be an integer, the degree of freedom of the denominator of an F test simultaneously testing all hypotheses is retained, after rounding.

Argument rhs and null are equivalent. This redondance enable compatibility between lava::compare, compare2, multcomp::glht, and glht2.

Value

A glht object.

See Also

createContrast to create contrast matrices.
estimate2 to pre-compute quantities for the small sample correction.

Examples

library(multcomp)

## Simulate data
mSim <- lvm(c(Y1,Y2,Y3)~ beta * eta, Z1 ~ E, Z2 ~ E, Age[40:5]~1)
latent(mSim) <- "eta"
set.seed(10)
n <- 1e2

df.data <- lava::sim(mSim, n, latent = FALSE, p = c(beta = 1))

#### Inference on a single model ####
e.lvm <- estimate(lvm(Y1~E), data = df.data)
summary(glht2(e.lvm, linfct = c("Y1~E + Y1","Y1")))

#### Inference on separate models ####
## fit separate models
lvmX <- estimate(lvm(Z1 ~ E), data = df.data)
lvmY <- estimate(lvm(Z2 ~ E + Age), data = df.data)
lvmZ <- estimate(lvm(c(Y1,Y2,Y3) ~ eta, eta ~ E), 
                 data = df.data)

#### create mmm object #### 
e.mmm <- mmm(X = lvmX, Y = lvmY, Z = lvmZ)

#### create contrast matrix ####
resC <- createContrast(e.mmm, linfct = "E")

#### adjust for multiple comparisons ####
e.glht2 <- glht2(e.mmm, linfct = c(X="E"), df = FALSE)
summary(e.glht2)

Hessian With Small Sample Correction.

Description

Extract the hessian from a latent variable model, with small sample correction

Usage

hessian2(object, indiv, cluster, as.lava, ...)

## S3 method for class 'lvmfit'
hessian2(
  object,
  indiv = FALSE,
  cluster = NULL,
  as.lava = TRUE,
  ssc = lava.options()$ssc,
  ...
)

## S3 method for class 'lvmfit2'
hessian2(object, indiv = FALSE, cluster = NULL, as.lava = TRUE, ...)

Arguments

Details

When argument object is a lvmfit object, the method first calls estimate2 and then extract the hessian.

Value

An array containing the second derivative of the likelihood relative to each sample (dim 3) and each pair of model coefficients (dim 1,2).

See Also

estimate2 to obtain lvmfit2 objects.

Examples

#### simulate data ####
n <- 5e1
p <- 3
X.name <- paste0("X",1:p)
link.lvm <- paste0("Y~",X.name)
formula.lvm <- as.formula(paste0("Y~",paste0(X.name,collapse="+")))

m <- lvm(formula.lvm)
distribution(m,~Id) <- Sequence.lvm(0)
set.seed(10)
d <- lava::sim(m,n)

#### latent variable models ####
e.lvm <- estimate(lvm(formula.lvm),data=d)
hessian2(e.lvm)

Compute the Hessian Matrix From the Conditional Moments

Description

Compute the Hessian matrix from the conditional moments.

Usage

.hessian2(
  dmu,
  dOmega,
  d2mu,
  d2Omega,
  epsilon,
  OmegaM1,
  missing.pattern,
  unique.pattern,
  name.pattern,
  grid.mean,
  grid.var,
  grid.hybrid,
  name.param,
  leverage,
  n.cluster,
  weights
)

Details

calc_hessian will perform the computation individually when the argument index.Omega is not null.

Influence Function With Small Sample Correction.

Description

Extract the influence function from a latent variable model. It is similar to lava::iid but with small sample correction.

Usage

iid2(object, ...)

## S3 method for class 'lvmfit'
iid2(
  object,
  robust = TRUE,
  cluster = NULL,
  as.lava = TRUE,
  ssc = lava.options()$ssc,
  ...
)

## S3 method for class 'lvmfit2'
iid2(object, robust = TRUE, cluster = NULL, as.lava = TRUE, ...)

## S3 method for class 'lvmfit2'
iid(x, robust = TRUE, cluster = NULL, as.lava = TRUE, ...)

Arguments

Details

When argument object is a lvmfit object, the method first calls estimate2 and then extract the variance-covariance matrix.

Value

A matrix containing the 1st order influence function relative to each sample (in rows) and each model coefficient (in columns).

See Also

estimate2 to obtain lvmfit2 objects.

Examples

#### simulate data ####
n <- 5e1
p <- 3
X.name <- paste0("X",1:p)
link.lvm <- paste0("Y~",X.name)
formula.lvm <- as.formula(paste0("Y~",paste0(X.name,collapse="+")))

m <- lvm(formula.lvm)
distribution(m,~Id) <- Sequence.lvm(0)
set.seed(10)
d <- sim(m,n)

#### latent variable model ####
e.lvm <- estimate(lvm(formula.lvm),data=d)
iid.tempo <- iid2(e.lvm)

Display the i.i.d. Decomposition

Description

Extract the i.i.d. decomposition and display it along with the corresponding coefficient.

Usage

iid2plot(object, param)

Arguments

Jackknife iid Decomposition from Model Object

Description

Extract iid decomposition (i.e. influence function) from model object.

Usage

iidJack(object, ...)

## Default S3 method:
iidJack(
  object,
  data = NULL,
  grouping = NULL,
  cpus = 1,
  keep.warnings = TRUE,
  keep.error = TRUE,
  cl = NULL,
  trace = TRUE,
  ...
)

Arguments

Value

A matrix with in row the samples and in columns the parameters.

Examples

n <- 20
set.seed(10)
mSim <- lvm(c(Y1,Y2,Y3,Y4,Y5) ~ 1*eta)
latent(mSim) <- ~eta
categorical(mSim, K=2) <- ~G
transform(mSim, Id ~ eta) <- function(x){1:NROW(x)}
dW <- lava::sim(mSim, n, latent = FALSE)

#### LVM ####
## Not run: 
m1 <- lvm(c(Y1,Y2,Y3,Y4,Y5) ~ 1*eta)
latent(m1) <- ~eta
regression(m1) <- eta ~ G
e <- estimate(m1, data = dW)

iid1 <- iidJack(e)
iid2 <- iid(e)
attr(iid2, "bread") <- NULL

apply(iid1,2,sd)
apply(iid2,2,sd)
quantile(iid2 - iid1)

## End(Not run)

Expected Information With Small Sample Correction.

Description

Extract the expected information matrix from a latent variable model. Similar to lava::information but with small sample correction.

Usage

information2(object, as.lava, ssc, ...)

## S3 method for class 'lvmfit'
information2(object, as.lava = TRUE, ssc = lava.options()$ssc, ...)

## S3 method for class 'lvmfit2'
information2(object, as.lava = TRUE, ...)

## S3 method for class 'lvmfit2'
information(x, ...)

Arguments

Details

When argument object is a lvmfit object, the method first calls estimate2 and then extract the information matrix.

Value

A matrix with as many rows and columns as the number of coefficients.

See Also

estimate2 to obtain lvmfit2 objects.

Examples

#### simulate data ####
n <- 5e1
p <- 3
X.name <- paste0("X",1:p)
link.lvm <- paste0("Y~",X.name)
formula.lvm <- as.formula(paste0("Y~",paste0(X.name,collapse="+")))

m <- lvm(formula.lvm)
distribution(m,~Id) <- Sequence.lvm(0)
set.seed(10)
d <- lava::sim(m,n)

#### linear models ####
e.lm <- lm(formula.lvm,data=d)

#### latent variable models ####
e.lvm <- estimate(lvm(formula.lvm),data=d)
information(e.lvm)
information2(e.lvm)
information2(e.lvm)[1:4,1:4] -  solve(vcov(e.lm))

Compute the Expected Information Matrix From the Conditional Moments

Description

Compute the expected information matrix from the conditional moments.

Usage

.information2(
  dmu,
  dOmega,
  OmegaM1,
  missing.pattern,
  unique.pattern,
  name.pattern,
  grid.mean,
  grid.var,
  name.param,
  leverage,
  weights = NULL,
  n.cluster
)

Details

calc_information will perform the computation individually when the argument index.Omega is not null.

Normalize var1 and var2

Description

Convert var1 and var2 from formula or covariance to character.

Usage

initVarLink(
  var1,
  var2,
  rep.var1 = FALSE,
  format = "list",
  Slink = c(lava.options()$symbols[1], "~"),
  Scov = lava.options()$symbols[2]
)

initVarLinks(var1, format = "list", ...)

Arguments

Value

See argument format.

Examples

initVarLink(y ~ x1)
initVarLink("y ~ x1")
initVarLink(y ~ x1 + x2)
initVarLink("y ~ x1 + x2")
initVarLink(y ~ x1 + x2, rep.var1 = TRUE)
initVarLink(y ~ x1 + x2, rep.var1 = TRUE, format = "formula")
initVarLink(y ~ x1 + x2, rep.var1 = TRUE, format = "txt.formula")
initVarLink("y", "x1", format = "formula")

initVarLink("y ~ x1:0|1")

initVarLinks(y ~ x1)
initVarLinks("y ~ x1")
initVarLinks(c("y ~ x1","y~ x2"))
initVarLinks(c(y ~ x1,y ~ x2))
initVarLinks(c("y ~ x1","y ~ x2"), format = "formula")
initVarLinks(c(y ~ x1,y ~ x2), format = "formula")
initVarLinks(c("y ~ x1","y~ x2"), format = "txt.formula")
initVarLinks(c(y ~ x1,y ~ x2), format = "txt.formula")

Integrate a Gaussian/Student Density over a Triangle

Description

Consider a univariate random variable X, two multivariate random variables Y and Z, and t1 and t2 two real numbers. This function can compute either P[|X|>t1,|X]>|Y1|,...,|X]>|Yp|] if zmin is not specified, P[|Z1|<t2,...,|Zq|<t2,|X|>t1,|X]>|Y1|,...,|X]>|Yp|] if zmin is specified.

Usage

intDensTri(
  mu,
  Sigma,
  df,
  n,
  x.min,
  z.max = NULL,
  type = "double",
  proba.min = 1e-06,
  prune = NULL,
  distribution = "pmvnorm"
)

Arguments

Details

Argument type:

• \"raw\": mesh with points inside the domain

• \"double\": mesh with points outside the domain

• \"fine\": mesh with points inside the domain plus additional rectangles trying to fill the missing domain.

Argument Sigma and mu: define the mean and variance-covariance of the random variables X, Y, Z (in this order). The length of the argument z.max is used to define the dimension of Z. The dimension of X is always 1.

Value

A numeric.

Examples

library(mvtnorm)

p <- 2
Sigma <- diag(p)
mu <- rep(0, p)

## bivariate normal distribution
z2 <- qmvt(0.975, mean = mu, sigma = Sigma, df = 1e3)$quantile

# compute integral
intDensTri(mu = mu, Sigma = Sigma, n=5, x.min=0, type = "fine")$value-1/2
intDensTri(mu = mu, Sigma = Sigma, n=30, x.min=0, type = "raw")$value-1/2
intDensTri(mu = mu, Sigma = Sigma, n=50, x.min=0, type = "raw")$value-1/2

intDensTri(mu = mu, Sigma = Sigma, df = 5, n=5, x.min=0, distribution = "pmvt")$value-1/2
res <- intDensTri(mu = mu, Sigma = Sigma, df = 5, n=10, x.min=0, distribution = "pmvt")
res$value-1/2
ggplot2::autoplot(res)

## trivariate normal distribution
## Not run: 
p <- 3
Sigma <- diag(p)
mu <- rep(0, p)

res2 <- intDensTri(mu = mu, Sigma = Sigma, n=5, x.min = 0, z.max = 10)
ggplot2::autoplot(res2)
ggplot2::autoplot(res2, coord.plot = c("x","z1"))
res2

## End(Not run)

#### when the distribution is far from 0
## Not run: 
eq1 <- intDensTri(mu = c(10,0), Sigma = diag(1,2), 
                  x.min = 2, n=10)
eq1$value-1
ggplot2::autoplot(eq1)

eq2 <- intDensTri(mu = c(10,0,0), Sigma = diag(1,3),
                  x.min=2, z.max = 10, type = "raw",
                  n=10)
ggplot2::autoplot(eq2, coord.plot = c("y1","z1"))
eq2$value-1

## more variables
p <- 5
Sigma <- diag(p)
mu <- rep(0, p)

res2 <- intDensTri(mu = mu, Sigma = Sigma, n=5, x.min = 1, z.max = c(2,2))
res2$grid

## End(Not run)

Leverage With Small Sample Correction.

Description

Extract leverage values from a latent variable model, with small sample correction.

Usage

leverage2(object, format, ssc, ...)

## S3 method for class 'lvmfit'
leverage2(object, format = "wide", ssc = lava.options()$ssc, ...)

## S3 method for class 'lvmfit2'
leverage2(object, format = "wide", ...)

Arguments

Details

The leverage are defined as the partial derivative of the fitted values with respect to the observations.

leverage_i = \frac{\partial \hat{Y}_i}{\partial Y_i}

See Wei et al. (1998).

When argument object is a lvmfit object, the method first calls estimate2 and then extract the leverage.

Value

a matrix containing the leverage relative to each sample (in rows) and each endogenous variable (in column).

References

Bo-Cheng Wei et al., Generalized Leverage and its applications (1998), Scandinavian Journal of Statistics 25:1:25-37.

See Also

estimate2 to obtain lvmfit2 objects.

Examples

#### simulate data ####
set.seed(10)
m <- lvm(Y1~eta,Y2~eta,Y3~eta)
latent(m) <- ~eta
d <- lava::sim(m,20, latent = FALSE)

#### latent variable models ####
e.lvm <- estimate(m, data = d)
leverage2(e.lvm)

Power of a Matrix

Description

Compute the power of a matrix.

Usage

matrixPower(object, power, symmetric, tol = 1e-12, print.warning = TRUE)

Arguments

Value

A matrix.

Examples

## symmetric matrix
set.seed(10)
M <- matrix(rnorm(20*6),20,6)
Sigma <- var(M)
Sigma.half <- matrixPower(Sigma, power = 1/2, symmetric = TRUE)
round(Sigma.half %*% Sigma.half - Sigma,5)

iSigma <- matrixPower(Sigma, power = -1, symmetric = TRUE)
round(iSigma %*% Sigma,5)

iSigma.half <- matrixPower(Sigma, power = -1/2, symmetric = TRUE)
round(iSigma.half %*% iSigma.half - iSigma,5)

## non symmetric matrix
set.seed(10)
M <- matrix(abs(rnorm(9)), 3, 3) + diag(1,3,3)
M-t(M)

iM <- matrixPower(M, power = -1, symmetric = FALSE)
round(iM %*% M,5)

iM.half <- matrixPower(M, power = -1/2, symmetric = FALSE)
round(iM.half %*% iM.half %*% M,5)

Data-driven Extension of a Latent Variable Model

Description

Procedure adding relationship between variables that are supported by the data.

Usage

modelsearch2(
  object,
  link,
  data,
  method.p.adjust,
  method.maxdist,
  n.sample,
  na.omit,
  alpha,
  nStep,
  trace,
  cpus
)

## S3 method for class 'lvmfit'
modelsearch2(
  object,
  link = NULL,
  data = NULL,
  method.p.adjust = "fastmax",
  method.maxdist = "approximate",
  n.sample = 1e+05,
  na.omit = TRUE,
  alpha = 0.05,
  nStep = NULL,
  trace = TRUE,
  cpus = 1
)

Arguments

Details

method.p.adjust = "max" computes the p-values based on the distribution of the max statistic. This max statistic is the max of the square root of the score statistic. The p-value are computed integrating the multivariate normal distribution.

method.p.adjust = "fastmax" only compute the p-value for the largest statistic. It is faster than "max" and lead to identical results.

method.p.adjust = "gof" keep adding links until the chi-squared test (of correct specification of the covariance matrix) is no longer significant.

Value

A list containing:

• sequenceTest: the sequence of test that has been performed.

• sequenceModel: the sequence of models that has been obtained.

• sequenceQuantile: the sequence of rejection threshold. Optional.

• sequenceIID: the influence functions relative to each test. Optional.

• sequenceSigma: the covariance matrix relative to each test. Optional.

• initialModel: the model before the sequential search.

• statistic: the argument statistic.

• method.p.adjust: the argument method.p.adjust.

• alpha: [numeric 0-1] the significance cutoff for the p-values.

• cv: whether the procedure has converged.

Examples

## simulate data 
mSim <- lvm()
regression(mSim) <- c(y1,y2,y3,y4)~u
regression(mSim) <- u~x1+x2
categorical(mSim,labels=c("A","B","C")) <- "x2"
latent(mSim) <- ~u
covariance(mSim) <- y1~y2
transform(mSim, Id~u) <- function(x){1:NROW(x)}

set.seed(10)
df.data <- lava::sim(mSim, n = 1e2, latent = FALSE)

## only identifiable extensions
m <- lvm(c(y1,y2,y3,y4)~u)
latent(m) <- ~u
addvar(m) <- ~x1+x2

e <- estimate(m, df.data)

## Not run: 
resSearch <- modelsearch(e)
resSearch

resSearch2 <- modelsearch2(e, nStep = 2)
resSearch2

## End(Not run)


## some extensions are not identifiable
m <- lvm(c(y1,y2,y3)~u)
latent(m) <- ~u
addvar(m) <- ~x1+x2 

e <- estimate(m, df.data)

## Not run: 
resSearch <- modelsearch(e)
resSearch
resSearch2 <- modelsearch2(e)
resSearch2

## End(Not run)

## for instance
mNI <- lvm(c(y1,y2,y3)~u)
latent(mNI) <- ~u
covariance(mNI) <- y1~y2
## estimate(mNI, data = df.data)
## does not converge

Compute Key Quantities of a Latent Variable Model

Description

Compute conditional mean, conditional variance, their first and second derivative regarding model parameters, as well as various derivatives of the log-likelihood.

Usage

moments2(
  object,
  param,
  data,
  weights,
  Omega,
  Psi,
  initialize,
  usefit,
  update.dmoment,
  update.d2moment,
  score,
  information,
  hessian,
  vcov,
  dVcov,
  dVcov.robust,
  residuals,
  leverage,
  derivative
)

## S3 method for class 'lvm'
moments2(
  object,
  param = NULL,
  data = NULL,
  weights = NULL,
  Omega = NULL,
  Psi = NULL,
  initialize = TRUE,
  usefit = TRUE,
  update.dmoment = TRUE,
  update.d2moment = TRUE,
  score = TRUE,
  information = TRUE,
  hessian = TRUE,
  vcov = TRUE,
  dVcov = TRUE,
  dVcov.robust = TRUE,
  residuals = TRUE,
  leverage = TRUE,
  derivative = "analytic"
)

## S3 method for class 'lvmfit'
moments2(
  object,
  param = NULL,
  data = NULL,
  weights = NULL,
  Omega = NULL,
  Psi = NULL,
  initialize = TRUE,
  usefit = TRUE,
  update.dmoment = TRUE,
  update.d2moment = TRUE,
  score = TRUE,
  information = TRUE,
  hessian = TRUE,
  vcov = TRUE,
  dVcov = TRUE,
  dVcov.robust = TRUE,
  residuals = TRUE,
  leverage = TRUE,
  derivative = "analytic"
)

Arguments

Details

For lvmfit objects, there are two levels of pre-computation:

• a basic one that do no involve the model coefficient (conditionalMoment.lvm).

• an advanced one that require the model coefficients (conditionalMoment.lvmfit).

Examples

m <- lvm(Y1~eta,Y2~eta,Y3~eta)
latent(m) <- ~eta

d <- lava::sim(m,1e2)
e <- estimate(m, d)

## basic pre-computation
res1 <- moments2(e, data = d, initialize = TRUE, usefit = FALSE,
                score = TRUE, information = TRUE, hessian = TRUE, vcov = TRUE,
                dVcov = TRUE, dVcov.robust = TRUE, residuals = TRUE, leverage = FALSE,
                derivative = "analytic")
res1$skeleton$param$Sigma

## full pre-computation
res2 <- moments2(e, param = coef(e), data = d, initialize = TRUE, usefit = TRUE,
                score = TRUE, information = TRUE, hessian = TRUE, vcov = TRUE,
                dVcov = TRUE, dVcov.robust = TRUE, residuals = TRUE, leverage = FALSE,
                derivative = "analytic")
res2$moment$Omega

Find the Number of Steps Performed During the Sequential Testing

Description

Find the number of steps performed during the sequential testing.

Usage

nStep(object)

## S3 method for class 'modelsearch2'
nStep(object)

Arguments

Value

an integer.

Examples

## Not run: 
mSim <- lvm(Y~G+X1+X2)
addvar(mSim) <- ~Z1+Z2+Z3+Z4+Z5+Z6
df.data <- lava::sim(mSim, 1e2)

mBase <- lvm(Y~G)
addvar(mBase) <- ~X1+X2+Z1+Z2+Z3+Z4+Z5+Z6
e.lvm <- estimate(mBase, data = df.data)
res <- modelsearch2(e.lvm, method.p.adjust = "holm")
nStep(res)

## End(Not run)

Effective Sample Size.

Description

Extract the effective sample size, i.e. sample size minus the loss in degrees of freedom caused by the estimation of the parameters.

Usage

nobs2(object, ssc, ...)

## S3 method for class 'lvmfit'
nobs2(object, ssc = lava.options()$ssc, ...)

## S3 method for class 'lvmfit2'
nobs2(object, ...)

Arguments

Details

When argument object is a lvmfit object, the method first calls estimate2 and then extract the leverage.

Value

Numeric vector of length the number of endogenous variables.

See Also

estimate2 to obtain lvmfit2 objects.

Residuals With Small Sample Correction.

Description

Extract residuals from a latent variable model. Similar to stats::residuals but with small sample correction.

Usage

residuals2(object, type, format, ssc, ...)

## S3 method for class 'lvmfit'
residuals2(
  object,
  type = "response",
  format = "wide",
  ssc = lava.options()$ssc,
  ...
)

Arguments

Details

When argument object is a lvmfit object, the method first calls estimate2 and then extract the residuals.

The raw residuals are defined by observation minus the fitted value:

\varepsilon = (Y_1 - \mu_1, ..., Y_m - \mu_m)

The studentized residuals divided the raw residuals relative to each endogenous variable by the modeled variance of the endogenous variable.

\varepsilon_{stud} =(\frac{Y_1 - \mu_1}{\sigma_1}, ..., \frac{Y_m - \mu_m}{\sigma_m})

The normalized residuals multiply the raw residuals by the inverse of the square root of the modeled residual variance covariance matrix.

\varepsilon_{norm} = \varepsilon \Omega^{-1/2}

Value

a matrix containing the residuals relative to each sample (in rows) and each endogenous variable (in column).

See Also

estimate2 to obtain lvmfit2 objects.

Examples

#### simulate data ####
set.seed(10)
n <- 101

Y1 <- rnorm(n, mean = 0)
Y2 <- rnorm(n, mean = 0.3)
Id <- findInterval(runif(n), seq(0.1,1,0.1))
data.df <- rbind(data.frame(Y=Y1,G="1",Id = Id),
           data.frame(Y=Y2,G="2",Id = Id)
           )

#### latent variable models ####
library(lava)
e.lvm <- estimate(lvm(Y ~ G), data = data.df)
residuals(e.lvm)
residuals2(e.lvm)
residuals(e.lvm) - residuals2(e.lvm)

Depreciated Method For Small Sample Correction

Description

Depreciated method for small sample correction, now replaced by the estimate2 method.

Usage

sCorrect(object, ...)

## Default S3 method:
sCorrect(object, ...)

sCorrect(x, ...) <- value

## Default S3 replacement method:
sCorrect(x, ...) <- value

Arguments

Simulate Repeated Measurements over time

Description

Simulate repeated measurements over time (one factor model).

Usage

sampleRepeated(n, n.Xcont = 2, n.Xcat = 2, n.rep = 5, format = "long")

Arguments

Value

a data.frame object.

Examples

sampleRepeated(10, format = "wide")
sampleRepeated(10, format = "long")

Score With Small Sample Correction

Description

Extract the (individual) score a the latent variable model. Similar to lava::score but with small sample correction.

Usage

score2(object, indiv, cluster, as.lava, ...)

## S3 method for class 'lvmfit'
score2(
  object,
  indiv = FALSE,
  cluster = NULL,
  as.lava = TRUE,
  ssc = lava.options()$ssc,
  ...
)

## S3 method for class 'lvmfit2'
score2(object, indiv = FALSE, cluster = NULL, as.lava = TRUE, ...)

## S3 method for class 'lvmfit2'
score(x, indiv = FALSE, cluster = NULL, as.lava = TRUE, ...)

Arguments

Details

When argument object is a lvmfit object, the method first calls estimate2 and then extract the confidence intervals.

Value

When argument indiv is TRUE, a matrix containing the score relative to each sample (in rows) and each model coefficient (in columns). Otherwise a numeric vector of length the number of model coefficients.

See Also

estimate2 to obtain lvmfit2 objects.

Examples

#### simulate data ####
n <- 5e1
p <- 3
X.name <- paste0("X",1:p)
link.lvm <- paste0("Y~",X.name)
formula.lvm <- as.formula(paste0("Y~",paste0(X.name,collapse="+")))

m <- lvm(formula.lvm)
distribution(m,~Id) <- Sequence.lvm(0)
set.seed(10)
d <- lava::sim(m,n)

#### linear models ####
e.lm <- lm(Y~X1+X2+X3, data = d)

#### latent variable models ####
m.lvm <- lvm(formula.lvm)
e.lvm <- estimate(m.lvm,data=d)
e2.lvm <- estimate2(m.lvm,data=d)
score.tempo <- score(e2.lvm, indiv = TRUE)
colSums(score.tempo)

Compute the Corrected Score.

Description

Compute the corrected score.

Usage

.score2(
  dmu,
  dOmega,
  epsilon,
  OmegaM1,
  missing.pattern,
  unique.pattern,
  name.pattern,
  name.param,
  name.meanparam,
  name.varparam,
  n.cluster,
  weights
)

Arguments

Regressor of a Formula.

Description

Return the regressor variables contained in the formula

Usage

selectRegressor(object, ...)

## S3 method for class 'formula'
selectRegressor(object, format = "call", ...)

Arguments

Examples

## Not run: 

selectRegressor <- lavaSearch2:::selectRegressor
selectRegressor.formula <- lavaSearch2:::selectRegressor.formula

selectRegressor(Y1~X1+X2)
selectRegressor(Y1~X1+X2, format = "vars")

selectRegressor(Y1~X1+Y1)
selectRegressor(Y1+Y2~X1+Y1, format = "vars")

selectRegressor(~X1+X2)
selectRegressor(~X1+X2, format = "vars")


## End(Not run)

Response Variable of a Formula

Description

Return the response variable contained in the formula.

Usage

selectResponse(object, ...)

## S3 method for class 'formula'
selectResponse(object, format = "call", ...)

Arguments

Value

See argument format.

Examples

## Not run: 

selectResponse <- lavaSearch2:::selectResponse
selectResponse.formula <- lavaSearch2:::selectResponse.formula

selectResponse(Y1~X1+X2)
selectResponse(Y1~X1+X2, format = "vars")
selectResponse(Surv(event,time)~X1+X2, format = "vars")

selectResponse(Y1~X1+Y1)
selectResponse(Y1+Y2~X1+Y1, format = "vars")

selectResponse(~X1+X2)
selectResponse(~X1+X2, format = "vars")

## End(Not run)

Set a Link to a Value

Description

Generic interface to set a value to a link in a lvm object.

Usage

setLink(object, ...)

## S3 method for class 'lvm'
setLink(object, var1, var2, value, warnings = FALSE, ...)

Arguments

Examples

library(lava)
set.seed(10)

m <- lvm()
regression(m) <- c(y1,y2,y3)~u
regression(m) <- u~x1+x2
latent(m) <- ~u
covariance(m) <- y1 ~ y2

m1 <- setLink(m, y3 ~ u, value = 1)
estimate(m1, lava::sim(m,1e2))
# m1 <- setLink(m, u ~ y3, value = 1)

m2 <- setLink(m, y1 ~ y2, value = 0.5)
estimate(m2, lava::sim(m,1e2))

Pre-computation for the Score

Description

Pre-compute quantities that are necessary to compute the score of a lvm model.

Usage

skeleton(object, X, endogenous, latent, n.cluster, index.Omega)

skeletonDtheta(
  object,
  X,
  endogenous,
  latent,
  missing.pattern,
  unique.pattern,
  name.pattern,
  n.cluster,
  index.Omega
)

skeletonDtheta2(object)

Arguments

Details

When the user specifies names for the coefficients (e.g. Y1[mu:sigma]) or uses constraints (Y1~beta*X1), as.lava=FALSE will use the names specified by the user (e.g. mu, sigma, beta) while as.lava=TRUE will use the name of the first link defining the coefficient.

Examples

## Not run: 
skeleton <- lavaSearch2::skeleton
skeleton.lvm <- lavaSearch2::skeleton.lvm
skeleton.lvmfit <- lavaSearch2::skeleton.lvmfit

## without constrain
m <- lvm(Y1~X1+X2+eta,Y2~X3+eta,Y3~eta)
latent(m) <- ~eta

e <- estimate(m, lava::sim(m,1e2))
M.data <- as.matrix(model.frame(e))

skeleton(e$model, as.lava = TRUE,
         name.endogenous = endogenous(e), n.endogenous = 3,
         name.latent = latent(e), 
         update.value = FALSE)
skeleton(e, data = M.data, p = pars(e), as.lava = TRUE,
         name.endogenous = endogenous(e), n.endogenous = 3,
         name.latent = latent(e), 
         update.value = TRUE)

## with constrains
m <- lvm(Y[mu:sigma] ~ beta*X1+X2)
e <- estimate(m, lava::sim(m,1e2))
M.data <- as.matrix(model.frame(e))

skeleton(e$model, as.lava = TRUE,
         name.endogenous = "Y", n.endogenous = 1,
         name.latent = NULL, 
         update.value = FALSE)$skeleton

skeleton(e, data = M.data, p = pars(e), as.lava = FALSE,
         name.endogenous = "Y", n.endogenous = 1,
         name.latent = NULL, 
         update.value = FALSE)$skeleton


## End(Not run)

Display the Type 1 Error Rate

Description

Display the type 1 error rate from the simulation results.

Usage

## S3 method for class 'calibrateType1'
summary(
  object,
  robust = FALSE,
  type = "type1error",
  alpha = 0.05,
  log.transform = TRUE,
  digits = 5,
  print = TRUE,
  ...
)

Arguments

Outcome of Linear Hypothesis Testing

Description

Estimates, p-values, and confidence intevals for linear hypothesis testing, possibly adjusted for multiple comparisons.

Usage

## S3 method for class 'glht2'
summary(
  object,
  confint = TRUE,
  conf.level = 0.95,
  transform = NULL,
  seed = NULL,
  rowname.rhs = TRUE,
  ...
)

Arguments

summary Method for modelsearch2 Objects

Description

summary method for modelsearch2 objects.

Usage

## S3 method for class 'modelsearch2'
summary(object, print = TRUE, ...)

Arguments

Details

The column dp.Info contains the percentage of extended models (i.e. model with one additional link) for which the information matrix evaluated at the value of the parameters of the initial model is non positive definie.

Latent Variable Model Summary After Small Sample Correction

Description

Summarize a fitted latent variable model. Similar to stats::summary with small sample correction.

Usage

summary2(object, robust, cluster, digit, ...)

## S3 method for class 'lvmfit'
summary2(
  object,
  robust = FALSE,
  cluster = NULL,
  digit = max(5, getOption("digit")),
  ssc = lava.options()$ssc,
  df = lava.options()$df,
  ...
)

## S3 method for class 'lvmfit2'
summary2(
  object,
  robust = FALSE,
  cluster = NULL,
  digit = max(5, getOption("digit")),
  ...
)

## S3 method for class 'lvmfit2'
summary(
  object,
  robust = FALSE,
  cluster = NULL,
  digit = max(5, getOption("digit")),
  ...
)

Arguments

Details

summary2 is the same as summary except that it first computes the small sample correction (but does not store it). So if summary2 is to be called several times, it is more efficient to pre-compute the quantities for the small sample correction using sCorrect and then call summary2.

summary2 returns an object with an element table2 containing the estimates, standard errors, degrees of freedom, upper and lower limits of the confidence intervals, test statistics, and p-values.

See Also

estimate2 to obtain lvmfit2 objects.

Examples

#### simulate data ####
m <- lvm(Y~X1+X2)
set.seed(10)
d <- lava::sim(m, 2e1)

#### latent variable models ####
e.lvm <- estimate(m, data = d)
summary(e.lvm)$coef

summary2(e.lvm)
summary2(e.lvm, ssc = "none")

Symmetrize a Matrix

Description

Complete the upper (or lower) extra-diagonal terms in order to obtain a symmetric matrix.

Usage

symmetrize(M, update.upper = TRUE)

Arguments

Examples

symmetrize <- lavaSearch2:::symmetrize

## example
M <- matrix(NA, 4, 4)
M[lower.tri(M)] <- 1:6

symmetrize(M, update.upper = TRUE) # good

M[upper.tri(M, diag = FALSE)] <- M[lower.tri(M, diag = FALSE)]
M # wrong

Apply Transformation to Summary Table

Description

Update summary table according to a transformation, e.g. log-transformtion. P-values are left unchanged but estimates, standard errors, and confidence intervals are updated.

Usage

transformSummaryTable(object, transform = NULL)

Arguments

Value

a data.frame

Run an Expression and Catch Warnings and Errors

Description

Similar to try but also returns warnings.

Usage

tryWithWarnings(expr)

Arguments

Details

from https://stackoverflow.com/questions/4948361/how-do-i-save-warnings-and-errors-as-output-from-a-function

Value

A list containing:

• value the result of the evaluation of the expression

• warnings warning(s) generated during the evaluation of the expression

• error error generated during the evaluation of the expression

Examples

FctTest <- function(x){
  return(log(x))
}
tryWithWarnings(FctTest(-1))
tryWithWarnings(FctTest(1))
tryWithWarnings(FctTest(xxxx))

Convert Variable Names to Dummy Variables Names.

Description

When dealing with categorical variables, the estimate function convert the categorical variables into dummy variables. This function convert a set of variable names to their corresponding name in the model with dummy variables

Usage

var2dummy(object, ...)

## S3 method for class 'list'
var2dummy(object, var, rm.first.factor = TRUE, ...)

## S3 method for class 'lvm'
var2dummy(object, data = NULL, ...)

Arguments

Examples

## Not run: 
var2dummy <- lavaSearch2:::var2dummy
var2dummy.list <- lavaSearch2:::var2dummy.list
var2dummy.lvm <- lavaSearch2:::var2dummy.lvm

m <- lvm()
regression(m) <- c(y1,y2,y3)~u
regression(m) <- u ~ X1+X2
var2dummy(m, var = c("X1","X2"))
categorical(m,labels=c("M","F","MF")) <- ~X1
var2dummy(m, var = c("X1","X2"))
categorical(m,labels=c("1","2","3")) <- ~X2
var2dummy(m, var = c("X1","X2"))

## End(Not run)

Variance-Covariance With Small Sample Correction

Description

Extract the variance-covariance matrix from a latent variable model. Similar to stats::vcov but with small sample correction.

Usage

vcov2(object, robust, cluster, as.lava, ...)

## S3 method for class 'lvmfit'
vcov2(
  object,
  robust = FALSE,
  cluster = NULL,
  as.lava = TRUE,
  ssc = lava.options()$ssc,
  ...
)

## S3 method for class 'lvmfit2'
vcov2(object, robust = FALSE, cluster = NULL, as.lava = TRUE, ...)

## S3 method for class 'lvmfit2'
vcov(object, robust = FALSE, cluster = NULL, as.lava = TRUE, ...)

Arguments

Details

When argument object is a lvmfit object, the method first calls estimate2 and then extract the variance-covariance matrix.

Value

A matrix with as many rows and columns as the number of coefficients.

See Also

estimate2 to obtain lvmfit2 objects.

Examples

#### simulate data ####
n <- 5e1
p <- 3
X.name <- paste0("X",1:p)
link.lvm <- paste0("Y~",X.name)
formula.lvm <- as.formula(paste0("Y~",paste0(X.name,collapse="+")))

m <- lvm(formula.lvm)
distribution(m,~Id) <- Sequence.lvm(0)
set.seed(10)
d <- lava::sim(m,n)

#### linear models ####
e.lm <- lm(formula.lvm,data=d)

#### latent variable models ####
e.lvm <- estimate(lvm(formula.lvm),data=d)
vcov0 <- vcov(e.lvm)
vcovSSC <- vcov2(e.lvm)

vcovSSC/vcov0
vcovSSC[1:4,1:4]/vcov(e.lm)

Inverse the Information Matrix

Description

Compute the inverse of the information matrix.

Usage

.info2vcov(information, attr.info = FALSE)

Arguments