Identifying the best way to measure the relationship

[Mohamed Elmahgoub]

Dear All

I want your help regarding identifying the best way to test the relationship between Xand Y

I have three variables:

Y reflects employees thriving
Xcultural adjustment
Zreflects Personal traits

Based on theory, Z(Personal traits) affects X(cultural adjustment), then X(cultural adjustment) affects (Y employees thriving), as explained the photo below.

I am interested in examining the impact of X(cultural adjustment) on (Y employees thriving), considering the impact of Z(Personal traits) on X(cultural adjustment). How can I statistically address this in my regression, knowing that all the three variables are continuous composite variables (created through using PCA for set of survey questions that have been measure on a measure from 1 - 5 likert scale and tested using Cronbach's alpha to test their reliability).

I really appreciate your help with that, and would you briefly tell me how to do it in Stata.

[Marcos Almeida]

I think you could select a structured equation model - sem - approach.

[Mohamed Elmahgoub]

I think you could select a structured equation model - sem - approach.

Thank you Marcos for your reply. I have only 100 surveys, I think SEM would need at least 300 observations. Am I correct? and if so, what would be the best alternative?

Really appreciate your help

Kind regards
Mohamed

[Joseph Coveney]

From your post, it's not really clear what you're trying to accomplish.

First up: "considering the impact of Z(Personal traits) on X(cultural adjustment)". According to your diagram, "the impact of Z(Personal traits) on X(cultural adjustment)" is outside of the study's scope. So it doesn't matter what "the impact of Z(Personal traits) on X(cultural adjustment)" is.

Second, you don't seem to have done any power analysis. Without formal consideration of the effect size that you would be loathe to miss, any "examining the impact of X(cultural adjustment) on (Y employees thriving)" is essentially going to be descriptive. So it doesn't matter whether you need 100 or 300 observations for SEM as long as you can get stable estimates.

Third, it's not clear why you are using principal component analysis of ordered-categorical responses in order to obtain a (several? how many components are retained?) continuous composite variable. If you're not going to use a measurement submodel (allowing for different factor loadings for each questionnaire item) in, say, gsem, then why not just use the sum score itself? (You mention a Likert scale.)

Maybe take some of the following into consideration.

You could keep things simple by using sum scores for each of the scales (square boxes in your diagram). If one or more of the scales is psychometrically validated, then use whatever algebra the literature recommends to compute the score from responses on the individual items, assuming that the literature formula generalizes to your 100 survey respondents.

You could keep things simple by restricting to your study's scope: regress Y c.X and assess the degree of association between scores on the two scales. If you don't like linear models for sum scores, then see here for an alternative. If there is extracurricular interest in whether personal traits has anything to do with the association of Y and X, then you could either stratify on Z (matching respondents within tertiles or quartiles or quintiles or deciles of Z) if you believe that its "impacting" is nonlinear—e.g., regress Y c.X##i.Z_cat—or otherwise more simply as regress Y c.X##c.Z.

If you wanted to keep the individual item responses as ordered categorical and allow the factor loadings to vary (as opposed to a sum score), then you could see whether a relatively simple SEM would converge with gsem with an oproit or ologit link. You could try setting something up like what's in your picture.

gsem (Y -> y?, oprobit) (X -> x?, oprobit) (Z -> z?, oprobit) (Y <- X) (X <- Z)