Measurement Invariance of Expectancy-Value Questionnaire in Physical Education

Purpose
Measurement invariance represents the equivalency of the factorial measurement and its underlying latent structure across different groups (Byrne, 2006). It is considered an important step to ensure that an instrument can be used for cross-sectional and longitudinal research (Vandenberg & Lance, 2000). The purpose of this study was to examine measurement invariance of the Expectancy-Value Questionnaire (EVQ; Eccles & Wigfield, 1995) in the domain of physical education across elementary and middle school students.
Methods
EVQ measures student expectancy beliefs and subjective values of the content. It is a 5-point likert scale with 5 items measuring expectancy beliefs and 6 measuring subjective values. Participants included 811 students (3rd-5th grades) from 13 elementary and 903 (6th-8th grades) from 13 middle schools. The schools were sampled from a large suburban school district representing the 100 largest public school systems across the country. Students completed the EVQ in their physical education classes.
Analysis/Results
Testing for measurement invariance primarily includes a series of hierarchical steps (Byne, 2006) to examine: (a) baseline models for each group, (b) configural invariance, (c) metric invariance, (d) factor variance invariance, and (e) factor covariance invariance. Based on covariance structures, confirmatory factor analyses were conducted for each group. Results showed satisfactory data-model fit for both elementary (S-B χ²=123.54, df=40, p<.05, CFI=.96, SRMR=.04, RMSEA=.05, CI₉₀: .04, .06) and middle school groups (S-B χ²=113.19, df=40, p<.05, CFI=.97, SRMR=.03, RMSEA=.05, CI₉₀: .04, .06). An equality test of covariance matrices between the two indicated a nonequivalence (p<.05). Multi-group structural equation models examining configural, metric, and factor-variance invariance produced good data-model fit according to Hu and Bentler’s (1999) criteria. However, invariant factor covariance model resulted in a poor data-model fit (S-B χ²=329.07, df=92, p<.05, CFI=.95, SRMR=.09, RMSEA=.04, CI₉₀: .03, .04) thus the equivalence constraint of factor covariance was released. Although model comparisons yielded significant ΔS-B χ² values (p<.05) among the first three multi-group models, ΔCFI values among these models were less or equal to -.01, therefore the null hypothesis of invariance should not be rejected (Cheung & Rensvold, 2002).
Conclusions
The results indicate that the factor covariance of physical education expectancy and value differs between elementary and middle school students. However, researchers normally examined these factors independently, rarely examined their relationship (Wigfield & Eccles, 2000). Hence, the findings of this study support that EVQ possesses equivalent factorial measurement and its underlying latent structure across elementary and middle school students.