A comparison of latent growth models for constructs measured by multiple indicators
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Latent growth modeling (LGM) of composites of multiple items (for example, means or sums of items) has been frequently used to analyze the growth of latent constructs. However, composites are only equivalent to latent constructs if the items’ factor loadings are equal to one and there is no measurement error (Bollen & Lennox, 1991). In this study, the adequacy of using univariate LGM to model composites of multiple items, as well three other alternative methods were evaluated through a Monte Carlo simulation study. The four methods evaluated in this study were the univariate LGM, the univariate LGM with fixed error variances, the univariate LGM with the correction for attenuation, and the curve-of-factors model (McArdle, 1988; Tisak and Meredith, 1990). This simulation study manipulated the number of items per construct, the number of measurement times, the sample size, the reliability of the composites, the invariance of item parameters, and whether the items were essentially tau-equivalent or essentially congeneric. One thousand datasets were simulated for each of the conditions. The results indicate that using univariate LGM with composites of multiple items only produces unbiased parameter estimates and standard errors if the items are essentially tau-equivalent. The univariate LGM with fixed error variances performed identically to the univariate LGM. The univariate LGM with the correction for attenuation produced unbiased parameter estimates when the items were essentially tauequivalent, but produced negatively biased estimates of standard errors. The curve-of-factors model was found to be the most appropriate method to analyze the growth of latent constructs measured by multiple items. The curve-of-factors model was able to provide unbiased parameter estimates and standard errors under all conditions evaluated in this study. However, with sample sizes of 100 or 200, a large percentage of chi-square statistics were positively biased and the fit indices indicated inadequate model fit. This study’s recommendation is that the curve-of-factors model should be preferred to analyze the growth of latent variables measured by multiple items, but the use of sample sizes larger than 200 is strongly recommended to help ensure that adequate fit statistics and fit indices are obtained for appropriate models.