6.4 Multinomial logistic regression analysis

The multinomial logistic regression deals with nominal responses with three or more categories.

Suppose we want to investigate the relationship between current marital status (indicated by the variable with the name “\(\texttt{WEA_MRTL_CURRENT_MCQ}\)”) and sex, age group, education level and province. For illustrative purposes, we create a new variable, “\(\texttt{WEA_MRTL_CURRENT_NEW}\),” which regroups the statuses into three categories: “Single,” “Married,” and “Others.” The first category, “Single,” means the respondent never married or never lived with a partner. The second category, “Married,” suggests the respondent is married or living with a partner in a common-law relationship. The last one, “Others,” represents the respondent as either Separated, Devoiced or Widowed. Then, we can use a multinomial logistic regression model with the following codes:

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

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; 
STRATA GEOSTRAT_TRM;             
WEIGHT WGHTS_ANALYTIC_TRM;                
RUN;

SPSS

Analyze \(\rightarrow\) Complex Samples \(\rightarrow\) Logistc Regression…
\(\rightarrow\) in the “Plan panel”,select the survey design 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” \(\rightarrow\) click “Statistics…” \(\rightarrow\) select “Estimate” and “Standard error” \(\rightarrow\) click “Continue” \(\rightarrow\) click “OK”.

Stata

svy linearized : mlogit  WEA_MRTL_CURRENT_New i.SEX_ASK_TRM i.Age_group_5 
       i.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)	1.5091	0.7897	1.5091	0.7722	1.5091	0.7722
SEX_ASK_TRM=“M”	0.4150	0.3551	0.4150	0.3472	0.4150	0.3472
Age Groups: relative to Age_Gpr0: Age 45-48
Age_Gpr1:Age 49-54	0.0252	0.6296	0.0252	0.6157	0.0252	0.6157
Age_Gpr2:Age 55-64	0.5188	0.5783	0.5188	0.5654	0.5188	0.5654
Age_Gpr3:Age 65-74	-0.2058	0.6391	-0.2058	0.6250	-0.2058	0.6250
Age_Gpr4:Age 75+	0.3587	0.6644	0.3587	0.6497	0.3587	0.6497
Education Levels: relative to Lower Education
Medium Education	-0.0016	0.5495	-0.0016	0.5374	-0.0016	0.5374
Higher Education lower	-0.2564	0.6279	-0.2564	0.6140	-0.2564	0.6140
Higher Education upper	0.1072	0.5439	0.1072	0.5318	0.1072	0.5318
Provinces: relative to Alberta
British Columbia	-0.1176	0.7319	-0.1176	0.7157	-0.1176	0.7157
Manitoba	-0.4794	0.7070	-0.4794	0.6913	-0.4794	0.6913
New Brunswick	-0.5986	0.7933	-0.5986	0.7758	-0.5986	0.7758
Newfoundland & Labrador	0.2169	0.8172	0.2169	0.7991	0.2169	0.7991
Nova Scotia	-0.1722	0.7322	-0.1722	0.7160	-0.1722	0.7160
Ontario	0.0488	0.6298	0.0488	0.6159	0.0488	0.6159
Prince Edward Island	0.9048	0.9387	0.9048	0.9180	0.9048	0.9180
Quebec	-0.2347	0.6805	-0.2347	0.6654	-0.2347	0.6654
Saskatchewan	0.0849	0.8042	0.0849	0.7864	0.0849	0.7864
3:Other
(Intercept)	1.7756	0.9228	1.7756	0.9024	1.7756	0.9024
SEX_ASK_TRM=“M”	-0.6869	0.4584	-0.6869	0.4483	-0.6869	0.4483
Age Groups: relative to Age_Gpr0: Age 45-48
Age_Gpr1:Age 49-54	-1.1872	0.7455	-1.1872	0.7290	-1.1872	0.7290
Age_Gpr2:Age 55-64	-0.1678	0.6837	-0.1678	0.6686	-0.1678	0.6686
Age_Gpr3:Age 65-74	0.0113	0.7520	0.0113	0.7353	0.0113	0.7353
Age_Gpr4:Age 75+	-0.4481	0.7719	-0.4481	0.7549	-0.4481	0.7549
Education Levels: relative to Lower Education
Medium Education	-0.2406	0.6505	-0.2406	0.6361	-0.2406	0.6361
Higher Education lower	-0.0115	0.7431	-0.0115	0.7267	-0.0115	0.7267
Higher Education upper	-0.2309	0.6477	-0.2309	0.6334	-0.2309	0.6334
Provinces: relative to Alberta
British Columbia	-0.1949	0.8127	-0.1949	0.7947	-0.1949	0.7947
Manitoba	-1.5001	0.8760	-1.5001	0.8566	-1.5001	0.8566
New Brunswick	-3.2512	1.1595	-3.2512	1.1338	-3.2512	1.1338
Newfoundland & Labrador	-0.9292	0.9574	-0.9292	0.9362	-0.9292	0.9362
Nova Scotia	-0.9059	0.8201	-0.9059	0.8020	-0.9059	0.8020
Ontario	-0.3458	0.6858	-0.3458	0.6706	-0.3458	0.6706
Prince Edward Island	0.7717	1.0176	0.7717	0.9951	0.7717	0.9951
Quebec	-1.0268	0.8057	-1.0268	0.7878	-1.0268	0.7878
Saskatchewan	-0.0518	0.8540	-0.0518	0.8351	-0.0518	0.8351