Design-based single-mediator approach for complex survey data

Figures & data

Figure 1. Single-mediator model with I covariates.

Table 1. Sample summary statistics for factors considered as covariates; 2010–2011 and 2014–2015 tobacco use supplement to the current population survey.

Characteristic	Sample count	Percent (%)*
Age group
18–24	2,149	11.6
25–44	11,503	37.4
45–64	13,660	41.7
65+	3,465	9.4
Sex
Male	14,905	52.2
Female	15,872	48.8
Highest level of education
Less than high school	4,756	16.0
High school (or equivalent)	13,070	42.3
Some college or a bachelor's degree	12,203	39.4
Graduate degree (or equivalent)	748	2.3
Employment record
Employed	17,844	58.6
Unemployed	2,630	9.6
Not in labor force	10,303	31.8
Marital status
Married (spouse is present or absent)	12,511	39.0
Widowed, divorced, or separated	10,174	30.6
Never married	8,092	30.4
Region of residency
Northeast	5,420	16.5
Midwest	8,641	27.9
South	11,688	42.2
West	5,028	13.4
Area of residency
Metropolitan	21,768	77.7
Non-metropolitan	9,009	22.3
Residing in a state with an Indian Reservation
No	10,433	32.2
Yes	20,344	67.8
Survey mode
Phone	17,395	56.5
In-person	13,382	43.5
Survey year
2010–2011	16,884	54.1
2014–2015	13,893	45.9

*All percentages except for the survey mode are based on the 2010–2011 and 2014–2015 population counts.

Table 2. Testing for the mediated effect: results for each step of the procedure.

Estimated quantity	Description	Estimate	Standard error
Step 1: Estimating the design-based model coefficients
${\widehat{\beta }}_1$	Estimated effect of race/ethnicity on cigarette purchase price	0.58	0.04
$\widehat{\gamma }$	Estimated effect of cigarette purchase price on the average number of cigarettes smoked per day	−0.41	0.03
${\widehat{\beta }}_2$	Estimated effect of race/ethnicity (non-Hispanic Black/African American versus non-Hispanic White) on the average number of cigarettes smoked per day	−4.73	0.15
Step 2: Testing for the mediated effect
${\widehat{\beta }}_1^{\mathrm{*}}{\widehat{\gamma }}^{\mathrm{*}}$	Mediated effect	−0.24	0.02
$Z_G$	Value of the generalized Sobel's test statistic	−9.57
Additional Step: Calculating the relative effect size
$\frac{{\widehat{\beta }}_1\widehat{\gamma }}{{\widehat{\beta }}_2+{\widehat{\beta }}_1\widehat{\gamma }}$	Relative effect size	0.05