i have a question concerning fixed parameters within formative (or causal) measurement models (FMM) like SES. my aim is to perform a SEM with exogenous FMM and endogen ordinal reflective measurement model (RMM). the model fit of WRMR = .907 looks appropriate, and comparable parameter estimates structure were obtained by a PLS-model. my problem for now is the following: apparantly the FMM regression weights are very sensitive due to the fixing value. the following model provide a value of .01 as a nice approximation.
is there a rule-of-thumb for the fixing value within FMMs? here is the corresponding model:
categorical: pride1 pride2 pride3; model: repu by; repu on firstname.lastname@example.org repu2 repu3; repu@0; pride by pride1 pride 2 pride3; pride on repu;
linda, thank you for the immediate reply. i have an additional question concerning the 'statistical fit' of formative indicators with a potential regard to scale purification. let's assume one has no access to PLS (within a theory 'building'-approach), then there would be no guidance for setting the metric via a discrete indicator-weight (in order to obtain trustful t-values).
is there an alternative to the PLS-pre-'testing' respectively would you denote this procedure as appropriate?
Hi Linda and/or Bengt, A student and I are trying to fit our first causal indicator measurement model. From the syntax on slide 246 of the Mplus Short Courses Topic 1 Handout, it looks to us as if there is no disturbance term for f - your formative construct. Are we interpreting that correctly? If so, this would seem to us to be more akin to what Bollen would call a composite indicator model than a causal indicator model and we would be interested in guidance regarding syntax we should use to give the construct a disturbance term? Thanks very much!
Yes, the formative model we give the specification for is what Bollen-Bauldry (2011) Psych Meth call composite indicators. What they refer to as causal indicators can simply be specified as a MIMIC-type model; no special syntax needed. See their Figure 4, where the causal indicators behave like regular covariates - to me, it is more of a conceptual distinction.
Bollen and Bauldry suggest on p.279 (or p.14) looking at the indicator's unique validity variance, which they define as the difference between the r-square for eta with all causal indicators and r-square for eta, less causal variable x_i.
Mplus provides r-square for the latent variable. How can I get (or compute) the second value to obtain the unique validity variance?