Modeling with Survey Design: Understanding the Issues with svyglm

Survey design is a crucial aspect of statistical modeling, especially when dealing with data from complex surveys such as those conducted by the National Center for Health Statistics (NCHS). The svyglm function in R is designed to handle survey data and provide estimates that are adjusted for the survey design. However, even with this powerful tool, there are potential issues that can arise, leading to unexpected results.

In this article, we’ll delve into one such issue that has been reported by users of svyglm, specifically when running unadjusted models versus full-adjusted standard errors. We’ll explore what might be causing these differences and how they can be resolved.

Understanding the Basics of svyglm

svyglm is a function in R that performs generalized linear mixed models (GLMMs) with survey design. When you run svyglm, you’re essentially estimating the relationship between one or more predictor variables and an outcome variable, while accounting for the survey design and its potential biases.

The basic syntax of svyglm is as follows:

unadjustedmodel <- svyglm(Y ~ X1 + X2,
                          family = gaussian(),
                          data   = nhanesDesign,
                          design = ageDesign)

In this example, we’re estimating the relationship between Y (the outcome variable) and two predictor variables X1 and X2, using a Gaussian distribution for the outcome. The data argument specifies the survey data frame (nhanesDesign), while the design argument specifies the design object used to describe the survey structure (ageDesign).

The Issue: Unadjusted vs Full-Adjusted Standard Errors

When running an unadjusted model using svyglm, you might expect to get standard errors for the coefficients. However, if you’re using a full-adjusted model (i.e., one that includes additional variables in the model), you may encounter issues with standard errors returning infinity (Inf).

To illustrate this issue, let’s consider two example models:

Unadjusted Model:

unadjustedmodel <- svyglm(HASMM ~ periocat3,
                         family = gaussian(),
                         data   = nhanesDesign,
                         design = ageDesign)

Full-Adjusted Model:

interactmodelsmmi <- svyglm(HASMM ~ periocat3 + RIAGENDR + RIDAGEYR +
                           DXDTOBMD  + BMXBMI + relevel(smoking, ref="Non-Smoker") +
                           education + DR1TKCAL + DR1TPROT + LBXVIDMS,
                           RIAGENDR*RIDAGEYR + DXDTOBMD*MGDCGSZ,
                           family = gaussian(),
                           data   = nhanesDesign,
                           design = ageDesign,
                           df=degf(nhanesDesign),
                           na.action=na.exclude)

As you can see, the only difference between these two models is the inclusion of additional variables in the full-adjusted model.

Why Do We Get Inf Standard Errors?

So, why do we get Inf standard errors when using a full-adjusted model versus an unadjusted one? The answer lies in the way that svyglm handles degrees of freedom and the survey design.

When you run an unadjusted model using svyglm, you’re essentially estimating the relationship between the predictor variables and the outcome variable, without accounting for any additional variables. In this case, the number of parameters being estimated is equal to the number of predictors (periocat3 in our example). However, when you use a full-adjusted model with multiple additional variables, the number of parameters being estimated increases significantly.

The problem arises because svyglm uses the standard estimate of residual degrees of freedom to calculate the standard errors. In this case, however, the residual degrees of freedom are negative (i.e., less than the number of predictors). This leads to the calculation of Inf standard errors, as the formula for standard error becomes undefined when the denominator is zero or negative.

Resolving the Issue: Specifying Degrees of Freedom

So, how can we resolve this issue? The answer lies in specifying degrees of freedom correctly. While it’s not possible to specify the degrees of freedom directly in the svyglm function, you can use the summary method with an additional argument for residual degrees of freedom.

To illustrate this, let’s modify our example code:

interactmodelsmmi <- svyglm(HASMM ~ periocat3 + RIAGENDR + RIDAGEYR +
                           DXDTOBMD  + BMXBMI + relevel(smoking, ref="Non-Smoker") +
                           education + DR1TKCAL + DR1TPROT + LBXVIDMS,
                           RIAGENDR*RIDAGEYR + DXDTOBMD*MGDCGSZ,
                           family = gaussian(),
                           data   = nhanesDesign,
                           design = ageDesign,
                           na.action=na.exclude)

summary(interactmodelsmmi, df.resid=degf(ageDesign))

By specifying df.resid=degf(ageDesign), we’re telling R to use the residual degrees of freedom calculated from the survey design object (ageDesign) when calculating the standard errors.

Additional Considerations

There are a few additional considerations that might be worth noting:

• When using svyglm, it’s essential to ensure that the design objects used to describe the survey structure are correctly specified. This includes specifying the correct design matrix, weights, and strata information.
• If you’re experiencing issues with standard errors returning infinity, try checking your residual degrees of freedom by adding an additional argument to the summary method (e.g., df.resid=degf(ageDesign)).
• Always verify that your model assumptions are met before interpreting the results.

By following these guidelines and considering additional factors, you should be able to resolve any issues with standard errors returning infinity when using svyglm.

Last modified on 2024-11-25