7.3 Linear regression in domain analysis

As mentioned in Chapter 6.2, there are only a few numerical variables in the CLSA Tracking cohort suitable for linear regression. We choose the self-reported height and weight variables to demonstrate the linear regression in domain analysis. Suppose that we want to investigate the relationship of self-reported height and weight within the subpopulation which are interviewed in English, we may apply the following codes.

R

LinearReg_EN<-svyglm(HWT_DHT_M_TRM~HWT_WGHT_KG_TRM+SEX_ASK_TRM+ 
                     Age_group_5 + Education + WGHTS_PROV_TRM, 
                     family = "gaussian",
                     design = subset(CLSA.design.anly, startlanguage = "en"))
summary(LinearReg_EN)

SAS

PROC SURVEYREG data = CLSAData ;
CLASS SEX_ASK_TRM(ref = 'F') Age_group_5(ref = '45-48') 
      Education(ref = 'Low Education') WGHTS_PROV_TRM(ref = 'AB');
MODEL HWT_DHT_M_TRM = HWT_WGHT_KG_TRM SEX_ASK_TRM Age_group_5 
      Education WGHTS_PROV_TRM / solution ;
DOMAIN  startlanguage; 
STRATA  GEOSTRAT_TRM ;
WEIGHT  WGHTS_ANALYTIC_TRM;
ODS output ParameterEstimates = EST;
RUN;
    
PROC PRINT data = EST;
WHERE  startlanguage ='en';
FORMAT _numeric_ 15.9; run; 

SPSS

Analyze \(\rightarrow\) Complex Samples \(\rightarrow\) General Linear Model… \(\rightarrow\) Select the file “CLSADesignAnyl.csaplan” in the Plan panel \(\rightarrow\) select [Target Variables] to the “Dependent Variable”, “Factor” and “Covariate” panels \(\rightarrow\) 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

svyset entity_id, strata(StraVar) weight(WGHTS_ANALYTIC_TRM) vce(linearized)
singleunit(certainty) 
svy linearized, subpop(if  startlanguage == "en"): 
regress HWT_DHT_M_TRM HWT_WGHT_KG_TRM i.SEX_ASK_TRM i.Age_group_5 
        ib3.Education i.WGHTS_PROV_TRM
estimates table, b(%10.0g) se(%10.0g)

Result comparison

	R		SAS		SPSS		Stata
Population Estimates	Coeff.	SE	Coeff.	SE	Coeff.	SE	Coeff.	SE
(Intercept)	1.5487	0.0218	1.5487	0.0221	1.5487	0.0218	1.5487	0.0218
HWT_WGHT_KG_TRM	0.0008	0.0002	0.0008	0.0002	0.0008	0.0002	0.0008	0.0002
SEX_ASK_TRM=“M”	0.0866	0.0076	0.0866	0.0077	0.0866	0.0076	0.0866	0.0076
Age Groups: relative to Age_Gpr0: Age 45-48
Age_Gpr1:Age 49-54	0.0077	0.0131	0.0077	0.0133	0.0077	0.0131	0.0077	0.0131
Age_Gpr2:Age 55-64	0.0185	0.0123	0.0185	0.0125	0.0185	0.0123	0.0185	0.0123
Age_Gpr3:Age 65-74	0.0053	0.0134	0.0053	0.0136	0.0053	0.0134	0.0053	0.0134
Age_Gpr4:Age 75+	0.0069	0.0139	0.0069	0.0141	0.0069	0.0139	0.0069	0.0139
Education Levels: relative to Lower Education
Medium Education	0.0203	0.0091	0.0203	0.0092	0.0203	0.0091	0.0203	0.0091
Higher Education lower	0.0232	0.0110	0.0232	0.0111	0.0232	0.0110	0.0232	0.0110
Higher Education upper	0.0265	0.0091	0.0265	0.0093	0.0265	0.0091	0.0265	0.0091
Provinces: relative to Alberta
British Columbia	-0.0143	0.0124	-0.0143	0.0125	-0.0143	0.0124	-0.0143	0.0124
Manitoba	0.0263	0.0189	0.0263	0.0191	0.0263	0.0189	0.0263	0.0189
New Brunswick	0.0048	0.0147	0.0048	0.0149	0.0048	0.0147	0.0048	0.0147
Newfoundland & Labrador	0.0166	0.0120	0.0166	0.0122	0.0166	0.0120	0.0166	0.0120
Nova Scotia	-0.0311	0.0127	-0.0311	0.0129	-0.0311	0.0127	-0.0311	0.0127
Ontario	-0.0075	0.0105	-0.0075	0.0106	-0.0075	0.0105	-0.0075	0.0105
Prince Edward Island	-0.0132	0.0159	-0.0132	0.0161	-0.0132	0.0159	-0.0132	0.0159
Quebec	-0.0134	0.0117	-0.0134	0.0118	-0.0134	0.0117	-0.0134	0.0117
Saskatchewan	0.0028	0.0157	0.0028	0.0159	0.0028	0.0157	0.0028	0.0157