Choosing the right parameterization for latent profile analyses using the TidyLPA package

I'm struggling choosing the right parameterization for the LPA i want to run (using the TidyLPA package). I've been reading, but I somehow stay confused about the right way to go and want to prevent going into the wrong direction. I'm relatively new to the field, so please bear with me if i'm asking a silly question..

I read in the description of the TidyLPA package ( ), the following information:

Model specification

In addition to the number of profiles (specified with the n_profiles argument), the model can be specified in terms of whether and how the variable variances and covariances are estimated.

The models are specified by passing arguments to the variance and covariance arguments. The possible values for these arguments are:

variances: “equal” and “varying” covariances: “varying”, “equal”, and “zero” If no values are specified for these, then the variances are constrained to be equal across classes, and covariances are fixed to 0 (conditional independence of the indicators).

These arguments allow for four models to be specified:

Equal variances and covariances fixed to 0 (Model 1)
Varying variances and covariances fixed to 0 (Model 2)
Equal variances and equal covariances (Model 3)
Varying variances and varying covariances (Model 6)

A little bit of background of my research (social science). Running analyses with:

  • 3 indicators
  • That are expected to be correlated (based on literature)
  • Cannot make a firm (theoretical) statement about the distribution of the indicators

So my questions are:

  1. Can we set a parameterization a priori (I would like that)? And if so, what would be the best way to go (variance = equal, covariance = equal?)? Do we need to do some testing beforehand?
  2. Or would it be better to run models with different parameterizations and choosing the right model (and thus, "ignoring" the parameterization beforehand?).

I sincerely hope I'm at the right and prevent me going into the wrong direction!

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