I have three questions regarding DSEM analyses and our data. We have 228 participants who filled in questionnaires 5 times a day, with random time intervals, for 11 days. So max 55 measures a day. We want to explore the reciprocal lagged associations between variables X,Y , Z.
Question 1: X was always filled in, Y and Z were only filled in when the participants were not alone, this was the case in 64% of all measurements. Is this kind of non-random missing an issue in DSEM?
Question 2: We would like to include within-person interaction terms with another variable (variable W) in our DSEM analyses, but there are 2 problems there. 1. We are not allowed to make product terms with the lagged variables. 2. We cannot add a lagged moderator (variable W) when there is no autoregressive path for this variable in the model. Is this in any way possible? If not, will this option be included in a future version of Mplus?
Question 3: Variables Y and Z have rather skewed distributions. Are there any recommendations about the max skewness of the data within the DSEM framework?
I have a question regarding the specification of within-person interaction terms in DSEM. I want to examine whether a continuous variable W (t-1) moderates the temporal association between a binary variable X (t-1) and binary outcome variable Y(t). I am not using any random effects given that there are only few individuals. I have specified the interaction term using the define command. However, I am unsure to whether I should fix the autocorrelation of the interaction term “inter on inter&1@0!”, given that the autocorrelation of X and W (that make up the interaction) are already in the model , or I should let this term be estimated freely (as in the syntax below)? Many thanks in advance!
%WITHIN% Y on Y&1;! carryover Y X on X&1;! carryover X W on W&1;! carryover W inter on inter&1! carryover interaction, Y on X&1;! spillover X Y on W&1;! spillover W Y on inter&1! Spillover interaction-term, the effect we are interested in.
I would recommend exploring the interaction effect (especially if you don't have missing data) using the observed centering. It would require some more data manipulation ahead of time - center X and W for each cluster then form the interaction term - observed centering for the interaction. Then shift the interaction by 1 period (use the cluster average for the first period) and treat it as an actual covariate (not a lagged dependent variable). You may find some useful information here
I would like to estimate a time-series model with DSEM including two time-varying covariates as within-variables. As I am using the tinterval option, I am working around the missings on my within-level predictor variables by including a fake autoregression of the predictors:
%within%: Y on pred1 pred2; pred1 on pred1&1@0; pred2 on pred2&1@0;
I wondered whether in this specification the covariance between my two predictors is estimated and accounted for in the regression of Y on pred1 and pred2 ? Or is it constrained to zero (as my predictors become dependent variables by inclusion of the fake autoregressive effects and I have not explicitly specified them to be correlated)? Do I need to specify "pred1 with pred2" in the model in order to account for the predictors' correlation?
thank you for your quick answer. I noticed that my question might not have been precise enough...
My predictor variables are actually dummy variables (which is why I do not want to freely estimate their AR effect as they happen to be quite stable over some time periods). The loading parameters of my dummy predictors are random effects that are allowed to covary on the between level. In this way, the correlation is somehow already included in the model.
1) Do you think I still need to include pred1 with pred2 ?
2) And as I think about it now, does it make any sense at all to estimate this model with the tinterval option? When my dummy predictors are treated as dependent variables, they are probably augmented for the inserted missing time points in the MCMC estimation using information such as their mean and variance? That would not make any sense for my dummy variables. Do you have any idea how I can include my dummy predictors while still making use of the tinterval option?
If pred1 and pred2 are stable - perhaps they shouldn't be considered missing, for example if you know when they change. Regardless pred1 on pred1&1@0; is not a good idea because it makes them random rather than stable. It is a tricky situation also because the dummies are highly correlated (thetrachoric correlation of -1).
I think the best possible solution would be some very specialized imputation for these covariates that accommodates all the information. You can also consider, modeling the covariates as categorical, model the between part as well, abandoning tinterval, switching to RDSEM which is safer when it comes to missing covariates. These methods all have merits and issues and it is hard for me to give a single method without thoroughly looking at your application. These two papers might help.
To address your point 2) however ... with that model you have correctly identified the problem ... the missing values will be imputed at random from the mean which is not good in your case. The imputed values will not be stable, will not be binary, and will not behave like dummies, i.e., pred1 + pred2 will not be 0 or 1.