nrba (version 0.3.1)

predict_response_status_via_glm: Fit a logistic regression model to predict response to the survey.

Description

A logistic regression model is fit to the sample data to predict whether an individual responds to the survey (i.e. is an eligible respondent) rather than a nonrespondent. Ineligible cases and cases with unknown eligibility status are not included in this model.

The function returns a summary of the model, including overall tests for each variable of whether that variable improves the model's ability to predict response status in the population of interest (not just in the random sample at hand).

This model can be used to identify auxiliary variables associated with response status and compare multiple auxiliary variables in terms of their ability to predict response status.

Usage

predict_response_status_via_glm(
  survey_design,
  status,
  status_codes = c("ER", "EN", "IE", "UE"),
  numeric_predictors = NULL,
  categorical_predictors = NULL,
  model_selection = "main-effects",
  selection_controls = list(alpha_enter = 0.5, alpha_remain = 0.5, max_iterations = 100L)
)

Value

A data frame summarizing the fitted logistic regression model.

Each row in the data frame represents a coefficient in the model. The column variable describes the underlying variable for the coefficient. For categorical variables, the column variable_category indicates the particular category of that variable for which a coefficient is estimated.

The columns estimated_coefficient, se_coefficient, conf_intrvl_lower, conf_intrvl_upper, and p_value_coefficient are summary statistics for the estimated coefficient. Note that p_value_coefficient is based on the Wald t-test for the coefficient.

The column variable_level_p_value gives the p-value of the Rao-Scott Likelihood Ratio Test for including the variable in the model. This likelihood ratio test has its test statistic given by the column LRT_chisq_statistic, and the reference distribution for this test is a linear combination of p F-distributions with numerator degrees of freedom given by LRT_df_numerator and denominator degrees of freedom given by LRT_df_denominator, where p is the number of coefficients in the model corresponding to the variable being tested.

Arguments

survey_design

A survey design object created with the survey package.

status

A character string giving the name of the variable representing response/eligibility status. The status variable should have at most four categories, representing eligible respondents (ER), eligible nonrespondents (EN), known ineligible cases (IE), and cases whose eligibility is unknown (UE).

status_codes

A named vector, with two entries named 'ER' and 'EN' indicating which values of the status variable represent eligible respondents (ER) and eligible nonrespondents (EN).

numeric_predictors

A list of names of numeric auxiliary variables to use for predicting response status.

categorical_predictors

A list of names of categorical auxiliary variables to use for predicting response status.

model_selection

A character string specifying how to select a model. The default and recommended method is 'main-effects', which simply includes main effects for each of the predictor variables.
The method 'stepwise' can be used to perform stepwise selection of variables for the model. However, stepwise selection invalidates p-values, standard errors, and confidence intervals, which are generally calculated under the assumption that model specification is predetermined.

selection_controls

Only required if model-selection isn't set to "main-effects". Otherwise, a list of parameters for model selection to pass on to stepwise_model_selection, with elements alpha_enter, alpha_remain, and max_iterations.

Details

See Lumley and Scott (2017) for details of how regression models are fit to survey data. For overall tests of variables, a Rao-Scott Likelihood Ratio Test is conducted (see section 4 of Lumley and Scott (2017) for statistical details) using the function regTermTest(method = "LRT", lrt.approximation = "saddlepoint") from the 'survey' package.

If the user specifies model_selection = "stepwise", a regression model is selected by adding and removing variables based on the p-value from a likelihood ratio rest. At each stage, a single variable is added to the model if the p-value of the likelihood ratio test from adding the variable is below alpha_enter and its p-value is less than that of all other variables not already in the model. Next, of the variables already in the model, the variable with the largest p-value is dropped if its p-value is greater than alpha_remain. This iterative process continues until a maximum number of iterations is reached or until either all variables have been added to the model or there are no unadded variables for which the likelihood ratio test has a p-value below alpha_enter.

References

• Lumley, T., & Scott A. (2017). Fitting Regression Models to Survey Data. Statistical Science 32 (2) 265 - 278. https://doi.org/10.1214/16-STS605

Examples

library(survey)

# Create a survey design ----
data(involvement_survey_str2s, package = "nrba")

survey_design <- survey_design <- svydesign(
  data = involvement_survey_str2s,
  weights = ~BASE_WEIGHT,
  strata = ~SCHOOL_DISTRICT,
  ids = ~ SCHOOL_ID + UNIQUE_ID,
  fpc = ~ N_SCHOOLS_IN_DISTRICT + N_STUDENTS_IN_SCHOOL
)

predict_response_status_via_glm(
  survey_design = survey_design,
  status = "RESPONSE_STATUS",
  status_codes = c(
    "ER" = "Respondent",
    "EN" = "Nonrespondent",
    "IE" = "Ineligible",
    "UE" = "Unknown"
  ),
  model_selection = "main-effects",
  numeric_predictors = c("STUDENT_AGE"),
  categorical_predictors = c("PARENT_HAS_EMAIL", "STUDENT_GRADE")
)