6 Variables: PD MF MA K IAH SBS

Transcription

1 options pageno=min nodate formdlim='-'; title 'Canonical Correlation, Journal of Interpersonal Violence, 10: '; data SunitaPatel; infile 'C:\Users\Vati\Documents\StatData\Sunita.dat'; input Group Gender PD MF MA SI IAH SBS F K; if gender ne 1 then delete; proc corr; var pd mf ma k iah sbs; PROC CANCORR redundancy VN='Homonegativity' WN='MMPI' VP=Homoneg_ WP=MMPI_ out=sol; VAR IAH SBS; WITH MA MF PD K; run; Canonical Correlation, Journal of Interpersonal Violence, 10: The CORR Procedure 6 Variables: PD MF MA K IAH SBS Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum PD MF MA K IAH SBS Pearson Correlation Coefficients, N = 80 Prob > r under H0: Rho=0 PD MF MA K IAH SBS PD MF MA K IAH SBS

2 Canonical Correlation Adjusted Canonical Correlation Approximate Standard Error The CANCORR Procedure Canonical Correlation Analysis Squared Canonical Correlation Eigenvalues of Inv(E)*H = CanRsq/(1-CanRsq) Eigenvalue Difference Proportion Cumulative As always, the first canonical correlation is larger than the second. Were there a third pair of canonical variates, the second canonical correlation would be larger than the third, and so on. The eigenvalue for each root = the squared canonical correlation minus (1 the squared canonical correlation. For the first root here, divided by ( ) =.1684 Test of H0: The canonical correlations in the current row and all that follow are zero Likelihood Ratio Approximate F Value Num DF Den DF Pr > F Statistic Multivariate Statistics and F Approximations S=2 M=0.5 N=36 Value F Value Num DF Den DF Pr > F Wilks' Lambda Pillai's Trace Hotelling-Lawley Trace Roy's Greatest Root The CANCORR Procedure Canonical Correlation Analysis Standardized Canonical Coefficients for the Homonegativity Homoneg_1 Homoneg_2 IAH SBS High Scores on Homoneg_1 result from high scores on the SBS and, to a lesser degree, on the IAH. High Scores on Homoneg_2 result from high scores on the SBS and low scores on the IAH (notice the negative sign on the Beta for IAH). Notice that the value of the two Beta weights

3 falls outside of the interval (0, r), where r is the loading in fact, the absolute value of the Beta for IAH even exceeds one. This is clear evidence of suppression. Standardized Canonical Coefficients for the MMPI MMPI_1 MMPI_2 MA MF PD K High scores on MMPI_1 reflect high scores on MA (hypomania), high scores on PD (psychopathic deviance), low scores on MF (high masculinity), and low scores on K (unusually frank). High scores on MMPI_2 reflect from high scores on MA and MF (unusually feminine). The CANCORR Procedure Canonical Structure Correlations Between the Homonegativity and Their Homoneg_1 Homoneg_2 IAH SBS Those who score high on Homneg_1 also score high on IAH and SBS. I ll call this canonical variate Aggressive Homophobia. Those who score high on Homoneg_2 score low on IAH but still aggress against gays. I ll call this canonical variate Equal Opportunity Bully. The mean of squared loading (MSL) for Aggressive Homophobia = ( )/2 =.627. Homoneg_1 captures 62.7% of the variance in IAH and SBS. The MSL for Equal Opportunity Bully = ( )/2 =.373. Homoneg_2 captures 37.3% of the variance in IAH and SBS Collectively, Homoneg_1 and Homoneg_2 capture = 1, all of the variance in IAH and SBS.

4 Correlations Between the MMPI and Their Canonical Variables MMPI_1 MMPI_2 MA MF PD K Those who score high on the MMPI_1 also score high on MA and PD and low on MF and K. I ll call this canonical variate Johnny Pissoff they are hypomanic, socially maladjusted and hostile, stereotypically masculine, and unusually frank. Those who score high on the MMPI_2 also score high on the MA and the MF. I ll call this canonical variate Feminine Hypomania. The MSL for Johnny Pissoff = ( )/4 = 22.7%. The MSL for Feminine Hypomania = ( )/4 = 28.9%. Collectively, the two MMPI canonical variates capture 22.7% % = 51.6% of the variance in the MMPI variables. Correlations Between the Homonegativity and the Canonical Variables of the MMPI MMPI_1 MMPI_2 IAH SBS Those who score high on Johnny Pissoff also admit to aggressing against gays and are disgusted by homosexuality. MMPI_1 explains ( )/2 = 9% of the variance in the homonegativity variables. Those who score high on Feminine Hypomania also score low on the IAH. MMPI_2 explains ( )/2 = 3.9% of the variance in the homonegativity variables. Collectively, the two MMPI canonical variates explain 9% + 3.9% = 12.9% of the variance in the homonegativity variables.

5 Correlations Between the MMPI and the Canonical Variables of the Homonegativity Homoneg_1 Homoneg_2 MA MF PD K Those who score high on Aggressive Homophobia tend to be manic, hostile, stereotypically masculine, and unusually frank. Those who score high on Equal Opportunity Bully tend to be manic and feminine. Canonical Variable Number The CANCORR Procedure Canonical Redundancy Analysis Standardized Variance of the Homonegativity Explained by Their Own Proportion Cumulative Proportion Canonical R-Square The Opposite Proportion Cumulative Proportion We computed these proportions earlier as mean squared loadings. Canonical Variable Number Standardized Variance of the MMPI Explained by Their Own Proportion Cumulative Proportion Canonical R-Square The Opposite Proportion Cumulative Proportion Notice that the second canonical variate of the MMPI captures more of the variance in the MMPI variables than does the first canonical variate of the MMPI. While the first pair of canonical variates always produces the largest canonical correlation, it is not true that each of the first canonical variates captures more of the variance in their own variables than do the second canonical variates. Here, the first weighted linear combination of the MMPI is constructed from that variance in the MMPI that is best related to the first linear combination of the Homonegativity, but that variance of the first MMPI is less than that of the second MMPI.

6 The CANCORR Procedure Canonical Redundancy Analysis Squared Multiple Correlations Between the Homonegativity and the First M Canonical Variables of the MMPI M 1 2 IAH SBS The squared correlation between IAH and MMPI_1 is.039. As shown below, this falls short of statistical significance. The R 2 for predicting IAH from MMPI_1 and MMPI_2 is.116. As shown below, this is significant. The squared correlation between SBS and MMPI_1 is.142. This is significant. The R 2 for predicting SBS from MMPI_1 and MMPI_2 is.143. This is significant. Below I reproduce these values with Proc Reg. Squared Multiple Correlations Between the MMPI and the First M of the Homonegativity M 1 2 MA MF PD K

7 proc corr; var Homoneg_1 Homoneg_2 MMPI_1 MMPI_2; run; The CORR Procedure 4 Variables: Homoneg_1 Homoneg_2 MMPI_1 MMPI_2 Variable Simple Statistics N Mean Std Dev Sum Minimum Maximum Homoneg_ Homoneg_ MMPI_ MMPI_ Pearson Correlation Coefficients, N = 80 Prob > r under H0: Rho=0 Homoneg_1 Homoneg_2 MMPI_1 MMPI_2 Homoneg_ Homoneg_ MMPI_ MMPI_ Notice that Homoneg_1 is absolutely independent of Homoneg_2 and that MMPI_1 is absolutely independent of MMPI_2. The highlighted values are the two canonical correlations, identical to the values produced by Proc Cancorr.

8 Reproducing the Squared Multiple Correlations Between the Homonegativity and the First M of the MMPI proc reg; model IAH = MMPI_1 MMPI_2 / scorr1; run; quit; Variable DF Parameter Estimate Root MSE R-Square Parameter Estimates Standard Error t Value Pr > t Squared Semi-partial Corr Type I Intercept < MMPI_ MMPI_ proc reg; model SBS = MMPI_1 MMPI_2 / scorr1; run; quit; Variable DF Parameter Estimate Root MSE R-Square Parameter Estimates Standard Error t Value Pr > t Squared Semi-partial Corr Type I Intercept < MMPI_ MMPI_ We saw these same values earlier, in the extensive output from Proc Cancorr.