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
)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,dependentandpredictorsare ignored.- dependent
The dependent variable (unquoted). Used with
predictorswhen no formula is given. Must be binary (0/1 or two-level factor).- predictors
Predictor variable(s) (unquoted, supports tidyselect). Used with
dependentwhen 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).
Value
An object of class "logistic_regression" containing:
- coefficients
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)
- model
The underlying
glmobject- formula
The formula used
- n
Sample size (listwise complete cases)
- dependent
Name of the dependent variable
- predictor_names
Names of predictor variables
- weighted
Logical indicating whether weights were used
- weight_name
Name of the weight variable (or NULL)
Use summary() for the full SPSS-style output with toggleable sections.
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)
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()
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)
#> Logistic Regression: high_satisfaction ~ age
#> Nagelkerke R2 = 0.000, chi2(1) = 0.28, p = 0.595 , Accuracy = 57.7%, N = 2421
# Multiple logistic regression
logistic_regression(survey_data, high_satisfaction ~ age + income + education)
#> Logistic Regression: high_satisfaction ~ age + income + education
#> Nagelkerke R2 = 0.209, chi2(3) = 357.46, p < 0.001 ***, Accuracy = 68.4%, N = 2115
# SPSS-style interface
logistic_regression(survey_data,
dependent = high_satisfaction,
predictors = c(age, income))
#> Logistic Regression: high_satisfaction ~ age + income
#> Nagelkerke R2 = 0.209, chi2(2) = 357.43, p < 0.001 ***, Accuracy = 68.4%, N = 2115
# Weighted logistic regression
logistic_regression(survey_data, high_satisfaction ~ age,
weights = sampling_weight)
#> Logistic Regression: high_satisfaction ~ age [Weighted]
#> Nagelkerke R2 = 0.000, chi2(1) = 0.28, p = 0.595 , Accuracy = 57.6%, N = 2437
# Grouped by region
survey_data |>
dplyr::group_by(region) |>
logistic_regression(high_satisfaction ~ age)
#> Logistic Regression: high_satisfaction ~ age [Grouped: region]
#> region = East: Nagelkerke R2 = 0.002, chi2(1) = 0.74, p = 0.390 , Accuracy = 58.3%, N = 465
#> region = West: Nagelkerke R2 = 0.000, chi2(1) = 0.03, p = 0.860 , Accuracy = 57.6%, N = 1956
# --- Three-layer output ---
result <- logistic_regression(survey_data, high_satisfaction ~ age + income)
result # compact one-line overview
#> Logistic Regression: high_satisfaction ~ age + income
#> Nagelkerke R2 = 0.209, chi2(2) = 357.43, p < 0.001 ***, Accuracy = 68.4%, N = 2115
summary(result) # full detailed SPSS-style output
#>
#> Logistic Regression Results
#> ---------------------------
#> - Formula: high_satisfaction ~ age + income
#> - Method: ENTER
#> - N: 2115
#>
#> Omnibus Tests of Model Coefficients
#> --------------------------------------------------
#> Chi-square df Sig.
#> --------------------------------------------------
#> Model 357.432 2 0.000 ***
#> --------------------------------------------------
#>
#> Model Summary
#> ------------------------------------------------------------
#> -2 Log Likelihood 2520.010
#> Cox & Snell R Square 0.155
#> Nagelkerke R Square 0.209
#> McFadden R Square 0.124
#> ------------------------------------------------------------
#>
#> Hosmer and Lemeshow Test
#> --------------------------------------------------
#> Chi-square df Sig.
#> --------------------------------------------------
#> 150.764 8 0.000
#> --------------------------------------------------
#>
#> Classification Table (cutoff = 0.50)
#> -----------------------------------------------------------------
#> Predicted
#> Observed 0 1 % Correct
#> -----------------------------------------------------------------
#> 0 508 380 57.2
#> 1 289 938 76.4
#> -----------------------------------------------------------------
#> Overall Percentage 68.4
#> -----------------------------------------------------------------
#>
#> Variables in the Equation
#> -----------------------------------------------------------------------------------------------
#> Term B S.E. Wald df Sig. Exp(B) Lower Upper
#> -----------------------------------------------------------------------------------------------
#> (Intercept) -2.252 0.212 112.853 1 0.000 0.105 ***
#> age 0.001 0.003 0.174 1 0.677 1.001 0.996 1.007
#> income 0.001 0.000 268.051 1 0.000 1.001 1.001 1.001 ***
#> -----------------------------------------------------------------------------------------------
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
summary(result, classification_table = FALSE) # hide classification
#>
#> Logistic Regression Results
#> ---------------------------
#> - Formula: high_satisfaction ~ age + income
#> - Method: ENTER
#> - N: 2115
#>
#> Omnibus Tests of Model Coefficients
#> --------------------------------------------------
#> Chi-square df Sig.
#> --------------------------------------------------
#> Model 357.432 2 0.000 ***
#> --------------------------------------------------
#>
#> Model Summary
#> ------------------------------------------------------------
#> -2 Log Likelihood 2520.010
#> Cox & Snell R Square 0.155
#> Nagelkerke R Square 0.209
#> McFadden R Square 0.124
#> ------------------------------------------------------------
#>
#> Hosmer and Lemeshow Test
#> --------------------------------------------------
#> Chi-square df Sig.
#> --------------------------------------------------
#> 150.764 8 0.000
#> --------------------------------------------------
#>
#> Classification Table (cutoff = 0.50)
#> -----------------------------------------------------------------
#> Predicted
#> Observed 0 1 % Correct
#> -----------------------------------------------------------------
#> 0 508 380 57.2
#> 1 289 938 76.4
#> -----------------------------------------------------------------
#> Overall Percentage 68.4
#> -----------------------------------------------------------------
#>
#> Variables in the Equation
#> -----------------------------------------------------------------------------------------------
#> Term B S.E. Wald df Sig. Exp(B) Lower Upper
#> -----------------------------------------------------------------------------------------------
#> (Intercept) -2.252 0.212 112.853 1 0.000 0.105 ***
#> age 0.001 0.003 0.174 1 0.677 1.001 0.996 1.007
#> income 0.001 0.000 268.051 1 0.000 1.001 1.001 1.001 ***
#> -----------------------------------------------------------------------------------------------
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05