I am currently working on a panel data set with T=21 and N=50, how can I check for heteroskedasticity in the panel data ?? I have got good residual vs quantile graph and the residuals are normally distributed. However I want to be sure of that fact. I have attached an illustration for that.
The results are obtained in SAS platform, if you have SAS expertise, please do suggest some ideas or ideas generally.
Panel Data is also known as Longitudinal data and checking for heteroskedasticity error is checking for uniform variation. You should check for auto correlation too. Look up Proc Mixed in SAS . You will get an estimate of the within subject variation. You can also see if it is significant or not.
Check http://www.ats.ucla.edu/stat/sas/seminars/sas_repeatedmeasures/ to understand better
Benzaman -
You can use a residual plot with the estimated residuals on the y-axis, and the predicted y values (or for simple regression through the origin, just x) on the x-axis (which is a size measure for the respondents). You can then see if there is a pattern which flairs, which would indicate heteroscedasticity.
I used weighted least squares (WLS) regression a great deal for finite population sample surveys of establishments for use in prediction for official statistics, and kept it in the error structure where it naturally belongs, rather than do a transformation.
Here are some references which might be of interest to you:
https://onlinecourses.science.psu.edu/stat501/node/279
https://www.researchgate.net/publication/263809034_Alternative_to_the_Iterated_Reweighted_Least_Squares_Method_-_Apparent_Heteroscedasticity_and_Linear_Regression_Model_Sampling
https://www.researchgate.net/publication/262972023_HETEROSCEDASTICITY_AND_HOMOSCEDASTICITY
https://www.researchgate.net/publication/263032446_Weighting_in_Regression_for_Use_in_Survey_Methodology
https://www.researchgate.net/publication/263036348_Properties_of_Weighted_Least_Squares_Regression_for_Cutoff_Sampling_in_Establishment_Surveys
https://www.researchgate.net/publication/261596397_Ken_Brewer_and_the_coefficient_of_heteroscedasticity_as_used_in_sample_survey_inference
Cheers - Jim
PS - Good advice from Alice. Panel data does require more consideration than the cross-sectional type data with which I was involved.
However, I scanned the attachment she provided, to see what it said about p-values, and saw this "Here the test has a p-value of 0.0705 which exceeds 0.05 and thus it is not significant." That was what I was concerned would be said. That is highly misleading, as 0.05 should not be arbitrarily chosen as a threshold. The p-value is a function of sample size, so your decision to "accept" or "reject" will be changed just by changing the sample size. The p-value is an incomplete statistic that is generally misleading when used without a type II error analysis or effect size investigation of some kind, or some kind of comparison.
Standard error is also changed by sample size changes, but they are less prone to misunderstanding and misuse.
Article Ken Brewer and the coefficient of heteroscedasticity as used...
Article HETEROSCEDASTICITY AND HOMOSCEDASTICITY
Article Weighting in Regression for Use in Survey Methodology
Article Properties of Weighted Least Squares Regression for Cutoff S...
Conference Paper Alternative to the Iterated Reweighted Least Squares Method ...
I would recommend including a specific term in the mixed model for within level 2 between level1 heterogeneity and estimating its size eg allowing the level 1 random term to be a function of time so that the process has become more (or less ) variable over time and you will be able to see the nature of this heteroscedasticity. If it is important the level 2 estimates and the SEs of parameters will be adjusted. Same for temporal autocorrelation.
https://www.researchgate.net/publication/233756428_Explaining_Fixed_Effects_Random_Effects_Modeling_of_Time-Series_Cross-Sectional_and_Panel_Data
Article Explaining Fixed Effects: Random Effects Modeling of Time-Se...
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