7.5 Multinomial logistic regression in domain analysis

In Chapter 6.4, we created the variable, \(\texttt{WEA_MRTL_CURRENT_NEW}\) representing the current marital status (“Single,” “Married,” and “Others”). Suppose we are interested in the current marital status of the subpopulation which uses English to answer the questionnaire.

R There is no official support for multinomial regression directly from the \(\texttt{survey}\) package in \(\texttt{R}\).

SAS

PROC SURVEYLOGISTIC data = CLSAData ;            
CLASS WEA_MRTL_CURRENT_NEW(ref = 'Single') WGHTS_PROV_TRM(ref = 'AB')
      Age_group_5(ref = '45-48') SEX_ASK_TRM(ref = 'F')
      Education(ref = 'Low Education')/param = ref;
MODEL WEA_MRTL_CURRENT_NEW = SEX_ASK_TRM Age_group_5 Education
      WGHTS_PROV_TRM /link = glogit; 
DOMAIN startlanguage;     
STRATA GEOSTRAT_TRM;             
WEIGHT WGHTS_ANALYTIC_TRM;  
ODS output  ParameterEstimates = EST;              
RUN; 

PROC SORT data = EST Out = MyParmEst ;
BY Response; 
WHERE  startlanguage = "en";
RUN; 

PROC PRINT data = MyParmEst; RUN;

SPSS

Analyze \(\rightarrow\) Complex Samples \(\rightarrow\) Logistc Regression…
\(\rightarrow\) in the “Plan” panel, select the file “\(\texttt{CLSADesignAnyl.csaplan}\)” \(\rightarrow\) click “Continue” \(\rightarrow\) select the corresponding variables to the “Dependent Variable”, “Factor” and “Covariate” panels \(\rightarrow\) click “Reference Category” and select “Lowest value” \(\rightarrow\) select “\(\texttt{startlanguage}\)” to the “Subpopulations” panel and enter the target category \(\rightarrow\) click “Statistics…” \(\rightarrow\) select “Estimate” and “Standard error” \(\rightarrow\) click “Continue” \(\rightarrow\) click “OK”.

Stata

svy linearized, subpop(if  startlanguage == "en"): mlogit WEA_MRTL_CURRENT_New  
  i.SEX_ASK_TRM i.Age_group_5 ib3.Education i.WGHTS_PROV_TRM, baseoutcome(1)
Result comparison
Population Estimates
SAS
SPSS
Stata
Population Est. Est. SE Est. SE Est. SE
2:Married
(Intercept) 1.9466 1.1853 1.9466 1.1591 1.9466 1.1591
SEX_ASK_TRM=“M” 0.3502 0.4382 0.3502 0.4285 0.3502 0.4284
Age Groups: relative to Age_Gpr0: Age 45-48
Age_Gpr1:Age 49-54 -0.8421 0.9684 -0.8421 0.9470 -0.8421 0.9469
Age_Gpr2:Age 55-64 -0.4370 0.9026 -0.4370 0.8826 -0.4370 0.8826
Age_Gpr3:Age 65-74 -1.3042 0.9379 -1.3042 0.9172 -1.3042 0.9171
Age_Gpr4:Age 75+ -0.0157 1.0214 -0.0157 0.9987 -0.0157 0.9987
Education Levels: relative to Lower Education
Medium Education 0.3665 0.6343 0.3665 0.6202 0.3665 0.6202
Higher Education lower 0.0851 0.6725 0.0851 0.6576 0.0851 0.6576
Higher Education upper 0.5684 0.6446 0.5684 0.6303 0.5684 0.6303
Provinces: relative to Alberta
British Columbia -0.4055 0.8759 -0.4055 0.8565 -0.4055 0.8565
Manitoba -0.6105 0.9204 -0.6105 0.9000 -0.6106 0.9000
New Brunswick -0.4589 1.0576 -0.4589 1.0342 -0.4592 1.0341
Newfoundland & Labrador 0.6142 1.0791 0.6142 1.0552 0.6142 1.0552
Nova Scotia 0.0791 1.0709 0.0791 1.0472 0.0790 1.0472
Ontario 0.2354 0.8047 0.2354 0.7869 0.2354 0.7869
Prince Edward Island 12.8690 0.8114 19.8690 0.0000 13.8779 0.7935
Quebec -0.5356 0.8771 -0.5356 0.8577 -0.5357 0.8577
Saskatchewan 1.5866 1.1386 1.5866 1.1134 1.5879 1.1140
3:Other
(Intercept) 1.6253 1.6272 1.6253 1.5912 1.6255 1.5911
SEX_ASK_TRM=“M” -0.6157 0.5394 -0.6157 0.5275 -0.6157 0.5274
Age Groups: relative to Age_Gpr0: Age 45-48
Age_Gpr1:Age 49-54 -1.4500 1.3597 -1.4500 1.3296 -1.4501 1.3295
Age_Gpr2:Age 55-64 -0.6046 1.2955 -0.6046 1.2668 -0.6046 1.2667
Age_Gpr3:Age 65-74 -0.3936 1.2713 -0.3936 1.2432 -0.3935 1.2431
Age_Gpr4:Age 75+ -0.3864 1.3586 -0.3864 1.3285 -0.3864 1.3284
Education Levels: relative to Lower Education
Medium Education 0.7692 0.8135 0.7692 0.7955 0.7692 0.7955
Higher Education lower 0.4620 0.8535 0.4620 0.8346 0.4620 0.8346
Higher Education upper 0.2891 0.8346 0.2891 0.8161 0.2891 0.8161
Provinces: relative to Alberta
British Columbia -0.8886 0.9615 -0.8886 0.9402 -0.8887 0.9402
Manitoba -2.3652 1.1535 -2.3652 1.1280 -2.3657 1.1280
New Brunswick -2.7147 1.3314 -2.7147 1.3020 -2.7162 1.3024
Newfoundland & Labrador -0.5965 1.2711 -0.5965 1.2429 -0.5967 1.2428
Nova Scotia -1.3207 1.2335 -1.3207 1.2062 -1.3208 1.2061
Ontario -0.6761 0.8822 -0.6761 0.8627 -0.6762 0.8627
Prince Edward Island 12.9517 0.8655 19.9517 6.9021 13.9607 0.8462
Quebec -1.2976 0.9965 -1.2976 0.9744 -1.2978 0.9744
Saskatchewan 1.2386 1.1998 1.2386 1.1733 1.2398 1.1738

Note:

Both \(\texttt{SAS}\) and \(\texttt{SPSS}\) detect that there is a quasi-complete separation in the dataset while \(\texttt{Stata}\) does not.This results in the slight differences in the estimates and the standard errors.