# Should I be using pooled OLS or Fixed effect regression for my model here and why?

I have run two different regression models, one fixed effect and one pooled OLS on my data. my data looks at the number of visits to hospital regressed over age, marriage, income, insurance etc.

I have the following different outputs:

areg  docvis hhkids age agesq married working linc addon, absorb(id)

Linear regression, absorbing indicators                Number of obs =    6209
F(  7,  5315) =    9.41
Prob > F      =  0.0000
R-squared     =  0.4187
Root MSE      =  4.5743

------------------------------------------------------------------------------
docvis |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
hhkids |   .6842771   .2283976     3.00   0.003     .2365241     1.13203
age |  -.2296306   .1000438    -2.30   0.022    -.4257574   -.0335037
agesq |   .0038488   .0010781     3.57   0.000     .0017352    .0059624
married |  -.0821362   .3648964    -0.23   0.822     -.797483    .6332105
working |  -.5626292   .2482206    -2.27   0.023    -1.049243    -.076015
linc |   .0877239   .2388579     0.37   0.713    -.3805356    .5559834
addon |   .2961511   .6367558     0.47   0.642    -.9521517    1.544454
_cons |   5.699316   2.413246     2.36   0.018     .9683623    10.43027
-------------+----------------------------------------------------------------
id |      F(886, 5315) =      3.949   0.000         (887 categories)


and

. reg docvis hhkids age agesq married working linc addon

Source |       SS       df       MS              Number of obs =    6209
-------------+------------------------------           F(  7,  6201) =   33.13
Model |  6896.48158     7  985.211654           Prob > F      =  0.0000
Residual |  184416.031  6201  29.7397244           R-squared     =  0.0360
Total |  191312.513  6208  30.8170929           Root MSE      =  5.4534

------------------------------------------------------------------------------
docvis |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
hhkids |  -.2391697   .1658536    -1.44   0.149    -.5643002    .0859609
age |  -.1507832   .0726872    -2.07   0.038    -.2932753    -.008291
agesq |   .0025111   .0008288     3.03   0.002     .0008863    .0041359
married |   .0999155   .2074759     0.48   0.630    -.3068092    .5066403
working |  -1.334794   .1698332    -7.86   0.000    -1.667726   -1.001862
linc |  -.2042591   .1686214    -1.21   0.226    -.5348155    .1262974
addon |    -.36392    .590928    -0.62   0.538    -1.522344    .7945038
_cons |   5.455084   1.587606     3.44   0.001     2.342826    8.567342
------------------------------------------------------------------------------


My question is this:

which is better, pooled OLS or fixed effect? How do i know which one is better, is there a test I can do on stata to see which one is more suited to my data? Additionally could someone explain why the results are different?

Lucky for you, there is a straightforward answer to this question (not always true when comparing models)!

The fixed effects regression is superior because it has greater R-squared and adjusted R-squared as well as smaller root MSE. In other words, the fixed effects explain a great deal of the variability in your outcome (number of doctor visits). The two regressions are different because in your data, even after controlling for all the other covariates, subjects attending different hospitals have different outcomes.

Without knowing the data, that might be due to a number of factors including: patients with different conditions attend different hospitals, doctors at different hospitals have different protocols for follow-up visits, etc.

After controlling for hospital fixed effects the estimates of the other coefficients change because they are correlated with hospital. For example, some hospitals might be more likely to admit patients with higher or lower income, age, etc.

Since your outcome variable is a count, and in particular is non negative, you may want to take it's log to be the outcome. Even better might be a Poisson regression.

• Thanks for the response, I feel so silly now for not looking at the descriptive statistics above. So is this model actually doing hospital fixed effects rather than person fixed effects? – summer_ZUGG Mar 28 at 15:06
• Sorry I assumed the id was of the hospital. If it's of the individual, then you'll need to modify the interpretation accordingly. – user242755 Mar 28 at 15:19
• Thank you for clarifying. So the reason my data differs is because the individuals themselves differ? would this perhaps be due to variables outside my model like ethnicity, lifestyle etc? – summer_ZUGG Mar 28 at 15:33