Perfectionism and Asian Canadians

PERFECTIONISM AND ASIAN CANADIANS 1

Appendix

Measurement Invariance of Perfectionism

A multiple group confirmatory factor analysis was conducted to test the cross-cultural invariance of the perfectionism measure using Mplus 6.02 with the full information maximum likelihood robust estimator (Muthén & Muthén, 2010). Along with the chi-square statistic, the following goodness- of-fit indices were used to evaluate the model: comparative fit index (CFI), Tucker–Lewis index (TLI), root-mean-square error of approximation (RMSEA), and standardized root-mean-square residual (SRMR). Values between .90 and .94 for the CFI and TLI indicate acceptable fit, whereas values of .95 and higher indicate relatively good fit. Values smaller than .08 for the RMSEA and SRMR indicate acceptable fit, whereas values smaller than .05 indicate close fit. As recommended by Vandenberg and Lance (2000), either a substantial change in CFI (CFI [mt] −.01) or a significant change in the chi square (p [lt] .01) was a condition to reject the null hypothesis of factorial invariance.

The first model tested a two-factor model with the same fixed and freed parameters in each group to estimate the configural invariance of the model. This model yielded an acceptable fit: 2 = 317.60, Satorra–Bentler (SB)2 = 284.25, df = 68, p [lt] .001, CFI = .92, TLI = .90, RMSEA = .10, SRMR = . 065. The average standardized factor loadings of self-oriented perfectionism (.76 in European Canadians and .75 in Asian Canadians) and socially prescribed perfectionism (.73 in European Canadians and .71 in Asian Canadians) were all acceptable. Subsequent models provided evidence for the invariance of factor loadings (SB2 = 5.20, df = 8, p [mt] .05, CFI = -.001), factors’ variances and covariance (SB2 = 1.09, df = 3, p [mt] .05, CFI [lt] −.001), and items’ residual (SB2 = 14.11, df = 10, p [mt] .05, CFI [lt] −.001). Testing the invariance of the intercepts (SB2 = 39.18, df = 10, p [lt] .05, CFI = −.011) revealed that the intercept of Item 8 (i.e., “My family expects me to me perfect”) could be considered noninvariant across samples. After relaxing this equality constraint, the scalar invariance of nine out of 10 items was assumed (SB2 = 17.64, df = 9, p [mt] .05, CFI = -.006), thus providing sufficient evidence of the most stringent form of measurement invariance for the two dimensions of perfectionism. A final model indicated that the latent means of SOP ( = 0.22, ϕ = 1.75, p [lt] .05, Cohen’s d = .13) and SPP ( = .33, ϕ = 1.24, p [lt] .01, Cohen’s d = .27) were significantly higher among Asian Canadians than European Canadians.

Measurement Model of Academic Satisfaction

The academic satisfaction scale contains five positively worded items and three negatively worded items. Reversed items are generally useful to reduce lenient responding. Nevertheless, reversed items create challenge for the unidimensionality of latent variables because positively and negatively worded items tend to load on separate factors despite the absence of substantial justification for a bidimensional factor structure (e.g., Spector, Van Katwyk, Brannick, & Chen, 1997). In this study, we explored the tenability of both the unidimensional and bidimensional factor structure of the PERFECTIONISM AND ASIAN CANADIANS 2 academic satisfaction scale. Results of the unidimensional model (without equality constraints across groups) failed to provide unambiguous evidence for the tenability of this factor model: SB2 = 219.81, df = 40, p [lt] .001, CFI = .906, TLI = .868, RMSEA = .11, SRMR = .060. Modification indices suggested that the addition of correlated uniqueness for the negatively worded items would significantly improve the model fit. This evidence thus pointed out the necessity of considering a bidimensional factor structure. Results of the bidimensional model (without equality constraints across groups) provided more convincing evidence for the goodness of fit of this model: SB2 = 98.29, df = 38, p [lt] .001, CFI = .968, TLI = .953, RMSEA = .068, SRMR = .033. The average standardized factor loadings of the positively worded items (.75 in European Canadians and .74 in Asian Canadians) and the negatively worded items (.70 in European Canadians and .72 in Asian Canadians) were all acceptable and the interfactor correlation suggested a moderately high level of overlap between the two dimensions of academic satisfaction (.78 in European Canadians and .73 in Asian Canadians). Further analyses provided evidence for the invariance of loadings (SB2 = 7.84, df = 6, p [mt] .05, CFI = -.001), variances/covariances (SB2 = 2.56, df = 3, p [mt] .05, CFI [lt] -.001), uniquenesses (SB2 = 8.31, df = 8, p [mt] .05, CFI = +.001), and intercepts (SB2 = 13.04, df = 8, p [mt] .05, CFI = -.003) across European Canadians and Asian Canadians. Overall, this bidimensional model of academic satisfaction was retained in subsequent analyses because it provided an invariably good fit to the data in both samples of European and Asian Canadians.

Multiple Group Latent Moderation Structural Models

Klein and Moosbrugger (2000). The approach described in the MPlus user’s manual cannot readily accommodate multiple group models. The online technical support service for Mplus was consulted in order to generate input codes that would enable the estimation of multiple group LMS models. A publicly available syntax code posted by Linda Muthén on the online Mplus discussion forum enabled us to properly estimate our multiple group LMS (http://www.statmodel.com/discussion/messages/11/7276.html?1305212732).

We further expanded these input codes in order to allow us to add cross-group equality constraints on the SOP, SPP, and SOP x SPP effects. Our annotated input codes for a model without cross-group equality constraints (SOP, SPP, and SOP x SPP freely estimated in each group) are reported in Table A1. Our annotated input codes for a model with cross-group equality constraints (SOP, SPP, and SOP x SPP constrained to equality across groups) are reported in Table A2.

Complementary Analyses of Reversed Academic Dissatisfaction

Our multiple group LMS models of academic satisfaction contained two outcomes: academic satisfaction and reversed academic dissatisfaction. The manuscript reported the main effects of SOP and SPP for both academic satisfaction and reversed academic dissatisfaction. The results were very similar PERFECTIONISM AND ASIAN CANADIANS 3 for both outcomes and, therefore, the manuscript did not present the predicted values of reversed academic dissatisfaction. It is important to note that the interpretation (in light of the four hypotheses of the 2 x 2 model) was identical for both academic satisfaction and reversed academic dissatisfaction. Nonetheless, the predicted values of reversed academic dissatisfaction of the four subtypes of perfectionism are presented in Table A3 for European Canadians and Asian Canadians.

Table A1

MPLUS Input Codes for the Multiple Group LMS model with the SOP, SPP, and SOP x SPP Effects Freely Estimated in Each Group

DATA: FILE IS "C:\Users\Desktop\MPLUS\AsianCan\Fall2010_AsianCan.dat"; VARIABLE: NAMES ARE id_code gpa mod perf1 perf2 perf3 perf4 perf5 perf6 perf7 perf8 perf9 perf10 acasat1 acasat2 acasat3 acasat4r acasat5r acasat6 acasat7 acasat8r gpar; USEVARIABLES ARE gpar cperf1 cperf2 cperf3 cperf4 cperf5 cperf6 cperf7 cperf8 cperf9 cperf10;

!GPA from 1(F) to 9(A+). !Centered scores of perfectionism.

MISSING ARE ALL (999); CLASSES = C(2); !Class 1 = European Canadians; Class 2 = Asian Canadians KNOWNCLASS IS C (mod = 1 mod = 2);

! The multiple group latent moderation structural model is estimated as a mixture model. ! The KNOWNCLASS code is the trick used to conduct a multiple group analysis.

DEFINE: cperf1 = perf1 - 4.013; !All variables are centered to facilitate simple slope analyses cperf2 = perf2 - 3.192; cperf3 = perf3 - 3.911; cperf4 = perf4 - 2.885; cperf5 = perf5 - 4.518; cperf6 = perf6 - 3.129; cperf7 = perf7 - 4.924; cperf8 = perf8 - 3.173; cperf9 = perf9 - 4.516; cperf10 = perf10 - 2.769;

ANALYSIS: TYPE IS MIXTURE RANDOM; !Random effects allow the parameter to vary across the two groups PERFECTIONISM AND ASIAN CANADIANS 4

ALGORITH = INTEGRATION; !Random effects require the data integration algorithm. ITERATIONS = 1000; CONVERGENCE = 0.00005; COVERAGE = 0.10; Table 1 to be continued

Table A1

Continued

OUTPUT: SAMPSTAT MODINDICES RESIDUAL STANDARDIZED CINTERVAL TECH1 TECH3; !Tech 3 is needed to obtain the ACOV matrix to estimate simple slopes !See http://www.quantpsy.org/interact/mlr2.htm

! The loadings, residuals, intercepts, variances, and covariances are constrained to equality across groups because they are not written in the class1 and class2 model. MODEL: %OVERALL% SOP BY cperf1@1 cperf3 cperf5 cperf7 cperf9; SPP BY cperf2@1 cperf4 cperf6 cperf8 cperf10; GRADE BY gpar@1; GRADE@1; GRADE ON SOP SPP; !Main effects of SOP and SPP SOPxSPP | SOP XWITH SPP; GRADE on SOPxSPP; !Interactive effect of SOP X SPP

! In this model, SOP, SPP, and SOP x SPP are freely estimated in each group because they are written in both the class1 and class2 models.

%C#1% !Class 1 = European Canadians GRADE on SOP; GRADE ON SPP; GRADE on SOPxSPP;

%C#2% !Class 2 = Asian Canadians GRADE on SOP; GRADE ON SPP; GRADE on SOPxSPP; Note. Our personal notes were added in bold characters after the symbol !. PERFECTIONISM AND ASIAN CANADIANS 5

Table A2

MPLUS Input Codes for the Multiple Group LMS model with the SOP, SPP, and SOP x SPP Effects Constrained to Equality Across Groups

! The first part of the input codes is identical in Table 1 and Table 2.

! The loadings, residuals, intercepts, variances, and covariances are constrained to equality across groups because they are not written in the class1 and class2 model (as per Table 1).

! In this model, SOP, SPP, and SOP x SPP are now constrained to equality across groups because they are written in the overall model rather than in both the class1 and class2 models (which are no longer included in the input codes).

MODEL: %OVERALL% SOP BY cperf1@1 cperf3 cperf5 cperf7 cperf9; SPP BY cperf2@1 cperf4 cperf6 cperf8 cperf10; GRADE BY gpar@1; GRADE@1; GRADE ON SOP SPP; !Main effects of SOP and SPP SOPxSPP | SOP XWITH SPP; GRADE on SOPxSPP; !Interactive effect of SOP X SPP

Note. Our personal notes were added in bold characters after the symbol !. PERFECTIONISM AND ASIAN CANADIANS 6

Table A3

Predicted Values of Reversed Academic Dissatisfaction for the Four Subtypes of Perfectionism in Asian Canadian and European Canadian Samples

Subtypes Asian Canadians European Canadians Pure SOP 0.51 1.05 Mixed perfectionism 0.26 0.17 Non perfectionism -0.26 0.27 Pure SPP -0.51 -0.72