The multivariate logistic model is used to assess the factors (IVs used: Age, gender [dropped due to no significant results in any model] partnership status, household size, education, professional position, Austrian citizenship, origin and income quintiles) influencing the unit response rates.

Binary logistic model definition

$$P(Y_i=response)=\frac{1}{1+exp(\beta_0+\beta_1age+\beta_2partner+\beta_3hhsize+\beta_4edu+\beta_5job+\beta_6citizen+\beta_7origin+\beta_8income)}$$.

log_models <- lapply(as.list(levels(WaveOne$Pumavers)), function(x){
  glm(id.net ~ age.cat +
        SD4.dic + # SD4 marital status
        SD5.dic + # SD5 household size
        edu +  # education
        job +  # ocupational position
        SD20 + # SD20 citizenship
        SD21.dic + # origin,
        quintil, # income
      data = WaveOne[WaveOne$id.bru==1,],
      subset = Pumavers==x,
      family = binomial())})

McFadden Pseudo R² for logistic regression

The following formula was applied:

$$R^2_{McFadden}=1-\frac{\ln L_1}{\ln L_0}$$.

Rsquared <- formatC(round(c(
  ZDF = 1 - log_models[[1]]$deviance/log_models[[1]]$null.deviance,
  Two = 1 - log_models[[2]]$deviance/log_models[[2]]$null.deviance,
  Five = 1 - log_models[[3]]$deviance/log_models[[3]]$null.deviance,
  Ten = 1 - log_models[[4]]$deviance/log_models[[4]]$null.deviance),
  3), format="f", digits=3)

Print Table 4

library(stargazer)
tab.html <- stargazer(log_models[[1]],
          log_models[[2]],
          log_models[[3]],
          log_models[[4]],
          type = "html",
          float = FALSE,
          intercept.bottom = FALSE,
          #decimal.mark = ",",
          #digit.separator = ".",
          header = FALSE,
          apply.coef = exp,
          t.auto = FALSE, 
          p.auto = FALSE, 
          report = "vct*",
          #rq.se = "ker",
          add.lines = list(c("McFadden Pseudo-R²",
                             Rsquared["ZDF"],
                             Rsquared["Two"],
                             Rsquared["Five"],
                             Rsquared["Ten"])),
          covariate.labels = c("Constant",
                               "65 years und older",
                               "Up to 24 years",
                               "Yes",
                               "Household (1-4 Persons)",
                               "Higher degree after Matura",
                               "Vocational or commercial school",
                               "Apprenticeship",
                               "Matura",
                               "Max. compulsory schooling",
                               "Worker",
                               "Civil servant",
                               "Pensioner",
                               "Unemployed (inactive)",
                               "Self-employed",
                               "Contract agents",
                               "No",
                               "EU15 with Austria",
                               "Quintil (5=highest)"),
          dep.var.caption = "Response Rate",
          dep.var.labels = c("Brochure",
                             "€2 token",
                             "€5 token",
                             "Voucher"),
          multicolumn = FALSE,
          model.names = TRUE,
          model.numbers = FALSE)

# Fix number of columns 
tab.html <- str_replace_all(tab.html,'colspan=\"5\"','colspan=\"6\"') %>%
  str_replace_all('colspan=\"4\"','colspan=\"5\"') %>%
  str_replace_all('<tr><td style=\"text-align:left\">',
                  '<tr><td style=\"text-align:left\"></td><td style=\"text-align:left\">') 

# Add age entry
tab.html[9] <- str_replace(tab.html[9], 
                           '<tr><td style=\"text-align:left\"></td>',
                            '<tr><td style=\"text-align:left\">Age</td>')

tab.html[10] <- str_replace(tab.html[10], 
                           '<tr><td style=\"text-align:left\"></td>',
                            '<tr><td style=\"text-align:left\">(Ref = 25 to 64 years)</td>')

# Add parnership entry
tab.html[15] <- str_replace(tab.html[15], 
                           '<tr><td style=\"text-align:left\"></td>',
                            '<tr><td style=\"text-align:left\">In partnership</td>')

tab.html[16] <- str_replace(tab.html[16], 
                           '<tr><td style=\"text-align:left\"></td>',
                            '<tr><td style=\"text-align:left\">(Ref = No)</td>')

# Add household size entry
tab.html[18] <- str_replace(tab.html[18], 
                           '<tr><td style=\"text-align:left\"></td>',
                            '<tr><td style=\"text-align:left\">Household size</td>')

tab.html[19] <- str_replace(tab.html[19], 
                           '<tr><td style=\"text-align:left\"></td>',
                            '<tr><td style=\"text-align:left\">(Ref = Household (5+))</td>')

# Add education entry
tab.html[21] <- str_replace(tab.html[21], 
                           '<tr><td style=\"text-align:left\"></td>',
                            '<tr><td style=\"text-align:left\">Education</td>')

tab.html[22] <- str_replace(tab.html[22], 
                           '<tr><td style=\"text-align:left\"></td>',
                            '<tr><td style=\"text-align:left\">(Ref = University degree)</td>')

# Add job entry
tab.html[36] <- str_replace(tab.html[36], 
                           '<tr><td style=\"text-align:left\"></td>',
                            '<tr><td style=\"text-align:left\">Professional position</td>')

tab.html[37] <- str_replace(tab.html[37], 
                           '<tr><td style=\"text-align:left\"></td>',
                            '<tr><td style=\"text-align:left\">(Ref = Clerk)</td>')

# Add citizenship entry
tab.html[54] <- str_replace(tab.html[54], 
                           '<tr><td style=\"text-align:left\"></td>',
                            '<tr><td style=\"text-align:left\">Austrian Citizenship</td>')

tab.html[55] <- str_replace(tab.html[55], 
                           '<tr><td style=\"text-align:left\"></td>',
                            '<tr><td style=\"text-align:left\">(Ref = Yes) </td>')


# Add origin entry
tab.html[57] <- str_replace(tab.html[57], 
                           '<tr><td style=\"text-align:left\"></td>',
                            '<tr><td style=\"text-align:left\">Origin</td>')

tab.html[58] <- str_replace(tab.html[58], 
                           '<tr><td style=\"text-align:left\"></td>',
                            '<tr><td style=\"text-align:left\">(Ref = non-EU15)</td>')

# Add income entry
tab.html[60] <- str_replace(tab.html[60], 
                           '<tr><td style=\"text-align:left\"></td>',
                            '<tr><td style=\"text-align:left\">Income</td>')

cat(tab.html)