Model for Panel Data with time-variant DV and time-invariant IVs

[Alex To]

Hello,

My panel data is short (N>T) and I would like to regress 4 time invariant IV on 1 time variant DV. From xtcdf, there is no cross section correlation. From xtserial, there is no autocorrelation. From xttest3, there is heteroskedascity. However, xttest3 only applies for fixed effects, which cannot handle time invariant IV. So I would appreciate some guidance on choosing the correct model and then testing it for heterskedscity, autocorrelation (and dealing with outliers at a later point)

Background: each participant looked at an image 6 times and their gaze time was measured (t=6, n=63), thus they each have 6 different gaze time measurements. They also took a survey capturing 4 attitudes metrics which do not change over time and are thus time-invariant. I would like to regress the 4 time-invariant attitude variables on their time-variant gaze time.

Thanks for any and all guidance

[Tom Scott]

Alex To do you expect change in gaze over time or are you trying to explain change? If so, then look into a random effects model or latent growth curve. If you are not expecting attitudes to explain change over time, I would think you could just generate an average score and predict average gaze time using OLS.

[Sebastian Kripfganz]

If all the independent variables are time-invariant, then estimating a panel model does not make much sense. As Tom said, just collapse the data into a cross-sectional data set and estimate the model by OLS.

Btw, in terms of terminology: You are regressing the dependent variable on the independent variables, not the other way round.

[Alex To]

Tom Scott
Sebastian Kripfganz

Thanks both for the suggestions and correction. I also just thought to average the gaze time and transform the panel data into a normal OLS, however I do expect gaze time to decrease overtime actually. So ideally, I would also be able to explain the change over time for this with a panel data regression. Is this not suitable use case? My readings on this forum do not yield similar cases to mine

I believe a random effects model could suit me, however xtgls is suitable when N<T, but N>T in my case

[Tom Scott]

Alex To Is there a reason you cant just regress change in gaze on your attitude measures using OLS with robust standard errors. Your dependent variable would be the difference in gaze time between time 1 and time 6.

If you do go with a random effects model, look into the 'mixed' or 'xtreg' commands. The command 'xtgls' was conceived for dealing with small N, large T panel datasets. Your dataset is a large N, small T one, so you should stick with -xtreg, re-.