6 Analytic weights and estimation of model parameters
Analytic use of survey data on estimation of model parameters has been discussed briefly in Chapter 2. The analytic weights, which are rescaled from the design weights (or inflation weights) with sum equaling to the sample size, are often used. They produce the same point estimates and variance estimates under non-stratified sampling. Under stratified sampling where strata have very different sizes, units in some large strata, such as the province of Ontario in the CLSA datasets, have much larger weights and observations from these large strata often dominate the analysis (Scott 2006; Thompson 2008). A common practice in creating analytic weights under stratified sampling is to rescale the weights within each stratum such that the total stratum weight equals to the stratum sample size. The resulting estimates of the model parameters are not identical to the estimates using the inflation weights but are more stable and also interpretable for the given finite population (Thompson 2008).
The analytic weights of the CLSA datasets are provided with the names \(\texttt{WGHTS_ANALYTIC_***}\). For the datasets from the Tracking cohort, the weights are given by the variable with the name \(\texttt{WGHTS_ANALYTIC_TRM}\) and are proportional to the inflation weights but rescaled to sum to the sample size within each province so that their mean value is one within each province. For the datasets from the Comprehensive cohort, the weights are given by the variable \(\texttt{WGHTS_ANALYTIC_COM}\) and are proportional to the inflation weights but rescaled to sum to the sample size within the individual DCS part of each province, so that their mean value is one within each individual DCS. The analytic weights \(\texttt{WGHTS_ANALYTIC_CLSAM}\) were also provided for the pooled data with the mean value of one within each individual DCS and provincial Non-DCS area.
Details of the analytic weights in other datasets are provided in the CLSA technical document on sample weights (Canadian Longitudinal Study on Aging 2020).The survey design can be declared similarly as in Chapter 4 except replacing the survey weight with \(\texttt{WGHTS_ANALYTIC_TRM}\).
R
SPSS
We declare the survey design by clicking “\(\texttt{Analyze}\)” \(\rightarrow\) \(\texttt{Complex Samples}\) \(\rightarrow\) \(\texttt{Prepare for Analysis}\) \(\rightarrow\) click “\(\texttt{Create a plan file}\)” and choose a location and name as \(\texttt{CLSADesignAnyl.csaplan}\) \(\rightarrow\) “\(\texttt{Next}\)”. Under Strata, select the variables “\(\texttt{StraVar}\)” and select “\(\texttt{WGHT_ANALYTIC_TRM}\)” under “Sampling Weight” and accept the default settings.