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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.

multiple regression fixed effects different models

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

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

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You provide the answer in your first sentence. Even if your sample size is huge, you need to test different hypotheses with different models.

In your example, models 1A, 2A and 3A are identical. This is more of a style or formatting issue than a statistical one. Someone (the author, an editor, a reviewer) thought the table would be clearer with six columns labeled as they are rather than with four columns labeled model 1, 2, 3, and 4. One reason they might think so is that the format they used makes it easier to compare the B models with the A models. For instance, we can see that the parameter for potential slack decreases when variables are added to the model.

If I were writing it, I'd probably have gone with 4 columns, but ... it's not a statistical issue.

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    $\begingroup$ Thank you Peter. So it's a matter of style in this case. But specifically for the models to tests. When I have multiple hypotheses. I should not aggregate all explanatory and interaction variables in the same test (statistical analysis) to analysis the data. But instead, run the models separately even if the dataset is the same? $\endgroup$
    – Volvic
    Commented Aug 27, 2016 at 12:59
  • $\begingroup$ It depends on exactly what your hypotheses are. It is certainly reasonable, in some instances, to run multiple models on the same data set. This may call for correction for multiple tests. $\endgroup$
    – Peter Flom
    Commented Aug 27, 2016 at 14:01

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