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I'm after some advice.

I have done a log transformation for my DV (this normalises the distribution), which is a continuous variable.

My IV is count data (but it's a 5 year moving average). The IV is strongly skewed to the right.

I have added some control variables to my model.

I have done some diagnostics, which I want to share with you.

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Everything looks pretty well, except for the QQ plot---I know it's not perfect, but do you think there's much harm?

What worries me a little more is what I find when I do AvPlots for my model---these are partial regression plots, i.e. they show x and y, having accounted for other variables in the model.

enter image description here

I would love to see the data points more spread-out. Perhaps I can achieve this by adding more variables to the model. But do you think this looks alright for a MLR? If not, what should I do/use then?

Any justified advice much appreciated.

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  • $\begingroup$ Please also include the summary(model) output $\endgroup$ May 21 at 9:43
  • $\begingroup$ I included some summary (didn't include everything, since I used factor() for countries and years, so the table would be too long. $\endgroup$
    – Ken Lee
    May 21 at 9:56
  • $\begingroup$ How many countries and years do you have, and what is the purpose of the model ? $\endgroup$ May 21 at 10:38
  • $\begingroup$ I've got 150 countries; I've got 25 years. I want to see whether more corporate investment to developing countries is associated with larger loans from the Bank (I argue that corporations may be pushing for larger loans there as their subsidiaries could benefit from that). // So far it seems that US corp investment has a negative "effect" on the loans' size. Essentially, if the model is sound, I will interpret this as the US corporations simply investing more in countries that receive smaller loans, as it would be unrealistic to argue that they push for smaller loans. // $\endgroup$
    – Ken Lee
    May 21 at 10:39
  • $\begingroup$ This would align with my interview evidence, where I found that corporations don't influence the Bank's loans' size. // I just want to make sure that my model is sound and I can draw conclusions from it. $\endgroup$
    – Ken Lee
    May 21 at 10:42
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I would not be too concerned with those diagnostics plots. In applied work, it is quite rare to get perfect plots.

My main suggestion, as noted in the comments is to remove Country and Year as fixed effects from the model and instead fit random intercepts, with something like

lmer(y ~ fixed_effects + (1|country) + (1|year), data = mydata)

where this example is using lmer from the lme4 package.

Random effects should achieve the same thing as fixed effects, but in a more parsimoneous way. Of course it will be a good idea to compare the inferences from both models.

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