SPSS AMOS allows the specification of a variable as ordered categorical. For example, 1) level of proficiency (PROFICIENCY: 0 = low, 1 = high), 2) social-economic status (SES: 1 = low, 2 = intermediate, and 3 = high). In AMOS, Tools/Data Recode is the where this specification happens. After moving the name of a variable to the box of "New and recoded variables" and select "Ordered-categorical" under the "Recoding rule" drop-down menu, the specification (a.k.a., data recoding) is completed. Next, if the user clicks the Details button, a new window pops up where the categories of the newly specified/recoded variable show up together with their boundary value(s). For the binary PROFICIENCY variable, there is only one boundary and its value is automatically 0. For the three-category SES variable, there are two boundaries which are automatically 0 and 1, respectively. Finally, let's also assume the two variables, PROFICIENCY and SES, both serve as endogenous variables (i.e., dependent variables) in the model. Such a model will need Bayesian estimation in AMOS.
My questions are related to these boundary/boundaries and their value(s).
- Since AMOS uses an ordered probit model to model an ordered categorical dependent variable, are the boundary/boundaries simply the threshold parameter(s) underlying the ordered categories of the newly specified/recoded ordered categorical dependent variable?
- If the boundary/boundaries are the threshold parameter(s) of the ordered categories, are the boundary value(s) automatically generated by AMOS what the software fixes the threshold parameter(s) to? Or are they the initial values of the threshold parameter(s) which could continue to evolve during the optimization process?
- If the boundary/boundaries are the threshold parameter(s) of the ordered categories, are they simply the negative(s) of the intercept parameter(s) of the ordered probit regression model?
- Finally, regarding the intercept parameters of the probit model of the three-category SES dependent variable, my understanding is that the model should consist of two equations with each one having its own intercept. Accordingly, there should be two different intercept estimates which correspond to the two equations of the ordered probit model predicting a three-category dependent variable. Then, why does AMOS only produce a single intercept estimate for the ordered probit model which consists of two equations, instead of two different intercept estimates with one for each equation?
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