SET_CORRELATION: Cohen's Set Correlation Analysis

In SIMPLE.REGRESSION: OLS, Moderated, Logistic, and Count Regressions Made Simple

Cohen's Set Correlation Analysis

Description

Performs Cohen's set correlation analysis of associations between two sets of variables while statistically controlling for one or more other variables. Estimates of overall, multivariate association between the two sets of variables are provided, along with partial correlations and output from OLS regression analyses for each dependent variable.

Usage

SET_CORRELATION(data, IVs, DVs, IV_covars=NULL, DV_covars=NULL,
                Ncases=NULL, verbose=TRUE, display_cormats=FALSE)

Arguments

data	Either a dataframe of raw data (where the rows are cases and the columns are the variables), or a square correlation matrix with row and column names.
IVs	The name(s) of the independent/predictor variable(s) in data. Example: IVs = c('var1', 'var2', 'var3')
DVs	The name(s) of the dependent variable(s) in data. Example: DVs = c('var4', 'var5', 'var6')
IV_covars	The name(s) of the variable(s), if any, to be partialled out of the IVs. Example: IV_covars = c('var7', 'var8')
DV_covars	The name(s) of the variable(s), if any, to be partialled out of the DVs. Example: DV_covars = c('var9', 'var10')
Ncases	The number of cases. Required only when the input (data) is a correlation matrix.
verbose	Should detailed results be displayed in console? The options are: TRUE (default) or FALSE.
display_cormats	Should the variable correlation matrices be displayed in console? The options are: TRUE or FALSE(default).

Details

Set correlation analysis and canonical correlation analysis are both fully multivariate methods for examining associations between two sets of variables. However, in CCA the focus is on linear combinations of predictor and criterion variables, which are often difficult to interpret. In contrast, in set correlation analysis the focus is typically on the associations between two sets of variables while statistically controlling for other variables (rather than on linear combinations). The outcome variables of interest in set correlation analysis are the (possibly partialled) dependent variables themselves and not composites of variables.

A key feature of set correlation analysis is the option of examining the overlap between two sets of variables while statistically controlling for one or more other variables. The covariates that are removed from one set of variables (e.g., the DVs) may or may not be the same covariates that are removed from the other set of variables (e.g., the IVs).

In the present function, when there is a wish to statistically remove the same covariates from both sets (i.e., from both the IVs and DVs), then simply enter the same covariate names on both the IV_covars and DV_covars arguments.

The options together result in five different types of data scenarios that can be examined:

Whole, in which the associations between two sets (IVs and DVs) are assessed without any partialling out whatsoever;

Partial, in which the associations between two sets (IVs and DVs) are assessed while partialling the same covariates (one or more) out of both the IVs and DVs;

X Semipartial, in which the associations between two sets (IVs and DVs) are assessed while partialling one or more covariates out of the IV set while leaving the variables in the DV set untouched (unpartialled);

Y Semipartial, in which the associations between two sets (IVs and DVs) are assessed while partialling one or more covariates out of the DV set while leaving the variables in the IV set untouched (unpartialled); and

Bipartial, in which the associations between two sets (IVs and DVs) are assessed while partialling one or more covariates out of the DV set and while partialling one or more other (different) covariates out of the IV set.

The set correlation analyses in this function are conducted using only the correlations between the variables. When raw data are entered into the function, the variable correlation matrix is computed and becomes the sole basis of all further set correlation analyses.

Value

An object of class "SET_CORRELATION". The object is a list containing the following components:

bigR	The Pearson correlation matrix for the variables in the analyses.
Ryy	The correlations between the DVs.
Rxx	The correlations between the IVs.
Rx_y	The correlation between the DVs and IVs.
betas	The standardized betas.
se_betas	The standard errors of the standardized betas.
t	The t test values for the standardized betas.
pt	The p values for the t tests for the standardized betas.

Author(s)

Brian P. O'Connor

References

Cohen, J. (1982). Set correlation as a general multivariate data-analytic method. Multivariate Behavioral Research, 17(3), 301-341.

Cohen, J. (1988). Set correlation and multivariate Methods. In J. Cohen, Statistical power analysis for the behavioral sciences (2nd ed., pp. 467-530). Mahwah, NJ: Erlbaum.

Cohen, J. (1993). Set correlation. In G. Keren & C. Lewis (Eds.), A handbook for data analysis in the behavioral sciences: Statistical issues (pp. 165-198). Mahwah, NJ: Erlbaum.

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Multiple dependent variables: Set correlation. In, Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed., pp. 608-628). Lawrence Erlbaum Associates.

Examples

# data from Cohen et al. (2003)
Cohen_2003_p621 <- '
 1.0
 .53  1.0  
 .62  .61  1.0
 .19  .23  .03  1.0
-.09  .10  .10 -.02  1.0
 .08  .18  .12  .02  .05  1.0
 .02  .02  .03  .00  .06  .22  1.0
-.12 -.10 -.06 -.02  .18 -.07 -.01  1.0
 .08  .15  .12 -.02  .02  .36 -.05 -.03  1.0'

Cohen_2003_p621_noms <- c('ADHD', 'CD', 'ODD', 'Sex', 'Age', 'MONLY', 
                          'MWORK', 'MAGE', 'Poverty')

Cohen_2003_p621 <- data.matrix( read.table(text=Cohen_2003_p621, fill=TRUE, 
                                           col.names=Cohen_2003_p621_noms,
                                           row.names=Cohen_2003_p621_noms ))
Cohen_2003_p621[upper.tri(Cohen_2003_p621)] <- 
  t(Cohen_2003_p621)[upper.tri(Cohen_2003_p621)]

# whole
SET_CORRELATION(data=Cohen_2003_p621, 
                IVs = c('Sex', 'Age', 'MONLY', 'MWORK', 'MAGE', 'Poverty'), 
                DVs = c('ADHD', 'CD', 'ODD'), 
                IV_covars = NULL, 
                DV_covars = NULL,
                Ncases = 701) 

# bipartial
SET_CORRELATION(data=data_DeLeo_2013, 
                IVs = c('Grade_Point_Average','Family_Morals','Social_Support',
                        'Intolerance_of_Deviance','Impulsivity','Social_Interaction_Anxiety'), 
                DVs = c('Problematic_Internet_Use','Tobacco_Use','Alcohol_Use','Illicit_Drug_Use'), 
                IV_covars = c('Age','Parents_Income'), 
                DV_covars = c('Gambling_Behavior','Unprotected_Sex'),
                display_cormats=TRUE) 

# X semipartial
SET_CORRELATION(data=data_DeLeo_2013, 
                IVs = c('Grade_Point_Average','Family_Morals','Social_Support',
                        'Intolerance_of_Deviance','Impulsivity','Social_Interaction_Anxiety'), 
                DVs = c('Problematic_Internet_Use','Tobacco_Use','Alcohol_Use','Illicit_Drug_Use'), 
                IV_covars = c('Age','Parents_Income'), 
                DV_covars = NULL) 

# partial
SET_CORRELATION(data=data_DeLeo_2013, 
                IVs = c('Grade_Point_Average','Family_Morals','Social_Support',
                        'Intolerance_of_Deviance','Impulsivity','Social_Interaction_Anxiety'), 
                DVs = c('Problematic_Internet_Use','Tobacco_Use','Alcohol_Use','Illicit_Drug_Use'), 
                IV_covars = c('Age','Parents_Income'), 
                DV_covars = c('Age','Parents_Income')) 

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