Performance of Latent Growth Curve Models with Binary Variables

ABSTRACT

A Monte Carlo simulation examined estimation difficulties and parameter and standard error bias for mean and variance estimates of binary latent growth curve models using mean and variance adjusted diagonally weighted least squares (WLSMV) and robust maximum likelihood (MLR). Small and medium effects of slope means and variances for longitudinal designs with three, five, and seven time points and sample sizes of 100, 200, 500, and 1000 were examined. Results indicated that more time points, larger sample size, and more symmetric distributions were associated with fewer improper solutions, lower parameter and standard error bias, better Type I error rates, and better coverage. WLSMV and MLR performed acceptably with at least five time points and sample size of 500, but WLSMV performance depended on the model specification. Three time points and 100 cases appeared to be too few for accurate estimation of binary latent growth curve models for any method.

KEYWORDS:

• Latent growth curve
• binary
• categorical
• longitudinal
• simulation

Acknowledgement

We appreciate helpful comments from Todd Bodner, Joel Steele, Liu-Qin Yang and the Portland State University Stats Lunch group, Mariska Barendse and participants at the 2018 Modern Modeling Methods conference, as well as financial support from Portland State University. We are grateful to Katherine A. Werth and Sage Fuentes for assistance with assembling the tables.

Notes

¹ Beginning with version 4.2, Mplus allows the user to request ML estimates scaled as probit estimates.

² Muthén and Asparouhov (2002) suggested setting all thresholds equal to 0 and setting only the first scale factor equal to 1. This specification is equivalent to the one used here, because of the dependence between y* location and variance in the binary case.

³ There are two other model specifications that are equivalent to this one: (a) setting the first threshold equal to 0 and freely estimating all remaining threshold values, while setting the first scale factor to 1 and setting the remaining scale factors equal to one another, or (b) setting the first threshold equal to 0, setting the remaining thresholds equal to one another, while setting the first scale factor equal to 1 and setting all remaining scale factors equal.

⁴ Another equivalent specification to the specification in Example 6.4 is to freely estimate the factor mean, set the first threshold equal to 0, freely estimate the remaining thresholds, set the first scale factor equal to 1, and freely estimate the remaining scale factors.

⁵ Population covariance matrices are available from the first author upon request.