mariposa (version 0.7.3)

logistic_regression: Run a Logistic Regression

Description

logistic_regression() performs binary logistic regression with SPSS-compatible output. Wraps stats::glm(family = binomial) and adds odds ratios, pseudo R-squared measures, classification table, and model tests matching SPSS LOGISTIC REGRESSION output.

Supports two interface styles:

• Formula interface: logistic_regression(data, high_satisfaction ~ age + income)

• SPSS-style: logistic_regression(data, dependent = high_satisfaction, predictors = c(age, income))

Usage

logistic_regression(
  data,
  formula = NULL,
  dependent = NULL,
  predictors = NULL,
  weights = NULL,
  conf.level = 0.95,
  factors = c("dummy", "numeric")
)

Value

For ungrouped data, an object of class c("logistic_regression", "glm", "lm") — the fitted glm itself, with mariposa-specific slots attached:

coef_table

Tibble with B, S.E., Wald, df, Sig., Exp(B), CI_lower, CI_upper

model_summary

List with minus2LL, cox_snell_r2, nagelkerke_r2, mcfadden_r2

omnibus_test

List with chi_sq, df, p for overall model test

classification

List with table, overall_pct, pct_correct_0, pct_correct_1

hosmer_lemeshow

List with chi_sq, df, p (goodness-of-fit test)

n

Sample size (listwise complete cases; weighted N when weighted)

formula, dependent, predictor_names, weighted, weight_name, is_grouped, conf.level

Call metadata.

Because the object inherits from "glm", all standard generics (predict(), anova(), vcov(), confint(), residuals(), fitted(), coef(), broom::tidy(), broom::glance(), broom::augment()) dispatch natively without unwrapping. summary() returns the SPSS-style mariposa summary; for the raw glm summary use stats::summary.glm() on the same object.

For grouped data, returns a list of class "logistic_regression"

with $groups holding one fitted glm-inheriting result per group.

Arguments

data

Your survey data (a data frame or tibble). If grouped (via dplyr::group_by()), separate regressions are run for each group.

formula

A formula specifying the model (e.g., y ~ x1 + x2). If provided, dependent and predictors are ignored.

dependent

The dependent variable (unquoted). Used with predictors when no formula is given. Must be binary (0/1 or two-level factor).

predictors

Predictor variable(s) (unquoted, supports tidyselect). Used with dependent when no formula is given.

weights

Optional survey weights (unquoted variable name). When specified, weighted maximum likelihood estimation is used, matching SPSS WEIGHT BY behavior.

conf.level

Confidence level for odds ratio intervals (default 0.95).

factors

How factor predictors are entered into the model: "dummy" (default, matches base R glm()) expands a factor with L levels into L - 1 contrasts; "numeric" silently coerces factor levels to their integer codes, matching SPSS LOGISTIC REGRESSION default behavior when no /CATEGORICAL subcommand is given. The "numeric" mode emits a one-line cli::cli_inform() listing the coerced variables. Note that for ordered factors, "dummy" applies R's default polynomial contrasts (terms suffixed .L, .Q, .C), not treatment dummies; convert with factor(x, ordered = FALSE) first if you want dummy coding.

Details

Understanding the Results

The output includes five sections matching SPSS LOGISTIC REGRESSION output:

• Omnibus Test: Tests whether the model as a whole is significant. A significant chi-square means the model predicts better than chance.

• Model Summary: -2 Log Likelihood and pseudo R-squared values. Lower -2LL = better fit. Higher R-squared = more variance explained.

• Hosmer-Lemeshow Test: Goodness-of-fit test. A non-significant result (p > 0.05) means the model fits the data well.

• Classification Table: How well the model classifies cases. Shows percentage correctly predicted for each group and overall.

• Coefficients: B, Wald test, odds ratios (Exp(B)), and CIs.

Interpreting odds ratios (Exp(B)):

• Exp(B) > 1: Predictor increases the odds of the outcome

• Exp(B) < 1: Predictor decreases the odds of the outcome

• Exp(B) = 1: Predictor has no effect on the odds

When to Use This

Use logistic_regression() when:

• Your dependent variable is binary (yes/no, 0/1, pass/fail)

• You want to predict group membership from one or more predictors

• You need odds ratios to interpret predictor effects

For continuous outcomes, use linear_regression instead.

Technical Details

Dependent Variable: Must be binary. Factors with exactly 2 levels are automatically converted to 0/1 (first level = 0, second level = 1). Numeric variables must contain only 0 and 1 values.

Missing Data: Listwise deletion is used (matching SPSS LOGISTIC REGRESSION default behavior).

Weights: When weights are specified, they are treated as frequency weights (matching SPSS WEIGHT BY behavior).

Pseudo R-squared: Three measures are reported:

• Cox & Snell R-squared (bounded below 1)

• Nagelkerke R-squared (adjusted to reach 1)

• McFadden R-squared (1 - LL_model/LL_null)

Factor Predictors: By default (factors = "dummy"), factor predictors are expanded into L - 1 contrasts via R's stats::model.matrix(), matching base R glm(): unordered factors get treatment (dummy) contrasts against the first level, while ordered factors get R's default polynomial contrasts (.L/.Q/.C terms). Pass factors = "numeric" to silently coerce factor levels to their integer codes (SPSS LOGISTIC REGRESSION default without an explicit /CATEGORICAL subcommand).

Grouped Analysis: When data is grouped via dplyr::group_by(), a separate regression is run for each group (matching SPSS SPLIT FILE BY).

See Also

linear_regression for continuous outcome variables.

chi_square for testing associations between categorical variables.

summary.logistic_regression for detailed output with toggleable sections.

Other regression: linear_regression(), marginal_effects()

Examples

library(dplyr)
data(survey_data)

# Create binary DV
survey_data$high_satisfaction <- ifelse(survey_data$life_satisfaction >= 4, 1, 0)

# Bivariate logistic regression
logistic_regression(survey_data, high_satisfaction ~ age)

# Multiple logistic regression
logistic_regression(survey_data, high_satisfaction ~ age + income + education)

# SPSS-style interface
logistic_regression(survey_data,
                    dependent = high_satisfaction,
                    predictors = c(age, income))

# Weighted logistic regression
logistic_regression(survey_data, high_satisfaction ~ age,
                    weights = sampling_weight)

# Grouped by region
survey_data |>
  dplyr::group_by(region) |>
  logistic_regression(high_satisfaction ~ age)

# Factor predictors: dummy-coding (default, matches base R glm())
logistic_regression(survey_data, high_satisfaction ~ age + education)

# Factor predictors: SPSS-style ordinal-as-scale
logistic_regression(survey_data, high_satisfaction ~ age + education,
                    factors = "numeric")

# --- Three-layer output ---
result <- logistic_regression(survey_data, high_satisfaction ~ age + income)
result                                    # compact one-line overview
summary(result)                           # full detailed SPSS-style output
summary(result, classification = FALSE)   # hide classification table