Why is Hyso test is used in panel regression ?

Dear all,

I recently conducted a 3 (between-subject: two intervention groups and one control group) x 5 (within-subject: 5 dependent variables) field experiment in which two behavior interventions (indenpendent variables) are investigated in terms of their effects on 5 pro-environmental behaviors (dependent variables). In this experiment, I also measured two psychological variables (proposed mediators), socio-demographic variables (proposed moderators) and several covariates. The experiment aims to examine (1) the intervention effects on pro-environmental behaviors (main effect analysis); (2) the psychological mechanisms underlying intervention effects (mediation analysis); and (3) the boundary conditions of intervention effects (moderation analysis). We established 7 hypotheses regarding the main, mediating, and moderating effects before the experiment began (this is a preregistered experiment). Specifically, there are 2, 2, and 3 hypotheses concerning the main, mediating, and moderating effects that need to be tested.

I have a few questions as to multiple-testing correction.

1) As there are multiple dependent variables (5 pro-environmental behaviors) and our hypotheses apply only to the general pro-environmental behavior, I need to test each hypothesis for each dependent variable. Hence, there are five exploratory analyses for each hypothesis test. I decide to use the method proposed by Benjamini and colleagues to control for the false discovery rate (FDR). Should I apply the FDR procedure to the 5 tests regarding each hypothesis respectively (i.e., using FDR procedure for multiple-testing concerning H1, H2, ... H7, seperately) OR should I apply the FDR procedure to all 5*7=35 tests?

2) I used OLS regression to test each hypothesis. When testing the main effects, the coefficients of the intervention dummies are of interest, but there are also several covariates that need to be controlled in the regression. Should I apply FDR procedure only to the p-values of the variables of interest (i.e., theoretically meaningful) or to the p-values of all variables included in the regression (intervention dummies plus covariates)? Similarly, when testing the moderating effects, the coefficients of the interventionXmoderator interaction terms are of interest. Should I apply FDR only to the p values of these interaction terms or to the p-values of all variables included in the regression?

3) Assume that I conduct bootstrap method to test the mediating effects, as bootstrap concerns the product of two coefficients (a*b) instead of individual coefficients, how should I use the FDR procedure in this case?

I appreciate any help for my questions.

I want to estimate the effect of socio-economic status on private tuition expenditure (cross section data with cluster)  using the hurdle model in India. Having gone through a number of literature, I understand that it is a two part model (probit + Ols (lognormal with log (y)) or hurdle model (probit + truncated regression (on  y not on log y)).  In both models , the equations are not combined and can be estimated separately. However, in the case of a lognormal model, estimating E(y/x, y>0) is not an issue but E(y/x). I want to estimate E(y/x) too.

When  I run lognormal regression with district  fixed effects, the magnitude (even sign) of the coefficient of few covariates diffres (gets reversed) as compared to the  model without fixed effects. To the best of my knowledge , we don't have a command for estimation of truncated normal regression for fixed effects in Stata 14 or 16. so, I can't do such a comparison in this case.

Should I trade off district unobserved heterogeneity in favour of truncated normal regression for estimating E(y/x) ? What if the effects of the  unobserved heterogeneity would be as severe as in the case of lognormal regression?

Var=Variable

Thank You for your insights:)

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I would appreciate any advise and suggestions, and if my question is unclear, please let me know.

Thanks in advance.

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