

Integration Dimensions Question 

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I have a two level model with five random slopes S1S5 (LV on LV). At level two, all five are loading on a single factor: Q. All L2 residualvariances for S1S5 are fixed to 0.0. It seems that there should be a single dimension of integration at level2. Mplus is trying to do a five dimensional integration at level2. What determines the number of integration dimensions? 


I think this is the model that has also been sent to Mplus Support. As we mentioned there it should be reformulated into a statistically equivalent model that doesn't not involve "g by s" with zero s residual variances (g has variance zero also in what was sent to us). In general, some latent variables with (residual) variances fixed 0 actually lead to numerical integration in Mplus. For example when the latent variable is regressed on other variables as it is here. Also, if the mean of the latent variable is free we cannot use just 1 integration point because the mean won't be estimated then. Mplus has many special situations that can be handled so that they do not lead to numerical integration, but some situations are too complex. Generally models with 0 variance latent variables can be reparameterized to avoid these components. In this model the latent variables s1s5 can be removed because they are 0, so is g. 

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