# Why different models to tests with same data in multiple regression

Why many papers when testing different hypothesis with one dataset they tend to separate in different models to analyse?

Example Model 1: $y = c + \beta_1 Ctrl1 + \beta_2 Ctrl2 + \beta_3 Expla1 + \beta_4 Expla2 + \beta_5 (Expla1*Expla2)$

Model 2: $y = c + \beta_1 Ctrl1 + \beta_2 Ctrl2 + \beta_3 Expla1 + \beta_4 Expla3 + \beta_5 (Expla1 * Expla3)$

and not: $y = c + \beta_1 Ctrl1 + \beta_2 Ctrl2 + \beta_3 Expla1 + \beta_4 Expla2 + \beta_5 Expla3 + \beta_6 (Expla1 * Expla2) + \beta_7 (Expla1*Expla3)$

In the real case they use 8 control variables, and test 3 different models where they always use Expla1 and change for the other while they also try an interaction.

Is it just because too many variables to analyse can lead to a multiple regression less powerful?

Edit

I think a image speak better than words. This is an extract from Deb, P., David, P., & O'Brien, J. (2016). When is cash good or bad for firm performance?. Strategic Management Journal.

Each model use the same dataset. I personnally use the same control and explanatory variables (except square of cash) but with a different dataset. Also, I have to use in my case GMM/DPD method with Eviews 9 (to correct for autocorrelation).

My results are inconsistent for "cash", only 2B significant. For the explanatory variables industry competition (positive significance) and industry growth (negative significance). In the interactions I only have cash*industry growth who is statistically significant.

So I did try an multiple regression adding all models (all explanatory and interactions together). In this case cash is not significant, while 2/3 explanatory are significant and 2/3 as well for the interaction.

It's why I'm wondering which way to conduct the analysis is more reliable? Carry independent models as the paper did or doing all variables together.

Thanks

• Without having seen the paper, or more details it is impossible to say. Can you maybe edit that in? Aug 27, 2016 at 9:13
• @Repmat Please see the edit. Aug 27, 2016 at 9:45