7  Modeling

library(tidyverse)
library(scales)
library(janitor)
library(survey)
library(srvyr)
library(gtsummary)

A one-way ANOVA is equivalent to a linear model with a single categorical variable. A two-sample t-test is equivalent to an ANOVA with a two-level categorical predictor.

7.1 ANOVA

ANOVA tests whether the mean outcome is the same across groups. It is equivalent to the linear model. A full explanation of ANOVA is here, but with survey analysis, the equal variances assumption does not apply because of the weighting.

apistrat |>
  ggplot(aes(x = hsg_cut, y = api00)) +
  geom_boxplot()

svyglm(
  api00 ~ hsg_cut,
  design = apistrat_des
) |>
  gtsummary::tbl_regression(intercept = TRUE)

Characteristic

Beta

95% CI

1

p-value
(Intercept) 759 722, 795 <0.001
hsg_cut


    [0,12] — —
    (12,25] -100 -145, -56 <0.001
    (25,100] -154 -198, -109 <0.001
1

CI = Confidence Interval

7.2 Linear Regression

apistrat |>
  ggplot(aes(x = api99, y = api00)) +
  geom_point() +
  facet_wrap(vars(hsg_cut))

svyglm(
  api00 ~ api99 + hsg_cut,
  design = apistrat_des
) |>
  gtsummary::tbl_regression(intercept = TRUE)

Characteristic

Beta

95% CI

1

p-value
(Intercept) 62 35, 90 <0.001
api99 0.95 0.91, 0.98 <0.001
hsg_cut


    [0,12] — —
    (12,25] 2.7 -8.2, 14 0.6
    (25,100] 7.1 -4.4, 19 0.2
1

CI = Confidence Interval

7.3 Logistic Regression

apistrat_des |>
  summarize(
    .by = meals_cut,
    met_pct = survey_mean(
      sch.wide == "Yes", na.rm = TRUE, proportion = TRUE, vartype = "ci"
    )
  ) |>
  ggplot(aes(x = meals_cut, y = met_pct)) +
  geom_col(width = .4) +
  geom_errorbar(aes(ymin = met_pct_low, ymax = met_pct_upp), width = .1)

svyglm(
  sch.wide ~ api99 + meals_cut,
  design = apistrat_des,
  family = quasibinomial
) |>
  gtsummary::tbl_regression(intercept = TRUE) |>
  as_gt() |>
  gt::tab_caption("Logistic regression of meeting school-wide target by API in 1999.")
Table 7.1: Logistic regression of meeting school-wide target by API in 1999.

Characteristic

log(OR)

1

95% CI

1

p-value
(Intercept) -3.4 -7.3, 0.41 0.080
api99 0.01 0.00, 0.01 0.013
meals_cut


    [0,12] — —
    (12,25] 0.87 -0.49, 2.2 0.2
    (25,100] 1.8 0.13, 3.4 0.034
1

OR = Odds Ratio, CI = Confidence Interval