EFFECTS OF ITEM FORMATS ON CONSTRUCT VALIDITY OF PISA-LIKED MEASUREMENT MODELS OF MATHEMATICAL COMPETENCIES: APPLICATION OF METHOD EFFECTS EXAMINATION BY CTCU AND CTCM
Abstract:
The purposes of this descriptive research were to 1) investigate fit indices (included chi-square/df, GFI, AGFI, CFI, RFI SRMR and RMSEA) of The general measurement model of mathematical competencies (GENE model), The measurement model of mathematical competencies by Correlated Trait Factors and Correlated Uniquenesses technique (CTCU model), The measurement model of mathematical competencies by Correlated Trait Factors and Correlated Method Factors technique (CTCM model). 2) to analyze effects of item formats on construct validity of the measurement models of mathematical competencies. The research sample consisted of 549 Bangkok ninth grade students. Variables of GENE model consisted of 3 latent variables: formulating situations mathematically, employing mathematical concepts, and interpreting mathematical outcomes. These latent variables were measured by 27 observed variables. The research instruments were the 3 Pisa-liked tests of mathematical competencies which each items of test used the identical question, but used different answer formats. Data were analyzed by confirmatory factor analysis. The conclusions were as follows: 1. The adjusted GENE model fit the empirical data (chi-square = 281.98, p = 0.752, df = 299, GFI = 0.96, AGFI = 0.95, CFI = 1.00, RFI = 0.98, SRMR = 0.031, RMSEA = 0.000). The CTCU model was not fit to the empirical data (chi-square = 1213.06, df = 294, GFI = 0.86, AGFI = 0.82, CFI = 0.95, RFI = 0.92, SRMR = 0.058, RMSEA = 0.076). The CTCM model was not fit to the empirical data (chi-square = 1072.95, df = 291, GFI = 0.87, AGFI = 0.84, CFI = 0.96, RFI = 0.93, SRMR = 0.049, RMSEA = 0.070). 2. The comparison fit indices between GENE model (chi-square = 1456.41, p = 0.00, df = 306, GFI = 0.84, AGFI = 0.81, CFI = 0.92, RFI = 0.94, SRMR = 0.060, RMSEA = 0.080) and CTCU model found that CTCU model fit the empirical data more than GENE model at the .01 significant level, and all of correlation coefficient of error term form identical item formats were less value. It showed that effects of item formats were not occurred. The comparison fit indices between GENE model and CTCM model found that CTCM model fit the empirical data more than GENE model at the .01 significant level, and all factor loadings of item formats less than factor loadings of mathematical competencies. It showed that effects of item formats were not occurred.