R square value from results of Random effects panel regression

[Radhika Channanamchery]

Hi,

I have got a very low R square value of between effects, for an RE panel regression.
How do I proceed with these results? Please help with this. Thank you.




xtreg shareingca ci rf fertconsumption sharegiaingca,re

Random-effects GLS regression Number of obs = 24
Group variable: stateid Number of groups = 8

R-sq: within = 0.5696 Obs per group: min = 3
between = 0.0080 avg = 3.0
overall = 0.0095 max = 3

Wald chi2(4) = 18.31
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0011

---------------------------------------------------------------------------------
shareingca | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------+----------------------------------------------------------------
ci | -.0291131 .0241929 -1.20 0.229 -.0765304 .0183042
rf | -.0025849 .0013045 -1.98 0.048 -.0051416 -.0000283
fertconsumption | .0081021 .0049064 1.65 0.099 -.0015142 .0177184
sharegiaingca | -.089107 .0352151 -2.53 0.011 -.1581273 -.0200866
_cons | 12.84383 4.307265 2.98 0.003 4.401743 21.28591
----------------+----------------------------------------------------------------
sigma_u | 9.6008013
sigma_e | .45464036
rho | .99776258 (fraction of variance due to u_i)
---------------------------------------------------------------------------------

[Carlo Lazzaro]

Radhika:
with 24 observations (8 N x 3T) any inference procedure would be unreliable.
I'd stick with descriptive statistics in your case.

[Erik Ruzek]

A lot of people will feel similarly as Carlo. However, the small sample problem is one that methodologists working on random effects models have spent a fair bit of effort on and developed some nice tools for. Stata's mixed has corrections for small sample sizes. I don't know what your xtset variable is, but let's pretend that it is id:

mixed shareingca ci rf fertconsumption sharegiaingca || id: , dfmethod(kroger) reml

dfmethod(kroger) takes care of inflated Type1-error rates for fixed effects and reml (restricted maximum likelihood) estimation helps to protect against downward bias in the variance estimates. There will still be huge uncertainty in all estimates, but these are known methods for helping with small sample sizes in random effects models. See McNeish (2017) in MBR for further discussion.

The other option is to go Bayesian (help bayes mixed), where you provide reasonable prior distributions for the parameters of interest. There is a lot of guidance out there about how to choose appropriate priors. McNeish (2016) also has a nice article on this in the SEM journal.

[Radhika Channanamchery]

Radhika:
with 24 observations (8 N x 3T) any inference procedure would be unreliable.
I'd stick with descriptive statistics in your case.

Thank you Carlo for your message

[Radhika Channanamchery]

A lot of people will feel similarly as Carlo. However, the small sample problem is one that methodologists working on random effects models have spent a fair bit of effort on and developed some nice tools for. Stata's mixed has corrections for small sample sizes. I don't know what your xtset variable is, but let's pretend that it is id:

mixed shareingca ci rf fertconsumption sharegiaingca || id: , dfmethod(kroger) reml

dfmethod(kroger) takes care of inflated Type1-error rates for fixed effects and reml (restricted maximum likelihood) estimation helps to protect against downward bias in the variance estimates. There will still be huge uncertainty in all estimates, but these are known methods for helping with small sample sizes in random effects models. See McNeish (2017) in MBR for further discussion.

The other option is to go Bayesian (help bayes mixed), where you provide reasonable prior distributions for the parameters of interest. There is a lot of guidance out there about how to choose appropriate priors. McNeish (2016) also has a nice article on this in the SEM journal.

Thank you for your kind suggestions