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Assessing model fit over time

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Hello, I'm currently working with panel data over a three year period. I have only worked with cross sectional data, so my knowledge with time-series is limited, hence my post on this forum.


I have panel data going from 2010-2013. I'm currently applying an logistic regression model (logit) with a binary dependent variable (external accountant) 1 if they get advice from external accountants, and 0 otherwise.

I structure my data with the following command

HTML Code:
xtset Company_ID Year
Code:
Sort by Company_ID year

My main model consists of all years ( 2010-2013), where I accordingly adjust for time-series dependence in my residuals and adjusts standard errors for clustering on each company. This part is ok, I get my results and I am happy.

However, I also want to adress the development "over time"; and here I am on unrecognized territories. I therefore ran 3 new models for each seperate year ( 2011, 2012, 2013), where some variables gradually goes from significant to insignificant etc.


My question is how do I adress these the development over time in Stata? I have for now said something about the R^2 which actually increases over time ( thereby making my results stronger?)

I was also thinking that I may say something about assessment of fit over time? I then read something about the Lstat function in Stata ( http://www.columbia.edu/~so33/SusDev/Lecture_10.pdf ) - is it possible to use the command of -lstat- on my binary dependent variable and see if it classifies is more correctly over time? And is it possibile to check whether the results become more or less rational over time(maybe with an increasing R2 or higher "correct classification"?

If anyone have any experience with this, I would appreciate the feedback.

Best regards, Jens H

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