Interpreting Regression Effects

Description

The purpose of this package is to provide methods to interpret multiple linear regression and canonical correlation results including beta weights, structure coefficients, validity coefficients, product measures, relative weights, all-possible-subsets regression, dominance analysis, commonality analysis, and adjusted effect sizes.

Author(s)

Kim Nimon <kim.nimon@gmail.com>, Fred L. Oswald, J. Kyle Roberts

References

Beaton, A. E. (1973) Commonality. (ERIC Document Reproduction Service No. ED111829)

Butts, C. T. (2009). yacca: Yet Another Canonical Correlation Analysis Package. R package version 1.1.

Mood, A. M. (1969) Macro-analysis of the American educational system. Operations Research, 17, 770-784.

Nimon, K., Lewis, M., Kane, R. & Haynes, R. M. (2008) An R package to compute commonality coefficients in the multiple regression case: An introduction to the package and a practical example. Behavior Research Methods, 40(2), 457-466.

Nimon, K., & Oswald, F. L. (2013). Understanding the results of multiple linear regression: Beyond standardized regression coefficients. Organizational Research Methods, 16, 650-674.

See Also

regr commonalityCoefficients canonCommonality calc.yhat boot.yhat booteval.yhat plotCI.yhat aps commonality dominance dombin rlw

All Possible Subsets Regression

Description

The function runs all possible subsets regression and returns data needed to run commonality and dominance analysis.

Usage

  aps(dataMatrix, dv, ivlist)

Arguments

Details

Function returns all possible subset information that is used by commonality and dominance. If data are missing, non-missing data are eliminated based on listwise deletion for full model.

Value

Author(s)

Kim Nimon <kim.nimon@gmail.com>

References

Nimon, K., & Oswald, F. L. (2013). Understanding the results of multiple linear regression: Beyond standardized regression coefficients. Organizational Research Methods, 16, 650-674.

See Also

calc.yhat commonality dominance rlw

Examples

  ## APS regression predicting miles per gallon based 
  ## on vehicle weight, type of 
  ## carborator, & number of engine cylinders
     apsOut<-aps(mtcars,"mpg",list("wt","carb","cyl"))

  ## APS regression predicting paragraph comprehension based 
  ## on thre verbal tests: general info, sentence comprehension,
  ## & word classification
 
  ## Use HS dataset in MBESS 
     if (require ("MBESS")){
     data(HS)
  ## APS
     apsOut<-aps(HS,"t6_paragraph_comprehension",list("t5_general_information","t7_sentence",
                                         "t8_word_classification"))
     }

Bootstrap metrics produced from calc.yhat

Description

This function is input to boot to bootstrap metrics computed from calc.yhat.

Usage

  boot.yhat(data, indices, lmOut,regrout0)

Arguments

Details

This function is input to boot to bootstrap metrics computed from calc.yhat.

Value

The output of boot.yhat when used in conjunction with boot is of class boot and is not further described here. The output is designed to be useful as input for booteval.yhat

Author(s)

Kim Nimon <kim.nimon@gmail.com>

References

Nimon, K., & Oswald, F. L. (2013). Understanding the results of multiple linear regression: Beyond standardized regression coefficients. Organizational Research Methods, 16, 650-674.

See Also

lm calc.yhat boot booteval.yhat

Examples

  ## Bootstrap regression results predicting paragraph     
  ## comprehension based on three verbal tests: general info, 
  ## sentence comprehension, & word classification
 
  ## Use HS dataset in MBESS 
     if (require ("MBESS")){
     data(HS)

  ## Regression
     lm.out<-lm(t6_paragraph_comprehension~
                t5_general_information+t7_sentence+t8_word_classification,data=HS)

  ## Calculate regression metrics
     regrOut<-calc.yhat(lm.out)

  ## Bootstrap results
     require ("boot")
     boot.out<-boot(HS,boot.yhat,100,lmOut=lm.out,regrout0=regrOut)
     }

Evaluate bootstrap metrics produced from calc.yhat

Description

This function evaluates the bootstrap metrics produced from boot.yhat.

Usage

  booteval.yhat(regrOut, boot.out, bty, level, prec)

Arguments

Details

This function evaluates the bootstrap metrics produced from boot.yhat.

Value

Confidence intervals are reported for predictor and all possible subset metrics as well as differences between appropriate predictors and all possible subset metrics. The function also output the means, standard errors, probabiltites, and reproducibility metrics for the dominance comparisons. Means and standard deviations are reported for Kendall's tau correlation between sample predictor metrics and the bootstrap statistics of like metrics.

Author(s)

Kim Nimon <kim.nimon@gmail.com>

References

Nimon, K., & Oswald, F. L. (2013). Understanding the results of multiple linear regression: Beyond standardized regression coefficients. Organizational Research Methods, 16, 650-674.

See Also

lm calc.yhat boot plotCI.yhat

Examples

  ## Bootstrap regression results predicting paragraph     
  ## comprehension based on four verbal tests: general info, 
  ## sentence comprehension, & word classification
 
  ## Use HS dataset in MBESS 
     if (require ("MBESS")){
     data(HS)

  ## Regression
     lm.out<-lm(t6_paragraph_comprehension~
                t5_general_information+t7_sentence+t8_word_classification,data=HS)

  ## Calculate regression metrics
     regrOut<-calc.yhat(lm.out)

  ## Bootstrap results
     require ("boot")
     boot.out<-boot(HS,boot.yhat,100,lmOut=lm.out,regrout0=regrOut)

  ## Evaluate bootstrap results
     result<-booteval.yhat(regrOut,boot.out,bty="perc")
     }

More regression indices for lm class objects

Description

Reports beta weights, validity coefficients, structure coefficients, product measures, commonality analysis coefficients, and dominance analysis weights for lm class objects.

Usage

calc.yhat(lm.out,prec=3)

Arguments

Details

Takes the lm class object and reports beta weights, validity coefficients, structure coefficients, product measures, commonality analysis coefficients, and dominance analysis weights.

Value

Author(s)

Kim Nimon <kim.nimon@gmail.com>

References

Nimon, K., & Oswald, F. L. (2013). Understanding the results of multiple linear regression: Beyond standardized regression coefficients. Organizational Research Methods, 16, 650-674.

Thomas, D. R., Zumbo, B. D., Kwan, E., & Schweitzer, L. (2014). On Johnson's (2000) relative weights method for assessing variable importance: A reanalysis. Multivariate Behavioral Research, 16, 49(4), 329-338.

Examples

  ## Predict paragraph comprehension based on three verbal
  ## tests: general info, sentence comprehension, & word
  ## classification
  
  ## Use HS dataset in MBESS 
     if (require("MBESS")){
     data(HS)
  
  ## Regression
     lm.out<-lm(t6_paragraph_comprehension~
                t5_general_information+t7_sentence+t8_word_classification,data=HS)
  
  ## Regression Indices
     regr.out<-calc.yhat(lm.out)
     }

Commonality Coefficents for Canonical Correlation

Description

The canonCommonality function produces commonality data for both canonical variables sets. Variables in a given canonical set are used to partition the variance of the canonical variates produced from the other canonical set and vica versa. Commonality data is supplied for the number of canonical functions requested.

Usage

  canonCommonality(A, B, nofns = 1)

Arguments

Details

The function canonCommonality has two required arguments and one optional argument. The first two arguments contain the two variable sets. The third argument is optional and defnes the number of canonical functions to analyze. Unless specifed, the number of canonical functions defaults to 1.

The function canonCommonality calls a function canonVariate to decompose canonical varites twice: the first time for the variable set identified in the first argument, the second time for the variable set identified in the second argument.

Value

The function canonCommonality returns commonality data for both canonical variable sets. For the number of functions requested, both canonical variates are analyzed. For each canonical variate analyzed, two tables are returned. The first table lists the commonality coefficients and their contribution to the total effect, while the second table lists the unique and common effects for each regressor. The function returns the resulting output ordering the output according to the function's paramaeters.

Author(s)

Kim Nimon <kim.nimon@gmail.com>

References

Nimon, K., Henson, R., & Gates, M. (2010). Revisiting interpretation of canonical correlation analysis: A tutorial and demonstration of canonical commonality analysis. Multivariate Behavioral Research, 45,702-724.

See Also

canonVariate

Examples

  ## Example parallels the R builtin cancor and the 
  ## yacca cca example
     data(LifeCycleSavings)
     pop <- LifeCycleSavings[, 2:3]
     oec <- LifeCycleSavings[, -(2:3)]
  ## Perform Commonality Coefficient Analysis
     canonCommonData<-canonCommonality(pop,oec,1)

  ## Use HS dataset in MBESS 
     if (require("MBESS")){
     data(HS)
     attach(HS)
  ## Create canonical variable sets
     MATH_REASON<-HS[,c("t20_deduction","t22_problem_reasoning")]
     MATH_FUND<-HS[,c("t21_numerical_puzzles","t24_woody_mccall","t10_addition")] 
  ## Perform Commonality Coefficient Analysis
     canonCommonData<-canonCommonality(MATH_FUND,MATH_REASON,1)
     detach(HS)      
     }

Canonical Commonality Analysis

Description

The canonCommonality function produces commonality data for a given canonical variable set. Using the variables in a given canonical set to partition the variance of the canonical variates produced from the other canonical set, commonality data is supplied for the number of canonical functions requested.

Usage

  canonVariate(A, B, nofns)

Arguments

Details

For each canonical function, canonVariate: (a) creates a dataset that combines the matrix of variables for a given canonical set and the canonicate variate for the other canonical set; (b) calls commonalityCoefficients, passing the dataset, the name of the canonical variate, and the names of the variates in a given canonical set; (c) saves resultant output.

Value

The function canonVariate returns commonality data for the canonical variable set input. For the number of functions requested, two tables are returned. The first table lists the commonality coefficients for each canonical function together with its contribution to the total effect, while the second table lists the unique and common effects for each regressor.

Note

This function is internal to canonCommonality, called during runtime and passed the appropriate parameters. This is not an end-user function.

Author(s)

Kim Nimon <kim.nimon@gmail.com>

References

Nimon, K., Henson, R., & Gates, M. (2010). Revisiting interpretation of canonical correlation analysis: A tutorial and demonstration of canonical commonality analysis. Multivariate Behavioral Research, 45,702-724.

See Also

canonCommonality

Compute CI

Description

This function retrieves the proper elements from boot.ci.

Usage

  ci.yhat(bty, CI)

Arguments

Details

This function retrieves the proper elements from boot.ci.

Value

This function returns the proper elements from boot.ci.

Note

This function is internal to the yhat package and not intended to be an end-user function.

Author(s)

Kim Nimon <kim.nimon@gmail.com>

References

Nimon, K., & Oswald, F. L. (2013). Understanding the results of multiple linear regression: Beyond standardized regression coefficients. Organizational Research Methods, 16, 650-674.

Combine upper and lower confidence intervals

Description

This function combines upper and lower confidence intervals along with sample statistics and optionally stars intervals that do not contain 0.

Usage

  combCI(lowerCI, upperCI, est, star=FALSE )

Arguments

Details

This function evaluates the bootstrap metrics produced from boot.yhat.

Value

Returns estimate with confidence interval in ( ). Optionally, confidence interval not containing 0 is starred.

Note

This function is internal to the yhat package and not intended to be an end-user function.

Author(s)

Kim Nimon <kim.nimon@gmail.com>

References

Nimon, K., & Oswald, F. L. (2013). Understanding the results of multiple linear regression: Beyond standardized regression coefficients. Organizational Research Methods, 16, 650-674.

Commonality Analysis

Description

This function conducts commonality analyses based on an all-possible-subsets regression.

Usage

  commonality(apsOut)

Arguments

Details

This function conducts commonality analyses based on an all-possible-subsets regression.

Value

The function returns a matrix containing commonality coefficients and percentage of regression effect for each each possible set of predictors.

Author(s)

Kim Nimon <kim.nimon@gmail.com>

References

Nimon, K., Lewis, M., Kane, R. & Haynes, R. M. (2008) An R package to compute commonality coefficients in the multiple regression case: An introduction to the package and a practical example.Behavior Research Methods, 40, 457-466.

Nimon, K., & Oswald, F. L. (2013). Understanding the results of multiple linear regression: Beyond standardized regression coefficients. Organizational Research Methods, 16, 650-674.

See Also

aps calc.yhat dominance rlw

Examples

  ## Predict paragraph comprehension based on three verbal
  ## tests: general info, sentence comprehension, & word
  ## classification

  ## Use HS dataset in MBESS 
     if (require ("MBESS")){
     data(HS)

  ## All-possible-subsets regression
     apsOut=aps(HS,"t6_paragraph_comprehension",
                    list("t5_general_information", "t7_sentence","t8_word_classification"))

  ## Commonality analysis
     commonality(apsOut)
     }

Commonality Coefficents

Description

Commonality Coefficients returns a list of two tables. The first table CC contains the list of commonality coefficients and the percent variance for each effect. The second CCTotByVar totals the unique and common effects for each independent variable.

Usage

  commonalityCoefficients(dataMatrix, dv, ivlist, imat=FALSE)

Arguments

Details

When echo flag is true, transitional matrices during commonality coefficient calculation are sent to output window. Default for this option is false. When set to true, the intermediate matrices for each commonality coefficient and regression combinations are printed in the output window.

Value

Author(s)

Kim Nimon <kim.nimon@gmail.com>

References

Nimon, K., Lewis, M., Kane, R. & Haynes, R. M. (2008) An R package to compute commonality coefficients in the multiple regression case: An introduction to the package and a practical example.Behavior Research Methods, 40, 457-466.

See Also

canonCommonality genList odd setBits

Examples

  ## Predict miles per gallon based on vehicle weight, type of 
  ## carborator, & number of engine cylinders
     commonalityCoefficients(mtcars,"mpg",list("wt","carb","cyl"))

  ## Predict paragraph comprehension based on four verbal
  ## tests: general info, sentence comprehension, word
  ## classification, & word type 
  ## Use HS dataset in MBESS 
     if (require ("MBESS")){
     data(HS)
  ## Commonality Coefficient Analysis
     commonalityCoefficients(HS,"t6_paragraph_comprehension",list("t5_general_information",
       "t7_sentence","t8_word_classification","t9_word_meaning"))
     }

Dominance Analysis

Description

For each level of dominance and pairs of predictors in the full model, this function indicates whether a predictor "x1" dominates "x2", predictor "x2" dominates "x1", or that dominance cannot be established between predictors.

Usage

  dombin(domOut)

Arguments

Details

For each level of dominance and pairs of predictors in the full model, this function indicates whether a predictor "x1" dominates "x2", predictor "x2" dominates "x1", or that dominance cannot be established between predictors.

Value

The function return a matrix that contains dominance level decisions (complete, conditional, and general) for each pair of predictors in the full model.

Author(s)

Kim Nimon <kim.nimon@gmail.com>

References

Nimon, K., & Oswald, F. L. (2013). Understanding the results of multiple linear regression: Beyond standardized regression coefficients. Organizational Research Methods, 16, 650-674.

See Also

aps calc.yhat commonality dominance rlw

Examples

  ## Predict paragraph comprehension based on three verbal
  ## tests: general info, sentence comprehension, & word
  ## classification

  ## Use HS dataset in MBESS 
     if (require("MBESS")){
     data(HS)

  ## All-possible-subsets regression
     apsOut=aps(HS,"t6_paragraph_comprehension",
                list("t5_general_information", "t7_sentence","t8_word_classification"))

  ## Dominance analysis
     domOut=dominance(apsOut)

  ## Dominance analysis
     dombin(domOut)
     }

Dominance Weights

Description

Computes dominance weights including conditional and general.

Usage

  dominance(apsOut)

Arguments

Details

Provides full dominance weights table that are used to compute conditional and general dominance weights as well as reports conditional and general dominance weights.

Value

Author(s)

Kim Nimon <kim.nimon@gmail.com>

References

Nimon, K., & Oswald, F. L. (2013). Understanding the results of multiple linear regression: Beyond standardized regression coefficients. Organizational Research Methods, 16, 650-674.

See Also

aps calc.yhat dombin rlw

Examples

  ## Predict paragraph comprehension based on three verbal
  ## tests: general info, sentence comprehension, & word
  ## classification

  ## Use HS dataset in MBESS 
     if (require ("MBESS")){
     data(HS)

  ## All-possible-subsets regression
     apsOut=aps(HS,"t6_paragraph_comprehension",
            list("t5_general_information", "t7_sentence","t8_word_classification"))

  ## Dominance weights
     dominance(apsOut)
     }

Effect Size Computation for lm

Description

Creates adjusted effect sizes for linear regression.

Usage

  effect.size(lm.out)

Arguments

Details

The function effect.size produces a family of effect size corrections for the R-squared metric produced from an lm class object. Suggestions for recommended correction are supplied, based on Yin and Fan (2001).

Value

Returns adjusted R-squared metric.

Author(s)

J. Kyle Roberts <kyler@smu.edu>

References

Yin, P., & Fan. X. (2001) Estimated R^2 shrinkage in multiple regression: A comparison of different analytical methods. The Journal of Experimental Education, 69, 203-224.

See Also

regr,yhat

Examples

     if (require("MBESS")){
     data(HS)
     attach(HS)
     lm.out<-lm(t20_deduction~t10_addition*t24_woody_mccall)
     effect.size(lm.out)
     detach(HS)
     }

Generate List R^2 Values

Description

Use the bitmap matrix to generate the list of R^2 values needed.

Usage

  genList(ivlist, value)

Arguments

Details

Returns the number of R^2 values that will be calculated in output tables.

Value

Returns newlist from generate list function call.

Note

This function is internal to commonalityCoefficients, called during runtime and passed the appropriate parameters. This is not an end-user function.

Author(s)

Kim Nimon <kim.nimon@gmail.com>

isOdd Function

Description

Function receives value and returns true if value is odd.

Usage

odd(val)

Arguments

Details

Determines value of parameter in argument.

Value

Returns true when value checked is odd. Otherwise, function returns a value false.

Note

This function is internal to commonalityCoefficients, called during runtime and passed the appropriate parameters. This is not an end-user function.

Author(s)

Kim Nimon <kim.nimon@gmail.com>

Plot CIs from yhat

Description

This function plots CIs that have been produced from booteval.yhat.

Usage

  plotCI.yhat(sampStat, upperCI, lowerCI, pid=1:ncol(sampStat), nr=2, nc=2)

Arguments

Details

This function plots CIs that have been produced from booteval.yhat.

Value

This returns a plot of CIs that have been produced from booteval.yhat.

Author(s)

Kim Nimon <kim.nimon@gmail.com>

References

Nimon, K., & Oswald, F. L. (2013). Understanding the results of multiple linear regression: Beyond standardized regression coefficients. Organizational Research Methods, 16, 650-674.

See Also

lm calc.yhat boot booteval.yhat

Examples

  ## Bootstrap regression results predicting paragraph     
  ## comprehension based on three verbal tests: general info, 
  ## sentence comprehension, & word classification 
 
  ## Use HS dataset in MBESS 
     if (require("MBESS")){
     data(HS)

  ## Regression
     lm.out<-lm(t6_paragraph_comprehension~
                t5_general_information+t7_sentence+t8_word_classification,data=HS)

  ## Calculate regression metrics
     regrOut<-calc.yhat(lm.out)

  ## Bootstrap results
     require ("boot")
     boot.out<-boot(HS,boot.yhat,100,lmOut=lm.out,regrout0=regrOut)

  ## Evaluate bootstrap results
     result<-booteval.yhat(regrOut,boot.out,bty="perc")

  ## Plot results
  ## plotCI.yhat(regrOut$PredictorMetrics[-nrow(regrOut$PredictorMetrics),],
  ## result$upperCIpm,result$lowerCIpm, pid=which(colnames(regrOut$PredictorMetrics) 
  ## %in% c("Beta","rs","CD:0","CD:1","CD:2","GenDom","Pratt","RLW") == TRUE),nr=3,nc=3)
     }

Regression effect reporting for lm class objects

Description

The regr reports beta weights, standardized beta weights, structure coefficients, adjusted effect sizes, and commonality coefficients for lm class objects.

Usage

regr(lm.out)

Arguments

Details

The function regr takes the lm class object and reports beta weights, standardized beta weights, structure coefficients, adjusted effect sizes, and commonality coefficients for lm class objects.

Value

Author(s)

J. Kyle Roberts <kyler@smu.edu>, Kim Nimon <kim.nimon@gmail.com>

References

Kraha, A., Turner, H., Nimon, K., Zientek, L., Henson, R. (2012). Tools to support multiple regression in the face of multicollinearity.Frontiers in Psychology, 3(102), 1-13.

See Also

commonalityCoefficients, effect.size

Examples

     if (require ("MBESS")){
     data(HS)
     attach(HS)
     lm.out<-lm(t20_deduction~t10_addition*t24_woody_mccall)
     regr(lm.out)
     detach(HS)
     }

Relative Weights

Description

The function computes relative weights.

Usage

  rlw(dataMatrix, dv, ivlist)

Arguments

Details

The function computes relative weights.

Value

The function returns relative weights for each predictor.

Author(s)

Kim Nimon <kim.nimon@gmail.com>

References

Nimon, K., & Oswald, F. L. (2013). Understanding the results of multiple linear regression: Beyond standardized regression coefficients. Organizational Research Methods, 16, 650-674.

Thomas, D. R., Zumbo, B. D., Kwan, E., & Schweitzer, L. (2014). On Johnson's (2000) relative weights method for assessing variable importance: A reanalysis. Multivariate Behavioral Research, 16, 49(4), 329-338.

See Also

aps calc.yhat commonality dominance

Examples

  ## Relative weights from regression model predicting paragraph 
  ## comprehension based on three verbal tests: general info, 
  ## sentence comprehension, & word classification
 
  ## Use HS dataset in MBESS 
     if (require ("MBESS")){
     data(HS)

  ## Relative Weights
     rwlOut<-rlw(HS,"t6_paragraph_comprehension",
                     c("t5_general_information","t7_sentence","t8_word_classification"))
     }

Decimal to Binary

Description

Creates the binary representation of n and stores it in the nth column of the matrix.

Usage

  setBits(col, effectBitMap)

Arguments

Details

Creates the binary representation of col and stores it in its associated column.

Value

Returns matrix effectBitMap of mean combinations in binary form.

Note

This function is internal to commonalityCoefficients, called during runtime and passed the appropriate parameters. This is not an end-user function.

Author(s)

Kim Nimon <kim.nimon@gmail.com>