Hello, We are collaborating on a project (we met at your workshops), and have some basic questions on GMM. We have BMI measurements at 10 unequal time points (ages 13, 14, 15, 16, 21, 27, 29, 32, 36, 42). Our end goal is to examine different growth trajectories of BMI using GMM. We decided to start with LGM. Is this correct? Here are our steps so far: 1. Basic LGM resulted in poor fit I S | bmi1@0 bmi2@1 bmi3@2 bmi4@3 bmi5@8 bmi6@14 bmi7@16 bmi8@19 bmi9@23 bmi10@29; 2. We freed various slope parameters to estimate, and still had poor fit 3. We decided to try a 3-part piecewise LGM model, and this was a good fit I1 S1 | bmi1@0 bmi2@1 bmi3@2 bmi4@3; I2 S2 | bmi5@8 bmi6@14 bmi7@16; I3 S3 | bmi8@19 bmi9@23 bmi10@29; We have significant amount of variance for the slopes and intercepts, so we assume that GMM may be justified. Is that correct? Thank you, Trynke Hoekstra and Celestina Barbosa-Leiker.
You do not have your piecewise growth model specified correctly. You should have only one intercept growth factor and the time scores should be specified for all outcomes with the time scores for each piece reflecting the part of the model that piece represents. See Example 6.11.
Significant variance for the growth factors is a necessary but not sufficient condition for GMM. The variance does not however imply unobserved heterogeneity.