# **6.2.1 Running the First Stage (welfare model)**

The entire process of small area estimation may be run in two stages. It is possible to test the first stage of the analysis before moving on to the simulation which makes use of the target data. To obtain the first stage of the analysis, the user must have the data ready, and it is recommended that the user has predefined as macros the variables to be used.

``` ` ́` ́` ́ .saemodelpovmapyxvar[aw=hhw],area(localityid_n)zvar(zvar)///
>varest(h3)vce(ell)alfatest(pp)
note:p_ageomittedbecauseofcollinearity WARNING:76observationsremovedduetolessthan3observationsinthecluster.
OLSmodel: ```

|`lny`|`Coef.`|`Std. Err.`|`z`|`P>|z|`|`[95% Conf.`|`Interval]`|
|---|---|---|---|---|---|---|
|`dw_bath`|`.1397767`|`.0200267`|`6.98`|`0.000`|`.100525`|`.1790283`|
|`dw_btype_d3`|`.0496587`|`.0211568`|`2.35`|`0.019`|`.0081921`|`.0911253`|
|`edu_postsec`|`.0816588`|`.0883387`|`0.92`|`0.355`|`-.0914818`|`.2547994`|
|`edu_prim`|`-.8848284`|`.1744707`|`-5.07`|`0.000`|`-1.226785`|`-.5428722`|
|`j_firm_access1`|`.0382874`|`.0129973`|`2.95`|`0.003`|`.0128132`|`.0637616`|
|`jud_erate`|`.8928555`|`.2215139`|`4.03`|`0.000`|`.4586962`|`1.327015`|
|`jud_occup_el_sh`|`-1.333666`|`.2481222`|`-5.38`|`0.000`|`-1.819977`|`-.8473555`|
|`p_activity_1_sh`|`-.204576`|`.0306396`|`-6.68`|`0.000`|`-.2646285`|`-.1445235`|
|`p_age`|`.0134131`|`.0023387`|`5.74`|`0.000`|`.0088293`|`.0179968`|
|`p_age2`|`-.0000788`|`.0000238`|`-3.31`|`0.001`|`-.0001255`|`-.0000321`|
|`p_ecstat_2_sh`|`-.2178931`|`.0840416`|`-2.59`|`0.010`|`-.3826117`|`-.0531745`|
|`p_ecstat_4_sh`|`.4529504`|`.0297431`|`15.23`|`0.000`|`.394655`|`.5112458`|
|`p_ecstat_hh_2`|`-.1803367`|`.0690036`|`-2.61`|`0.009`|`-.3155813`|`-.0450921`|
|`p_elder_sh`|`.4871691`|`.0363326`|`13.41`|`0.000`|`.4159585`|`.5583797`|
|`p_hhsize_1`|`-.1331209`|`.0253237`|`-5.26`|`0.000`|`-.1827544`|`-.0834874`|
|`p_isced_max_0`|`-.5169389`|`.0540608`|`-9.56`|`0.000`|`-.6228961`|`-.4109817`|
|`p_isced_max_1`|`-.3758244`|`.0257253`|`-14.61`|`0.000`|`-.426245`|`-.3254037`|
|`p_isced_max_2`|`-.221132`|`.0191942`|`-11.52`|`0.000`|`-.2587519`|`-.1835122`|
|`p_isced_max_4`|`.138612`|`.0286283`|`4.84`|`0.000`|`.0825016`|`.1947225`|
|`p_isced_max_5`|`.2343928`|`.024233`|`9.67`|`0.000`|`.1868969`|`.2818887`|
|`p_isced_max_6`|`.237176`|`.0802218`|`2.96`|`0.003`|`.0799442`|`.3944078`|
|`p_male`|`.1836228`|`.0218718`|`8.40`|`0.000`|`.140755`|`.2264906`|
|`p_marital_hh_1`|`-.052893`|`.030501`|`-1.73`|`0.083`|`-.1126738`|`.0068878`|
|`p_marital_hh_3`|`-.0809455`|`.0206275`|`-3.92`|`0.000`|`-.1213747`|`-.0405163`|
|`p_occup_pr_sh`|`.3670144`|`.0363299`|`10.10`|`0.000`|`.2958092`|`.4382196`|
|`p_workstat_1_sh`|`.5260943`|`.0270113`|`19.48`|`0.000`|`.4731532`|`.5790354`|
|`rooms_pc`|`.0470549`|`.0109036`|`4.32`|`0.000`|`.0256843`|`.0684255`|
|`_cons`|`7.132082`|`.1597874`|`44.63`|`0.000`|`6.818904`|`7.445259`|
|`Alpha model:`|||||||
|`Residual`|`Coef.`|`Std. Err.`|`z`|`P>|z|`|`[95% Conf.`|`Interval]`|
|`p_activity_1_sh`|`-.3447938`|`.1425119`|`-2.42`|`0.016`|`-.624112`|`-.0654756`|
|`p_ecstat_4_sh`|`-.8035096`|`.1585224`|`-5.07`|`0.000`|`-1.114208`|`-.4928114`|
|`p_ecstat_hh_4`|`-.3006224`|`.118973`|`-2.53`|`0.012`|`-.5338051`|`-.0674397`|

matrix presented by the PovMap software is equal to _σ_<sup>2 �</sup> ( _X_<sup>_′_</sup> _WX_ )<sup>_−_1 �</sup> _X_<sup>_′_</sup> _W_<sup>2</sup> _X_<sup>�</sup> ( _X_<sup>_′_</sup> _WX_ )<sup>_−_1�</sup> where _σ_<sup>2</sup> is an estimate of Var( _wchuch_ ). It is easy to see that the weights are included twice in the variance covariance estimator, which makes it non-standard.

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