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:
R
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
Result comparison
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 |