Ordinal regression tables

library(spicy)
library(MASS)        # polr()

This vignette covers ordinal regression — models for an ordered categorical response such as a Poor < Fair < Good < Very good health rating or a Likert agreement scale. The companion vignette Publication-ready regression tables covers the shared mechanics (vcov, ci_level, output formats, multi-model layouts, broom integration); here we focus on what is specific to ordinal fits.

table_regression() supports both ordinal engines:

MASS::polr() — proportional-odds cumulative logit (also probit / cloglog / cauchit via method =);
ordinal::clm() — the more flexible cumulative link model, with optional scale and partial-proportional-odds (nominal) effects.

The model used throughout is a self-rated-health rating regressed on age, sex, smoking, and physical activity, using the bundled sochealth survey data (?sochealth). self_rated_health is an ordered factor:

levels(sochealth$self_rated_health)
#> [1] "Poor"      "Fair"      "Good"      "Very good"

The proportional-odds model in one paragraph

A cumulative logit model with \(K\) ordered response categories estimates one slope per predictor (shared across all \(K-1\) cumulative splits — the proportional-odds assumption) plus \(K-1\) ordered thresholds (cut-points). A positive slope means that higher values of the predictor push the response toward higher categories. There is deliberately no per-category coefficient: that is the whole point of the proportional-odds restriction. The per-category structure reappears only in the marginal effects (below), where a one-unit change has a different effect on the probability of each category.

Basic table

Pass a fitted polr() object. table_regression() renders the shared slope coefficients with a Wald-\(z\) inference regime, followed by a subordinate Thresholds block listing the ordered cut-points with their own B / SE / CI / p (the field convention: summary.polr(), SPSS PLUM, SAS, Stata ologit, Bender & Grouven 1997):

fit <- polr(
  self_rated_health ~ age + sex + smoking + physical_activity,
  data = sochealth, Hess = TRUE
)
table_regression(fit)
#> Cumulative logit regression (proportional odds): self_rated_health
#> 
#>  Variable           │    B      SE       95% CI        p   
#> ────────────────────┼──────────────────────────────────────
#>  age                │   -0.00  0.00  [-0.01,  0.01]   .831 
#>  sex:               │                                      
#>    Female (ref.)    │     –     –          –          –    
#>    Male             │    0.02  0.11  [-0.20,  0.23]   .874 
#>  smoking:           │                                      
#>    No (ref.)        │     –     –          –          –    
#>    Yes              │   -0.27  0.14  [-0.53, -0.00]   .047 
#>  physical_activity: │                                      
#>    No (ref.)        │     –     –          –          –    
#>    Yes              │    0.03  0.11  [-0.19,  0.24]   .794 
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  Thresholds:        │                                      
#>    Poor | Fair      │   -2.98  0.24  [-3.45, -2.52]  <.001 
#>    Fair | Good      │   -1.02  0.21  [-1.43, -0.62]  <.001 
#>    Good | Very good │    1.04  0.21  [ 0.64,  1.45]  <.001 
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  n                  │ 1156                                 
#>  R² (McFadden)      │    0.00                              
#>  R² (Nagelkerke)    │    0.00                              
#>  AIC                │ 2761.2                               
#> 
#> Note. Cumulative logit regression (proportional odds).
#> Std. errors: Wald asymptotic (z).
#> Thresholds: latent-scale category cut-points.

Reading the table:

Each predictor has one coefficient row (proportional odds); factor predictors are grouped under their parent variable with the reference level carrying (ref.) and an em-dash.
Inference is Wald-\(z\) (df = Inf): ordinal MLE has no residual degrees of freedom, matching summary.polr(), Stata ologit, and SPSS PLUM.
A subordinate Thresholds block lists the cut-points (Poor | Fair, Fair | Good, Good | Very good) with B / SE / CI / p, like the predictor rows. They locate the category boundaries on the latent logit scale and replace the single intercept of a binary logit. They are reported on the log-odds scale and are never exponentiated. The \(z\)-test against zero is rarely of interest (it only asks whether the baseline cumulative split sits at 50/50), so do not over-read a “significant” threshold – the substantive headline is the odds ratios and marginal effects below. Hide the block with show_thresholds = FALSE to fall back to a compact footer line.
Below the fit-stats rule, the model-fit block reports N, two pseudo-\(R^2\) (McFadden, the Stata ologit default, and Nagelkerke, the SPSS PLUM default), and AIC. Override with show_fit_stats (e.g. show_fit_stats = c("nobs", "AIC", "BIC")).

Odds ratios: `exponentiate = TRUE`

On the logit scale a coefficient is a log cumulative-odds ratio. exponentiate = TRUE reports odds ratios instead, exponentiating the estimate and its CI bounds and rebranding the column header:

table_regression(fit, exponentiate = TRUE)
#> Cumulative logit regression (proportional odds): self_rated_health
#> 
#>  Variable           │   OR      SE       95% CI        p   
#> ────────────────────┼──────────────────────────────────────
#>  age                │    1.00  0.00  [ 0.99,  1.01]   .831 
#>  sex:               │                                      
#>    Female (ref.)    │     –     –          –          –    
#>    Male             │    1.02  0.11  [ 0.82,  1.26]   .874 
#>  smoking:           │                                      
#>    No (ref.)        │     –     –          –          –    
#>    Yes              │    0.76  0.10  [ 0.59,  1.00]   .047 
#>  physical_activity: │                                      
#>    No (ref.)        │     –     –          –          –    
#>    Yes              │    1.03  0.11  [ 0.83,  1.28]   .794 
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  Thresholds:        │                                      
#>    Poor | Fair      │   -2.98  0.24  [-3.45, -2.52]  <.001 
#>    Fair | Good      │   -1.02  0.21  [-1.43, -0.62]  <.001 
#>    Good | Very good │    1.04  0.21  [ 0.64,  1.45]  <.001 
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  n                  │ 1156                                 
#>  R² (McFadden)      │    0.00                              
#>  R² (Nagelkerke)    │    0.00                              
#>  AIC                │ 2761.2                               
#> 
#> Note. Cumulative logit regression (proportional odds).
#> Std. errors: Wald asymptotic (z).
#> Thresholds: latent-scale category cut-points (log-odds scale, not exponentiated).
#> OR = odds ratio.
#> Coefficients exponentiated and displayed as OR; SE on the OR scale (delta method); CI bounds exponentiated (asymmetric).

An OR above 1 raises the odds of being in a higher health category; below 1 lowers them. Smoking’s OR here is interpretable as “smokers have lower odds of better self-rated health.” The Thresholds rows stay on the log-odds scale (a cut-point is not an odds ratio, so it is never exponentiated); only the predictor coefficients become ORs, and the footer flags this.

Average marginal effects: a probability matrix

Odds ratios are multiplicative and live on the latent scale. For a reader-friendly, probability-scale summary, request average marginal effects (AME). Because an ordinal model predicts a probability for every response category, each predictor has one AME per category — the effect of the predictor on the probability of that category. table_regression() lays these out as the field-standard matrix: predictors in rows, response categories in columns (Long & Freese 2014; Williams 2012).

table_regression(fit, show_columns = c("b", "ame"))
#> Cumulative logit regression (proportional odds): self_rated_health
#> 
#>  Variable           │    B     AME Poor  AME Fair  AME Good  AME Very good 
#> ────────────────────┼──────────────────────────────────────────────────────
#>  age                │   -0.00      0.00      0.00     -0.00          -0.00 
#>  sex:               │                                                      
#>    Female (ref.)    │     –                                                
#>    Male             │    0.02     -0.00     -0.00      0.00           0.00 
#>  smoking:           │                                                      
#>    No (ref.)        │     –                                                
#>    Yes              │   -0.27      0.01      0.04     -0.01          -0.05 
#>  physical_activity: │                                                      
#>    No (ref.)        │     –                                                
#>    Yes              │    0.03     -0.00     -0.00      0.00           0.01 
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  Thresholds:        │                                                      
#>    Poor | Fair      │   -2.98                                              
#>    Fair | Good      │   -1.02                                              
#>    Good | Very good │    1.04                                              
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  n                  │ 1156                                                 
#>  R² (McFadden)      │    0.00                                              
#>  R² (Nagelkerke)    │    0.00                                              
#>  AIC                │ 2761.2                                               
#> 
#> Note. Cumulative logit regression (proportional odds).
#> Std. errors: Wald asymptotic (z).
#> Thresholds: latent-scale category cut-points.
#> AME = average marginal effect on a response-category probability.

How to read it, with the smoking = Yes row:

The four AME ... columns are the average change in the probability of each health category for a smoker versus a non-smoker, holding the other predictors at their observed values.
The effects sum to ≈ 0 across the row: a predictor redistributes probability mass between categories (the total probability is always 1). Here smoking moves mass out of the better categories and into the worse ones.
Cells are probabilities (the 0–1 scale, matching marginaleffects::avg_slopes() and the binary-glm AME). An AME of 0.04 is a change of 4 percentage points — not 4 percent. The footer note states this; reserve “percent” for multiplicative quantities such as odds ratios.

Request only the AME matrix (drop the coefficient column) with show_columns = "ame", or add the AME standard errors / CIs / p-values with "ame_se", "ame_ci", "ame_p" (or the "all_ame" bundle):

table_regression(fit, show_columns = "ame")
#> Cumulative logit regression (proportional odds): self_rated_health
#> 
#>  Variable           │ AME Poor  AME Fair  AME Good  AME Very good 
#> ────────────────────┼─────────────────────────────────────────────
#>  age                │     0.00      0.00     -0.00          -0.00 
#>  sex:               │                                             
#>    Female (ref.)    │                                             
#>    Male             │    -0.00     -0.00      0.00           0.00 
#>  smoking:           │                                             
#>    No (ref.)        │                                             
#>    Yes              │     0.01      0.04     -0.01          -0.05 
#>  physical_activity: │                                             
#>    No (ref.)        │                                             
#>    Yes              │    -0.00     -0.00      0.00           0.01 
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  n                  │  1156                                       
#>  R² (McFadden)      │     0.00                                    
#>  R² (Nagelkerke)    │     0.00                                    
#>  AIC                │  2761.2                                     
#> 
#> Note. Cumulative logit regression (proportional odds).
#> Std. errors: Wald asymptotic (z).
#> Thresholds: Poor|Fair = -2.98, Fair|Good = -1.02, Good|Very good = 1.04.
#> AME = average marginal effect on a response-category probability.

Marginal effects are computed with marginaleffects::avg_slopes() on the response (probability) scale, then cross-validated to it to machine precision. For a single-outcome model (binary glm, lm, mixed) the AME stays a single column — the per-category matrix appears only when the response has more than two categories.

Cluster-robust standard errors

Ordinal fits honour the cluster-robust vcov family ("CR0"–"CR3") via sandwich::vcovCL(). Pass the cluster as a formula, a column name, or a vector (see the main vignette, How to specify cluster):

table_regression(
  fit, vcov = "CR2", cluster = ~region,
  show_columns = c("b", "ame")
)
#> Cumulative logit regression (proportional odds): self_rated_health
#> 
#>  Variable           │    B     AME Poor  AME Fair  AME Good  AME Very good 
#> ────────────────────┼──────────────────────────────────────────────────────
#>  age                │   -0.00      0.00      0.00     -0.00          -0.00 
#>  sex:               │                                                      
#>    Female (ref.)    │     –                                                
#>    Male             │    0.02     -0.00     -0.00      0.00           0.00 
#>  smoking:           │                                                      
#>    No (ref.)        │     –                                                
#>    Yes              │   -0.27      0.01      0.04     -0.01          -0.05 
#>  physical_activity: │                                                      
#>    No (ref.)        │     –                                                
#>    Yes              │    0.03     -0.00     -0.00      0.00           0.01 
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  Thresholds:        │                                                      
#>    Poor | Fair      │   -2.98                                              
#>    Fair | Good      │   -1.02                                              
#>    Good | Very good │    1.04                                              
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  n                  │ 1156                                                 
#>  R² (McFadden)      │    0.00                                              
#>  R² (Nagelkerke)    │    0.00                                              
#>  AIC                │ 2761.2                                               
#> 
#> Note. Cumulative logit regression (proportional odds).
#> Std. errors: cluster-robust (CL), clusters by region.
#> Thresholds: latent-scale category cut-points.
#> AME = average marginal effect on a response-category probability.

The footer switches to name the estimator and the clustering variable. Heteroskedasticity-consistent (HC*) and the bootstrap / jackknife resamplers are not defined for ordinal fits and are refused with a clear spicy_unsupported_vcov error rather than a silent fallback.

Standard errors and confidence intervals

The three inference regimes differ in how the standard error and the confidence interval relate:

Wald (default): both come from the model information matrix. The CI is estimate ± z × SE (symmetric) and the p-value uses the same SE — SE, CI and p are one coherent set.
Robust / cluster-robust (vcov = "CR*"): the whole set switches to the sandwich estimator — SE, CI (± z × SE_robust) and p shift together, still coupled.
Profile likelihood (ci_method = "profile"): the CI is inverted from the likelihood-ratio statistic and is asymmetric — not estimate ± z × SE. Profile is a CI-only refinement: the estimate, SE, statistic and p-value stay Wald; only the CI changes. It covers the predictor coefficients (via confint()); the thresholds stay Wald. A robust vcov takes precedence (profile is model-based), so requesting both uses the robust Wald CIs.

Because a profile CI cannot be reconstructed from the SE, the footer discloses it (95% CIs: profile likelihood.) alongside the SE method — following APA 7 / SAMPL / STROBE and matching parameters::model_parameters():

table_regression(fit, ci_method = "profile", show_columns = c("b", "ci", "p"))
#> Cumulative logit regression (proportional odds): self_rated_health
#> 
#>  Variable           │    B         95% CI        p   
#> ────────────────────┼────────────────────────────────
#>  age                │   -0.00  [-0.01,  0.01]   .831 
#>  sex:               │                                
#>    Female (ref.)    │     –          –          –    
#>    Male             │    0.02  [-0.20,  0.23]   .874 
#>  smoking:           │                                
#>    No (ref.)        │     –          –          –    
#>    Yes              │   -0.27  [-0.53, -0.00]   .047 
#>  physical_activity: │                                
#>    No (ref.)        │     –          –          –    
#>    Yes              │    0.03  [-0.19,  0.24]   .794 
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  Thresholds:        │                                
#>    Poor | Fair      │   -2.98  [-3.45, -2.52]  <.001 
#>    Fair | Good      │   -1.02  [-1.43, -0.62]  <.001 
#>    Good | Very good │    1.04  [ 0.64,  1.45]  <.001 
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  n                  │ 1156                           
#>  R² (McFadden)      │    0.00                        
#>  R² (Nagelkerke)    │    0.00                        
#>  AIC                │ 2761.2                         
#> 
#> Note. Cumulative logit regression (proportional odds).
#> Std. errors: Wald asymptotic (z).
#> 95% CIs: profile likelihood.
#> Thresholds: latent-scale category cut-points.

The `ordinal::clm()` engine

ordinal::clm() is rendered through the same code path and supports the same columns. It is the engine to reach for when you need flexible link functions, scale effects, or a relaxation of proportional odds.

clm_fit <- ordinal::clm(
  self_rated_health ~ age + sex + smoking + physical_activity,
  data = sochealth
)
table_regression(clm_fit, show_columns = c("b", "ame"))
#> Cumulative logit regression (proportional odds): self_rated_health
#> 
#>  Variable           │    B     AME Poor  AME Fair  AME Good  AME Very good 
#> ────────────────────┼──────────────────────────────────────────────────────
#>  age                │   -0.00      0.00      0.00     -0.00          -0.00 
#>  sex:               │                                                      
#>    Female (ref.)    │     –                                                
#>    Male             │    0.02     -0.00     -0.00      0.00           0.00 
#>  smoking:           │                                                      
#>    No (ref.)        │     –                                                
#>    Yes              │   -0.27      0.01      0.04     -0.01          -0.05 
#>  physical_activity: │                                                      
#>    No (ref.)        │     –                                                
#>    Yes              │    0.03     -0.00     -0.00      0.00           0.01 
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  Thresholds:        │                                                      
#>    Poor | Fair      │   -2.98                                              
#>    Fair | Good      │   -1.02                                              
#>    Good | Very good │    1.04                                              
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  n                  │ 1156                                                 
#>  R² (McFadden)      │    0.00                                              
#>  R² (Nagelkerke)    │    0.00                                              
#>  AIC                │ 2761.2                                               
#> 
#> Note. Cumulative logit regression (proportional odds).
#> Std. errors: Wald asymptotic (z).
#> Thresholds: latent-scale category cut-points.
#> AME = average marginal effect on a response-category probability.

Scale effects and partial proportional odds

clm offers two relaxations of the basic model.

A scale component (scale = ~) lets the latent dispersion depend on covariates. The location coefficients remain a single shared block, so the table renders normally. Cluster-robust SEs are not available for scale fits (sandwich has no estimating-functions method for them), so CR* is refused up front with a clear spicy_unsupported_vcov error:

clm_scale <- ordinal::clm(
  self_rated_health ~ age + smoking, scale = ~ smoking,
  data = sochealth
)
table_regression(clm_scale)             # classical: renders normally
#> Cumulative logit regression (proportional odds): self_rated_health
#> 
#>  Variable           │    B      SE       95% CI        p   
#> ────────────────────┼──────────────────────────────────────
#>  age                │   -0.00  0.00  [-0.01,  0.01]   .884 
#>  smoking:           │                                      
#>    No (ref.)        │     –     –          –          –    
#>    Yes              │   -0.27  0.14  [-0.55,  0.01]   .060 
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  Thresholds:        │                                      
#>    Poor | Fair      │   -3.06  0.24  [-3.53, -2.60]  <.001 
#>    Fair | Good      │   -1.05  0.20  [-1.44, -0.66]  <.001 
#>    Good | Very good │    1.05  0.20  [ 0.66,  1.45]  <.001 
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  n                  │ 1156                                 
#>  R² (McFadden)      │    0.00                              
#>  R² (Nagelkerke)    │    0.01                              
#>  AIC                │ 2757.8                               
#> 
#> Note. Cumulative logit regression (proportional odds).
#> Std. errors: Wald asymptotic (z).
#> Thresholds: latent-scale category cut-points.

table_regression(clm_scale, vcov = "CR2", cluster = ~region)
#> Error in `validate_vcov_cluster_lists()`:
#> ! `vcov = "CR2"` is not available for `clm` models.
#> ℹ This class supports: classical. Robust standard errors for more model classes are being added; see ?table_regression.

A nominal component (nominal = ~, partial proportional odds) lets a predictor’s effect vary across the cut-points: it estimates a separate coefficient per cut-point for the nominal terms. These render as a labelled Non-proportional effects block — one row per cut-point — between the proportional coefficients and the thresholds:

clm_npo <- ordinal::clm(
  self_rated_health ~ age, nominal = ~ smoking,
  data = sochealth
)
table_regression(clm_npo)
#> Cumulative logit regression (partial proportional odds): self_rated_health
#> 
#>  Variable                        │    B      SE       95% CI        p   
#> ─────────────────────────────────┼──────────────────────────────────────
#>  age                             │   -0.00  0.00  [-0.01,  0.01]   .844 
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  Non-proportional effects:       │                                      
#>    smokingYes @ Poor | Fair      │    0.82  0.28  [ 0.28,  1.37]   .003 
#>    smokingYes @ Fair | Good      │    0.22  0.16  [-0.09,  0.53]   .160 
#>    smokingYes @ Good | Very good │    0.24  0.17  [-0.10,  0.58]   .165 
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  Thresholds:                     │                                      
#>    Poor | Fair                   │   -3.17  0.25  [-3.65, -2.69]  <.001 
#>    Fair | Good                   │   -1.03  0.20  [-1.42, -0.65]  <.001 
#>    Good | Very good              │    1.03  0.20  [ 0.64,  1.41]  <.001 
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  n                               │ 1156                                 
#>  R² (McFadden)                   │    0.00                              
#>  R² (Nagelkerke)                 │    0.01                              
#>  AIC                             │ 2756.1                               
#> 
#> Note. Cumulative logit regression (partial proportional odds).
#> Std. errors: Wald asymptotic (z).
#> Thresholds: latent-scale category cut-points.

Two caveats for the non-proportional terms, both surfaced by the table: robust / cluster SEs are not available (sandwich has no estimating-functions method, so a robust vcov is refused), and ci_method = "profile" covers the proportional coefficients only (the non-proportional and threshold rows stay Wald). Under exponentiate = TRUE each non-proportional coefficient becomes an odds ratio for its cut-point.

Several models side by side

The same fit can appear several times with different estimators, or different fits can be compared, with table_regression(list(...)). Per-model vcov is supplied as a list:

fit_min <- polr(self_rated_health ~ smoking, data = sochealth, Hess = TRUE)
table_regression(
  list(Unadjusted = fit_min, Adjusted = fit),
  show_columns = c("b", "ame_p")
)
#> Cumulative logit regression (proportional odds) comparison: self_rated_health
#> 
#>                                        Unadjusted                   Adjuste 
#>                       ────────────────────────────────────────────  ─────── 
#>  Variable           │    B     p Poor  p Fair  p Good  p Very good     B    
#> ────────────────────┼───────────────────────────────────────────────────────
#>  smoking:           │                                                       
#>    No (ref.)        │     –                                             –   
#>    Yes              │   -0.27    .067    .050    .218         .037    -0.27 
#>  age                │                                                 -0.00 
#>  sex:               │                                                       
#>    Female (ref.)    │                                                   –   
#>    Male             │                                                  0.02 
#>  physical_activity: │                                                       
#>    No (ref.)        │                                                   –   
#>    Yes              │                                                  0.03 
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  Thresholds:        │                                                       
#>    Poor | Fair      │   -2.97                                         -2.98 
#>    Fair | Good      │   -1.01                                         -1.02 
#>    Good | Very good │    1.06                                          1.04 
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  n                  │ 1156                                          1156    
#>  R² (McFadden)      │    0.00                                          0.00 
#>  R² (Nagelkerke)    │    0.00                                          0.00 
#>  AIC                │ 2755.3                                        2761.2  
#> 
#>                                    Adjusted               
#>                       ─────────────────────────────────── 
#>  Variable           │ p Poor  p Fair  p Good  p Very good 
#> ────────────────────┼─────────────────────────────────────
#>  smoking:           │                                     
#>    No (ref.)        │                                     
#>    Yes              │   .069    .052    .221         .038 
#>  age                │   .831    .831    .833         .831 
#>  sex:               │                                     
#>    Female (ref.)    │                                     
#>    Male             │   .874    .874    .875         .875 
#>  physical_activity: │                                     
#>    No (ref.)        │                                     
#>    Yes              │   .794    .794    .794         .794 
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  Thresholds:        │                                     
#>    Poor | Fair      │                                     
#>    Fair | Good      │                                     
#>    Good | Very good │                                     
#> ╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌
#>  n                  │                                     
#>  R² (McFadden)      │                                     
#>  R² (Nagelkerke)    │                                     
#>  AIC                │                                     
#> 
#> Note. Cumulative logit regression (proportional odds) models.
#> Std. errors: Wald asymptotic (z).
#> Thresholds: latent-scale category cut-points.
#> AME = average marginal effect on a response-category probability.

Output formats

The default console table shown above is one of several targets. The output argument also produces a raw data frame, a long broom-style tibble, and — with the corresponding Suggests package — rich gt, flextable, tinytable, Excel, or Word tables. The structure (the per-category AME matrix included) carries through to every format.

head(table_regression(fit, show_columns = c("b", "ame"), output = "data.frame"))
#>          Variable       B AME Poor AME Fair AME Good AME Very good
#> 1             age   -0.00     0.00     0.00    -0.00         -0.00
#> 2            sex:                                                 
#> 3   Female (ref.)     –                                           
#> 4            Male    0.02    -0.00    -0.00     0.00          0.00
#> 5        smoking:                                                 
#> 6       No (ref.)     –

table_regression(fit, show_columns = c("b", "ame"), output = "gt")

broom::tidy() returns the long frame, one row per (term, estimate_type); per-category AME rows carry the response category in the outcome_level-derived structure:

broom::tidy(table_regression(fit, show_columns = c("b", "ame")))
#> # A tibble: 23 × 15
#>    model_id outcome    term  estimate_type estimate std.error conf.low conf.high
#>    <chr>    <chr>      <chr> <chr>            <dbl>     <dbl>    <dbl>     <dbl>
#>  1 M1       self_rate… age   ame            3.91e-5 0.000183  -3.20e-4 0.000399 
#>  2 M1       self_rate… age   ame            1.20e-4 0.000565  -9.86e-4 0.00123  
#>  3 M1       self_rate… age   ame           -1.20e-5 0.0000570 -1.24e-4 0.0000997
#>  4 M1       self_rate… age   ame           -1.47e-4 0.000692  -1.50e-3 0.00121  
#>  5 M1       self_rate… age   B             -7.94e-4 0.00372   -8.09e-3 0.00650  
#>  6 M1       self_rate… sexM… ame           -8.52e-4 0.00539   -1.14e-2 0.00972  
#>  7 M1       self_rate… sexM… ame           -2.62e-3 0.0166    -3.52e-2 0.0299   
#>  8 M1       self_rate… sexM… ame            2.62e-4 0.00166   -3.00e-3 0.00352  
#>  9 M1       self_rate… sexM… ame            3.21e-3 0.0204    -3.67e-2 0.0431   
#> 10 M1       self_rate… sexM… B              1.73e-2 0.110     -1.97e-1 0.232    
#> # ℹ 13 more rows
#> # ℹ 7 more variables: statistic <dbl>, df <dbl>, p.value <dbl>,
#> #   test_type <chr>, is_intercept <lgl>, factor_term <chr>, factor_level <chr>

References

Agresti, A. (2010). Analysis of Ordinal Categorical Data (2nd ed.). Wiley.
Long, J. S., & Freese, J. (2014). Regression Models for Categorical Dependent Variables Using Stata (3rd ed.). Stata Press.
Williams, R. (2012). Using the margins command to estimate and interpret adjusted predictions and marginal effects. The Stata Journal, 12(2), 308–331.
Arel-Bundock, V., Greifer, N., & Heiss, A. (2024). How to Interpret Statistical Models Using marginaleffects in R and Python. Journal of Statistical Software.