Chinese Early Childhood Environment Rating Scale

Description

The CECERS uses a 9-point scoring system, 1-3 (inadequate), 5 (least acceptable), 7 (good), and 9 (excellent), to measure the quality of Chinese early children education (ECE) programs for children aged 3 to 6. The CECERS has a total of 51 items organized in eight categories: (1) Space and Furnishings (9 items); (2) Personal Care Routines (6 items); (3) Curriculum Planning and Implementation (5 items); (4) Whole-Group Instruction (7 items); (5) Activities (9 items); (6) Language-Reasoning (4 items); (7) Guidance and Interaction (5 items); (8) Parents and Staff (6 items).

Format

A data frame with 1383 rows and 95 variables:

Source

Kejian Li, Peng Zhang, Bi Ying Hu, Margaret R Burchinal, Xitao Fan, and Jinliang Qin. Testing the ‘thresholds’ of preschool education quality on child outcomes in china. Early Childhood Research Quarterly, 47:445–456, 2019.

General Function to Estimate Mixed Correlation Coefficient Matrix

Description

Estimate the correlation matrix for dataframes containing continuous and ordinal variable, in pairs or simultaneously, using MLE, IRLS, or IGMM.

Usage

MCCM_est(
  dataYX,
  order_indx,
  pair_est = FALSE,
  MLE = FALSE,
  R0 = NULL,
  app = TRUE,
  korder = 2,
  max_iter = 1000,
  max_tol = 1e-08,
  show_log = FALSE
)

Arguments

Value

See Also

esti_polyserial, esti_polychoric, est_mixedGMM, summary_MCCM_est, draw_correlation_matrix

Examples

library(mvtnorm)
library(MASS)
library(polycor)
library(lavaan)
set.seed(1997)
n = 10000
rho12=0.3
rho13=0.4
rho14=0.5
rho23=0.6
rho24=0.7
rho34=0.8

R = matrix(c(1,rho12,rho13,rho14,rho12,1,rho23,rho24,rho13,rho23,1,rho34,
rho14,rho24,rho34,1),4,4)
indc = c(3,4)
thresholds = list(c(),c(),0,0)
data1 = gen_mixed(n=n,R=R,indc=indc,thresholds=thresholds)
data2 = data.frame(data1$observed)

# pairwise MLE estimation
out_pair_MLE = MCCM_est(dataYX=data2,order_indx=indc,pair_est=TRUE,MLE=TRUE)
# pairwise IRLS estimation
out_pair_IRLS = MCCM_est(dataYX=data2,order_indx=indc,pair_est=TRUE,MLE=FALSE)
# simultaneous MLE estimation
out_sim_MLE = MCCM_est(dataYX=data2,order_indx=indc,pair_est=FALSE,MLE=TRUE)
# simultaneous IGMM estimation
out_sim_IGMM = MCCM_est(dataYX=data2,order_indx=indc,pair_est=FALSE,MLE=FALSE)

summary_MCCM_est(out_pair_MLE)
summary_MCCM_est(out_pair_IRLS)
summary_MCCM_est(out_sim_MLE)
summary_MCCM_est(out_sim_IGMM)

Parenteral_nutrition

Description

The Parenteral Nutrition data were collected from 543 patients of whom 386 were given parenteral nutrition alone, 145 were given enteral and parenteral nutrition, and 3 were given enteral nutrition only. There are 23 main discrete variables, such as: clinical stages(1-4), dietary status(1-3), NRS(0-6), PG-SGA-qualitative(1-3), etc.

Format

A data frame with 1086 rows and 29 variables:

Scaled Bivariate Normal Approximation

Description

Standard bivariate normal distribution approximated with Legendre polynomials.

Usage

Phixy(x, y, rho, korder = 3, app = TRUE)

Arguments

Value

P(X<=x,Y<=y).

Examples

library(mvtnorm)
pmvnorm(upper = c(1,-1),sigma = matrix(c(1,0.5,0.5,1),2,2))
Phixy(1,-1,0.5,2,app=TRUE)
Phixy(1,-1,0.5,app=TRUE)

Scaled Bivariate Normal Density

Description

Bivariate normal density with mean 0 variance 1.

Usage

dphixy(x, y, rho)

Arguments

Value

the density value.

Examples

library(mvtnorm)
dmvnorm(c(1,-1),sigma = matrix(c(1,0.5,0.5,1),2,2))
dphixy(1,-1,0.5)

Draw the Correlation Matrix

Description

Estimate the MCCM from dataframe and draw it with scatter plot of matrices (SPLOM). With bivariate scatter plots below the diagonal, histograms on the diagonal, and the polychoric correlation coefficients with standard errors above the diagonal. Correlation ellipses are drawn in the same graph. The red lines below the diagonal are the LOESS smoothed lines, fitting a smooth curve between two variables.

Usage

draw_correlation_matrix(
  data1,
  order_indx,
  pair_est = FALSE,
  MLE = FALSE,
  R0 = NULL,
  app = TRUE,
  korder = 2,
  max_iter = 1000,
  max_tol = 1e-08,
  show_log = FALSE
)

Arguments

Value

the SPLOM plot.

See Also

MCCM_est, summary_MCCM_est

Examples

library(mvtnorm)
library(MASS)
library(polycor)
library(lavaan)
set.seed(1997)
n = 10000
rho12=0.3
rho13=0.4
rho14=0.5
rho23=0.6
rho24=0.7
rho34=0.8

R = matrix(c(1,rho12,rho13,rho14,rho12,1,rho23,rho24,rho13,rho23,1,rho34,
rho14,rho24,rho34,1),4,4)
indc = c(3,4)
thresholds = list(c(),c(),0,0)
data1 = gen_mixed(n=n,R=R,indc=indc,thresholds=thresholds)
data2 = data.frame(data1$observed)

# pairwise MLE estimation
draw_correlation_matrix(data2,indc,TRUE,TRUE)
# pairwise IRLS estimation
draw_correlation_matrix(data2,indc,TRUE,FALSE)
# simultaneous MLE estimation
draw_correlation_matrix(data2,indc,FALSE,TRUE)
# simultaneous IGMM estimation
draw_correlation_matrix(data2,indc,FALSE,FALSE)

Estimating Mixed Correlation Matrix by IGMM

Description

An accelerated function to estimate a mixed correlation coefficient matrix, as well as its covariance matrix, for dataframes containing continuous and ordinal variable.

Usage

est_mixedGMM(
  dataYX,
  order_indx,
  R0 = NULL,
  app = TRUE,
  korder = 2,
  max_iter = 1000,
  max_tol = 1e-08,
  show_log = FALSE
)

Arguments

Value

References

arXiv:2404.06781

Examples

library(mvtnorm)
library(MASS)
set.seed(1997)
n = 500
rho12=0.3
rho13=0.4
rho14=0.5
rho23=0.6
rho24=0.7
rho34=0.8

R = matrix(c(1,rho12,rho13,rho14,rho12,1,rho23,rho24,rho13,rho23,1,rho34,
rho14,rho24,rho34,1),4,4)
indc = c(3,4)
thresholds = list(c(),c(),0,0)
data1 = gen_mixed(n=n,R=R,indc=indc,thresholds=thresholds)
data2 = data.frame(data1$observed)
out1 = est_mixedGMM(dataYX = data2,order_indx = indc)
print(out1$Rhat)
print(out1$COV)

Thresholds Estimation

Description

Function to calculate thresholds from ordinal variables.

Usage

est_thre(X)

Arguments

Value

the estimated value for thresholds.

Examples

library(mvtnorm)
set.seed(1997)
R1 = gen_CCM(4)
n = 1000
indc = 3:4
thresholds = list(c(),c(),c(-1),c(1))
data1 = gen_mixed(n,R1,indc,thresholds=thresholds)$observed
est_thre(data1[,3])
est_thre(data1[,4])

Polychoric Correlation

Description

Estimate the polychoric correlation coefficient.

Usage

esti_polychoric(X, maxn = 100, e = 1e-08, ct = FALSE)

Arguments

Value

References

Zhang, P., Liu, B., & Pan, J. (2024). Iteratively Reweighted Least Squares Method for Estimating Polyserial and Polychoric Correlation Coefficients. Journal of Computational and Graphical Statistics, 33(1), 316–328. https://doi.org/10.1080/10618600.2023.2257251

See Also

esti_polyserial

Examples

X = gen_polychoric(1000,0.5,0:1,-1:0)
result = esti_polychoric(X)
print(c(result$rho,result$std,result$iter))

Polyserial Correlation

Description

Estimate the polyserial correlation coefficient.

Usage

esti_polyserial(X, maxn = 100, e = 1e-08)

Arguments

Value

References

Zhang, P., Liu, B., & Pan, J. (2024). Iteratively Reweighted Least Squares Method for Estimating Polyserial and Polychoric Correlation Coefficients. Journal of Computational and Graphical Statistics, 33(1), 316–328. https://doi.org/10.1080/10618600.2023.2257251

See Also

esti_polychoric

Examples

X = gen_polyseries(1000,0.5,-1:1)
result = esti_polyserial(X)
result

Positive Semidefinite Correlation Matrix

Description

Generate a positive semidefinite correlation coefficients matrix

Usage

gen_CCM(d)

Arguments

Value

a correlation coefficients matrix.

Examples

X = gen_CCM(4)
print(X)

Continuous and Ordinal Simulated Data

Description

Generate multi-normal sample and segment it into ordinal.

Usage

gen_mixed(n, R, indc, thresholds)

Arguments

Value

Examples

library(mvtnorm)
set.seed(1997)
R1 = gen_CCM(6)
n = 1000
indc = 4:6
thresholds = list(
  c(),
  c(),
  c(),
  c(0),
  c(-0.5,0),
  c(0,0.5)
)
data1 = gen_mixed(n,R1,indc,thresholds)$observed
data1 = data.frame(data1)
table(data1$X4,data1$X5)
table(data1$X5,data1$X6)

Generate Polychoric Sample

Description

Generate polychoric sample with hidden distribution: binormal with correlation coefficient rho.

Usage

gen_polychoric(n, rho, a, b)

Arguments

Value

Polychoric sample with size n(in a 2*n matrix).

See Also

gen_polyseries gen_rho

Examples

gen_polychoric(100,0.5,-1:1,1:2)

Generate Polyseries Sample

Description

Generate polyseries sample with hidden distribution: binormal with correlation coefficient rho.

Usage

gen_polyseries(n, rho, a)

Arguments

Value

Polyseries sample with size n(in a 2*n matrix).

See Also

gen_rho gen_polychoric

Examples

gen_polyseries(100,0.5,-1:1)

Generate Specific Binormal Distribution

Description

Generate random number of binormal distribution with 0 mean unit variance and correlation coefficient rho.

Usage

gen_rho(n, rho)

Arguments

Value

Binormal random number with length n(in a 2*n matrix).

See Also

gen_polyseries gen_polychoric

Examples

gen_rho(100,0.5)

Mean Bias

Description

Calculate the MB of an array of estimates relative to the true value.

Usage

mb(rhohat, rho)

Arguments

Value

the mean bias of rhohat array.

See Also

mrb rmse

Examples

rho = 0.5
rhohat = 0.5 + rnorm(10)
mb(rhohat,rho)

Mean Relative Bias

Description

Calculate the MRB of an array of estimates relative to the true value.

Usage

mrb(rhohat, rho)

Arguments

Value

the mean relative bias of rhohat array.

See Also

mb rmse

Examples

rho = 0.5
rhohat = 0.5 + rnorm(10)
mrb(rhohat,rho)

Root Mean Squared Error

Description

Calculate the RMSE of an array of estimates relative to the true value.

Usage

rmse(rhohat, rho)

Arguments

Value

the root mean squared error of rhohat array.

See Also

mb mrb

Examples

rho = 0.5
rhohat = 0.5 + rnorm(10)
rmse(rhohat,rho)

Summary a MCCM Estimation Result

Description

Display the estimated correlation matrix and std matrix for a MCCM_est list.

Usage

summary_MCCM_est(out_MCCM)

Arguments

Value

The summary of estimation.

See Also

MCCM_est, draw_correlation_matrix