[Weiwen Ng]

My OLS Results:

. regress happinessindex lgva unemployementrateaged16 mentalhealth obesityqofprevalence17 smokingattributable
> deathsfromhea violentcrimeincludingsexualviole socialisolation lifeexpectancypca

Source | SS df MS Number of obs = 500
-------------+---------------------------------- F(8, 491) = 48.67
Model | 6.25298519 8 .781623148 Prob > F = 0.0000
Residual | 7.88592196 491 .016060941 R-squared = 0.4423
-------------+---------------------------------- Adj R-squared = 0.4332
Total | 14.1389071 499 .028334483 Root MSE = .12673

--------------------------------------------------------------------------------------------------
happinessindex | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------------------------------+----------------------------------------------------------------
lgva | .0406153 .0168767 2.41 0.016 .0074558 .0737748
unemployementrateaged16 | -.0226846 .0027359 -8.29 0.000 -.0280602 -.0173091
mentalhealth | -.2176063 .0351464 -6.19 0.000 -.2866622 -.1485503
obesityqofprevalence17 | .0382862 .0063163 6.06 0.000 .0258759 .0506965
smokingattributabledeathsfromhea | -.0057882 .0008938 -6.48 0.000 -.0075444 -.0040321
violentcrimeincludingsexualviole | .0026786 .0010592 2.53 0.012 .0005975 .0047597
socialisolation | .0036622 .0012284 2.98 0.003 .0012486 .0060758
lifeexpectancypca | -.0015486 .0022503 -0.69 0.492 -.0059699 .0028728
_cons | 7.062978 .2098355 33.66 0.000 6.650692 7.475264
--------------------------------------------------------------------------------------------------

My Gls Results:

 xtreg happinessindex lgva unemployementrateaged16 mentalhealth obesityqofprevalence17 smokingattributablede
> athsfromhea violentcrimeincludingsexualviole socialisolation lifeexpectancypca

Random-effects GLS regression Number of obs = 500
Group variable: nLAname Number of groups = 100

R-sq: Obs per group:
within = 0.3699 min = 5
between = 0.4887 avg = 5.0
overall = 0.4323 max = 5

Wald chi2(8) = 322.52
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

--------------------------------------------------------------------------------------------------
happinessindex | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------------------------+----------------------------------------------------------------
lgva | .053726 .0254011 2.12 0.034 .0039408 .1035113
unemployementrateaged16 | -.0168212 .0029602 -5.68 0.000 -.022623 -.0110193
mentalhealth | -.2248728 .0526844 -4.27 0.000 -.3281323 -.1216132
obesityqofprevalence17 | .0457305 .0091431 5.00 0.000 .0278104 .0636507
smokingattributabledeathsfromhea | -.0072916 .001115 -6.54 0.000 -.0094769 -.0051063
violentcrimeincludingsexualviole | .0039391 .001243 3.17 0.002 .001503 .0063753
socialisolation | .0036549 .00125 2.92 0.003 .0012049 .0061048
lifeexpectancypca | -.0018097 .0035733 -0.51 0.613 -.0088132 .0051938
_cons | 6.876862 .2955269 23.27 0.000 6.29764 7.456084
---------------------------------+----------------------------------------------------------------
sigma_u | .07486468
sigma_e | .09925072
rho | .36263771 (fraction of variance due to u_i)
--------------------------------------------------------------------------------------------------

My Tobit Results:

. xttobit happinessindex lgva unemployementrateaged16 mentalhealth obesityqofprevalence17 smokingattributable
> deathsfromhea violentcrimeincludingsexualviole socialisolation lifeexpectancypca

Fitting comparison model:

Fitting constant-only model:

Iteration 0: log likelihood = 181.94967
Iteration 1: log likelihood = 181.95017
Iteration 2: log likelihood = 181.95017

Fitting full model:

Iteration 0: log likelihood = 327.87198
Iteration 1: log likelihood = 327.91297
Iteration 2: log likelihood = 327.91297

Obtaining starting values for full model:

Iteration 0: log likelihood = 361.52137
Iteration 1: log likelihood = 364.04804
Iteration 2: log likelihood = 364.07196
Iteration 3: log likelihood = 364.07197

Fitting full model:

Iteration 0: log likelihood = 364.07197
Iteration 1: log likelihood = 364.07197 (backed up)

Random-effects tobit regression Number of obs = 500
Uncensored = 500
Limits: lower = -inf Left-censored = 0
upper = +inf Right-censored = 0

Group variable: nLAname Number of groups = 100
Random effects u_i ~ Gaussian Obs per group:
min = 5
avg = 5.0
max = 5

Integration method: mvaghermite Integration pts. = 12

Wald chi2(8) = 330.60
Log likelihood = 364.07197 Prob > chi2 = 0.0000

--------------------------------------------------------------------------------------------------
happinessindex | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------------------------+----------------------------------------------------------------
lgva | .0523589 .0246984 2.12 0.034 .0039508 .1007669
unemployementrateaged16 | -.0171554 .0030147 -5.69 0.000 -.0230641 -.0112467
mentalhealth | -.2249888 .050897 -4.42 0.000 -.3247451 -.1252325
obesityqofprevalence17 | .0450798 .0089681 5.03 0.000 .0275026 .062657
smokingattributabledeathsfromhea | -.007221 .0011034 -6.54 0.000 -.0093836 -.0050585
violentcrimeincludingsexualviole | .0038847 .0012265 3.17 0.002 .0014808 .0062886
socialisolation | .0036712 .0012383 2.96 0.003 .0012442 .0060981
lifeexpectancypca | -.0017946 .0034377 -0.52 0.602 -.0085323 .0049431
_cons | 6.895143 .2890244 23.86 0.000 6.328666 7.461621
---------------------------------+----------------------------------------------------------------
/sigma_u | .0737318 .0076861 9.59 0.000 .0586673 .0887963
/sigma_e | .1028686 .0036789 27.96 0.000 .095658 .1100792
---------------------------------+----------------------------------------------------------------
rho | .339385 .0520314 .2442626 .4460577
--------------------------------------------------------------------------------------------------
LR test of sigma_u=0: chibar2(01) = 72.32 Prob >= chibar2 = 0.000

Aishwarya, thanks for the full output.

Earlier, I said that if you thought you could meet the assumptions of censored linear regression (i.e. Tobit regression), you could try running the model with the lower limit set at 0, and the upper limit at 10, i.e.

xttobit happinessindex lgva unemployementrateaged16 mentalhealth obesityqofprevalence17 smokingattributable deathsfromhea violentcrimeincludingsexualviole socialisolation lifeexpectancypca, ll(0) ul(10)

Without doing so, you basically told Stata to run you a censored linear regression with no censoring (because you didn't tell the program where the upper and lower limits of the DV were, it assumed they were at +/- infinity). A priori, I would expect almost identical results to -xtreg-. You appear to have got ... almost identical results to -xtreg-. There's nothing to explain here.

I further cautioned that I thought that censored linear regression was a wrong model to begin with. I was trying to think of a model that was clearly superior to -xtreg-. This was the only alternative model that came to mind at the time, but given your description, this is not a case where censoring applies - I tried to make this clear, but I fear I have caused confusion, for which I apologize. Let me be clear: the clearest improvement would be to get the original data and use ordered logistic models (albeit you have to deal with the fact that you don't have repeat measures on the same individuals; I'm not quite sure how to do this).

You actually have a statistically significant, albeit small, effect of log gvpa on average satisfaction. It is what it is, and moreover, you said that you were expecting this from prior literature. I don't really see any major improvements to be made here (unless you can get the individual data).