I'm interested in running a multiple group latent growth model to test for invariance in growth parameters across two groups, by constraining particular parameters to be equal across groups (vs freely estimating) and doing LL chi-square model comparisons.

My groups are a little awkward because they're actually two independent studies. Both studies measured a variable across time in adolescence; the variables have been harmonized across studies and the range in ages/birth cohorts is relatively similar. However, one study had 5 waves of data collection and the other study has 3 waves. Say I wanted to know if the mean and variance of the intercept was invariant across studies.

From what I understand, a multiple group model with parameters constrained across groups is not possible to estimate using traditional FIML unless both groups have complete covariance structures. Males and females cannot be modeled in a multiple group CFA if all males happen to be missing values for one or more of the CFA manifest indicators. From what I understand, the logic extends to growth factors. While I'm not using groups from one study, rather im treating two independent studies as the groups in order to test for invariance of parameter estimates. If I run this model in Mplus, for example, where I specify a multiple group LGM with five time variables, the model fails to run because the study with three waves is being treated as if there is complete missing data on the 4th and 5th wave variables (i.e. incomplete covariance structure). This is the case even when I use age as the time metric (creating individually varying definition variables and fixing slope factor loadings to each individuals age at respective wave). Similar problem occurs if I specify a three time point multiple group LGM. One fix in Mplus is to use a pattern mixture procedure (see Kim et al., Widaman et al, below) by specifying a growth mixture model with known classes based on the grouping variable (in my case study). From what I understand, this is a fix because the mixture modeling estimation procedure does not require complete covariance structure as each study is assumed to be a derivative of one overall mixture. Parameters can be constrained across latent classes, covariance structures are allowed to be class (group) specific, allowing for LL model comparisons. According to Kim et al's simulation, running a multiple group LGM when both groups have complete covariance structure produces equivalent results when conducted through a pattern mixture procedure. Widaman et al. describe other work arounds not focused on mixture modeling procedures.

Does anyone know 1) if this is an issue with the FIML estimation procedure used by openmx and if so, 2.) are there recommended solutions?

thanks,

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3864537/

https://www.tandfonline.com/doi/full/10.1080/10705511.2013.797819

It should not be an issue, provided that the group with 3 waves of assessment has a 3x3 expected covariance matrix and an order-3 mean vector, and the group with 5 waves has a 5x5 expected covariance matrix and an order-5 mean vector (I'm assuming here that participants were sampled independently in both studies). In other words, don't construct the 3-wave group with a dataset that has columns full of

`NA`

s for waves 4 and 5 and treat all 5 waves as endogenous variables of the model. Obviously, you won't be able to test for factorial invariance for anything more than a first-degree (intercept and slope only) growth curve, since anything higher would be degenerate in the 3-wave group. And, if you allow a different residual variance at each wave, then obviously you won't be able to test for invariance w/r/t the wave 4 & 5 residual variances. How complicated is your model going to be, anyhow?Although you could do a growth mixture model in OpenMx if you wanted to, it shouldn't be necessary. That approach looks to be a workaround for a peculiarity of MPlus.