CANCOR {DFA.CANCOR}

Canonical correlation analysis

Description

Produces SPSS- and SAS-like output for canonical correlation analysis. Portions of the code were adapted from James Steiger (www.statpower.net).

Usage

CANCOR(data, set1, set2, plot, plotCV, plotcoefs, verbose)

Arguments

data

A dataframe where the rows are cases & the columns are the variables.

set1

The names of the continuous variables for the first set,
e.g., set1 = c('varA', 'varB', 'varC').

set2

The names of the continuous variables for the second set,
e.g., set2 = c('varD', 'varE', 'varF').

plot

Should a plot of the coefficients be produced?
The options are: TRUE (default) or FALSE.

plotCV

The canonical variate number for the plot, e.g., plotCV = 1.

plotcoefs

The coefficient for the plots.
The options are 'structure' (default) or 'standardized'.

verbose

Should detailed results be displayed in the console?
The options are: TRUE (default) or FALSE.

Value

If verbose = TRUE, the displayed output includes Pearson correlations, multivariate significance tests, canonical function correlations and bivariate significance tests, raw canonical coefficients, structure coefficients, standardized coefficients, and a bar plot of the structure or standardized coefficients.

The returned output is a list with elements

cancorrels

canonical correlations and their significance tests

mv_Wilks

The Wilks' lambda multivariate test

mv_Pillai

The Pillai-Bartlett multivariate test

mv_Hotelling

The Lawley-Hotelling multivariate test

mv_Roy

Roy's greatest characteristic root multivariate test

mv_BartlettV

Bartlett's V multivariate significance test

mv_Rao

Rao's' multivariate significance test

CoefRawSet1

raw canonical coefficients for Set 1

CoefRawSet2

raw canonical coefficients for Set 2

CoefStruct11

structure coefficients for Set 1 variables with the Set 1 variates

CoefStruct21

structure coefficients for Set 2 variables with the Set 1 variates

CoefStruct12

structure coefficients for Set 1 variables with the Set 2 variates

CoefStruct22

structure coefficients for Set 2 variables with the Set 2 variates

CoefStandSet1

standardized coefficients for Set 1 variables

CoefStandSet2

standardized coefficients for Set 2 variables

CorrelSet1

Pearson correlations for Set 1

CorrelSet2

Pearson correlations for Set 2

CorrelSet1n2

Pearson correlations between Set 1 & Set 2

set1_scores

Canonical variate scores for Set 1

set2_scores

Canonical variate scores for Set 2

Author(s)

Brian P. O'Connor

References

Manly, B. F. J., & Alberto, J. A. (2017). Multivariate statistical methods: A primer (4th Edition). Chapman & Hall/CRC, Boca Raton, FL.

Rencher, A. C. (2002). Methods of Multivariate Analysis (2nd ed.). New York, NY: John Wiley & Sons.

Sherry, A., & Henson, R. K. (2005). Conducting and interpreting canonical correlation analysis in personality research: A user-friendly primer. Journal of Personality Assessment, 84, 37-48.

Steiger, J. (2019). Canonical correlation analysis.
www.statpower.net/Content/312/Lecture%20Slides/CanonicalCorrelation.pdf

Tabachnik, B. G., & Fidell, L. S. (2019). Using multivariate statistics (7th ed.). New York, NY: Pearson.

Examples

# data that simulate those from De Leo & Wulfert (2013)
CANCOR(data = data_CANCOR$DeLeo_2013,
       set1 = c('Tobacco_Use','Alcohol_Use','Illicit_Drug_Use','Gambling_Behavior',
                'Unprotected_Sex','CIAS_Total'),
       set2 = c('Impulsivity','Social_Interaction_Anxiety','Depression',
                'Social_Support','Intolerance_of_Deviance','Family_Morals',
                'Family_Conflict','Grade_Point_Average'),
       plot = TRUE, plotCV = 1, plotcoefs='structure',
       verbose = TRUE)


	
# data from Ho (2014, Chapter 17)
CANCOR(data = data_CANCOR$Ho_2014,
       set1 = c("willing_use","likely_use","intend_use","certain_use"),
       set2 = c("perceived_risk","perceived_severity","self_efficacy",
                "response_efficacy","maladaptive_coping","fear"),
       plot = 'yes', plotCV = 1)

	
# data from Rencher (2002, pp. 366, 369, 372)
CANCOR(data = data_CANCOR$Rencher_2002,
       set1 = c("y1","y2","y3"),
       set2 = c("x1","x2","x3","x1x2","x1x3","x2x3","x1sq","x2sq","x3sq"),
       plot = 'yes', plotCV = 1)


# data from Tabachnik & Fidell (2019, p. 451, 460)    small dataset
CANCOR(data = data_CANCOR$TabFid_2019_small,
       set1 = c('TS','TC'),
       set2 = c('BS','BC'),
       plot = TRUE, plotCV = 1, plotcoefs='structure',
       verbose = TRUE)


# data from Tabachnik & Fidell (2019, p. 463)     complete dataset
CANCOR(data = data_CANCOR$TabFid_2019_complete,
       set1 = c("esteem","control","attmar","attrole"),
       set2 = c("timedrs","attdrug","phyheal","menheal","druguse"),
       plot = TRUE, plotCV = 1, plotcoefs='structure',
       verbose = TRUE)


# UCLA dataset   https://stats.oarc.ucla.edu/r/dae/canonical-correlation-analysis/
CANCOR(data = data_CANCOR$UCLA, 
       set1 = c("Locus_Control","Self_Concept","Motivation"),
       set2 = c("Read","Write","Math","Science","Sex"),
       plot = TRUE, plotCV = 1, plotcoefs='standardized',
       verbose = TRUE)