I asked about variables X and Y to the same respondents for two different product types. I mean, respondents firstly answered the items for Product1 then for Product2. In AMOS, I have two different models (Product1-Product2). We proposed that the effect of X on Y is stronger for product1. We have two Std. Estimates. The first beta is greater than the second one. Is this finding sufficient to confirm the hypothesis? Or do I still need the Chi-square difference test or something like it to prove the statistical significance? If not, what should I do for the statistical difference between these two betas?
Thanks ahead
Hello Mehmet,
that means you have a model with two IVs that refer to both products. As I assume the scales are identical, you can specify equality constraints on both *unstandardized* effects (Bs) and come the (now worse) chisquare value to the baseline chisquare value.
Alternatively, you will find an easy formula in this paper
Paternoster, R., Brame, R., Mazerolle, P., & Piquero, A. (1998). Using the correct statistical test for the equality of regression coefficients. Criminology, 36(4), 859-866.
Testing beta differences is not such a good idea as these will also differ, wenn the Bs are identical but both IVs have different standard deviations.
All the best
Holger
You cannot infer much from such a study as the time is fully confounded with the product type/number. You cannot say if the differences you see between the products is because of the products itself or because of the fact that you "primed" the respondents with the question on product 1 before you ask about product 2.
It would be interesting to see if you find differences in subsequent surveys on two pruducts which are essentially the same (w.r.t. the properties you are interested in; the respondents, however, should assume or believe that these are different products). This would have been a nice control.
One would usually use some kind of cross-over design and/or a design that considers wash-out effects.
Based on your explanation, I got to know that you need to apply Multigroup Analysis (MGA); where you will able to 1) Compare the full model by consideration of two type of products , 2) comparison of each hypothesized path ( or all paths). As you mentioned Chi-square difference test can be used for such comparison.
In addition , it is important to apply invariance tests ( configural, metric, scalar etc.)
Best,
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