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Multiple-Indicator Multilevel Growth Model: A Solution to Multiple Methodological Challenges in Longitudinal Studies

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Abstract

This paper described the versatility of the multiple-indicator multilevel (MIML) model in helping to resolve four common challenges in studying growth using longitudinal data. These challenges are (1) how to deal with changes in measurement over time and investigate temporal measurement invariance, (2) how to model residual dependence due to the nested nature of longitudinal data, (3) how to model observed trajectories that do not follow well-known functions commonly discussed in the methodology literature (e.g., a linear or quadratic curve), and (4) how to decide which predictors are relatively more important in explaining individuals’ change over time. With an example of psychological well-being from the Wisconsin Longitudinal Study, we illustrated how the four methodological challenges can be resolved using the 3-phase MIML procedures and the Pratt’s importance measures.

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Notes

  1. Other growth factors can also be modeled. For example, with sufficient time points, a higher order polynomial curve (such as a quadratic growth factor) can be incorporated to capture the non-linear trend in the observed trajectories.

  2. A minimum of four time points is recommended for growth models for two reasons. It is inflexible to make the model identify enough parameters in the growth model with less than four time points. Also, data with four time points give more power. See Muthén (1999) at http://www.statmodel.com/discussion/messages/14/20.html#POST16727.

  3. Readers should not confuse “normative” transformation with “normalized” transformation. Normative transformation is a linear transformation; it standardizes the raw scores into Z scores by subtracting the raw score from the mean then dividing by the standard deviation. Normalized transformation, on the other hand, stretches a distribution to make it nearly normal and spreads the data points in both tails of distribution, which is usually a non-linear transformation (Gorsuch 1983, p. 299). The normalized scores will affect factor analysis because the overall distribution of transformed scores will be different from that of the original raw scores. Therefore, normalized transformation is not recommended as a solution to the problem of changes in the observed score scaling.

  4. Note that missing data may lead to the estimation of the beta-weights using the ON command and simple correlations using the WITH command being based on different subjects in Mplus. This problem could distort the calculation of the Pratt’s measures; i.e., the sum of the Pratt’s measures would not add up to one. Instead of using the WITH command, one possible solution is to save the scores of the growth factors I and S and use the simple bivariate correlations obtained in SPSS. To save the scores of the growth factors I and S in Mplus, use the SAVEDATA and SAVE = FSCRES commands for the OUTPUT.

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Authors and Affiliations

  1. Department of ECPS, University of British Columbia, 2125 Main Mall, Vancouver, BC, V6T 1Z4, Canada

    Amery D. Wu, Yan Liu, Anne M. Gadermann & Bruno D. Zumbo

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  1. Amery D. Wu
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  2. Yan Liu
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  3. Anne M. Gadermann
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  4. Bruno D. Zumbo
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Correspondence to Bruno D. Zumbo.

Appendix: Mplus syntax for 3-level MIML growth model

Appendix: Mplus syntax for 3-level MIML growth model

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Wu, A.D., Liu, Y., Gadermann, A.M. et al. Multiple-Indicator Multilevel Growth Model: A Solution to Multiple Methodological Challenges in Longitudinal Studies. Soc Indic Res 97, 123–142 (2010). https://doi.org/10.1007/s11205-009-9496-8

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