Continuous-outcome linear-model table

Builds APA-style summary tables from a series of linear models for one or many continuous outcomes selected with tidyselect syntax.

A single focal predictor is supplied with by; each selected numeric outcome is fit as lm(outcome ~ by, ...), optionally extended with additive covariates via covariates and case weights via weights. Categorical by produces model-based estimated marginal means by level (covariate-adjusted via adjustment when covariates are present), plus an optional single difference for dichotomous predictors. Numeric by produces the slope and its confidence interval.

Inference adapts via vcov: classical OLS, "HC0"-"HC5" (heteroscedasticity-consistent), "CR0"-"CR3" (cluster-robust, requires cluster), or "bootstrap" / "jackknife" resampling. Effect sizes (Cohen's "d", Hedges' "g", Hays' "omega2", Cohen's "f2") are reported with optional noncentral t / F confidence intervals via effect_size_ci, and adapt under covariate adjustment (see effect_size).

Multiple output formats are available via output: a printed ASCII table ("default"), a plain wide data.frame ("data.frame"), a raw long data.frame ("long"), or rendered outputs ("tinytable", "gt", "flextable", "excel", "clipboard", "word").

Usage

table_continuous_lm(
  data,
  select = tidyselect::everything(),
  by,
  covariates = NULL,
  adjustment = c("proportional", "balanced"),
  exclude = NULL,
  regex = FALSE,
  weights = NULL,
  vcov = c("classical", "HC0", "HC1", "HC2", "HC3", "HC4", "HC4m", "HC5", "CR0", "CR1",
    "CR2", "CR3", "bootstrap", "jackknife"),
  cluster = NULL,
  boot_n = 1000,
  contrast = c("auto", "none"),
  statistic = FALSE,
  p_value = TRUE,
  show_n = TRUE,
  show_weighted_n = FALSE,
  effect_size = c("none", "f2", "d", "g", "omega2"),
  effect_size_ci = FALSE,
  r2 = c("r2", "adj_r2", "none"),
  ci = TRUE,
  labels = NULL,
  ci_level = 0.95,
  digits = 2,
  fit_digits = 2,
  effect_size_digits = 2,
  p_digits = 3,
  decimal_mark = ".",
  align = c("decimal", "center", "right"),
  output = c("default", "data.frame", "long", "tinytable", "gt", "flextable", "excel",
    "clipboard", "word"),
  excel_path = NULL,
  excel_sheet = "Linear models",
  clipboard_delim = "\t",
  word_path = NULL,
  verbose = FALSE
)

Arguments

data

A data.frame.

select

Outcome columns to include. If regex = FALSE, use tidyselect syntax or a character vector of column names (default: tidyselect::everything()). If regex = TRUE, provide a regular expression pattern (character string).

by

A single predictor column. Accepts an unquoted column name or a single character column name. The predictor can be:

numeric (continuous): treated as a continuous regressor. The table reports the slope of by and its CI from lm(y ~ by, ...).
factor or ordered factor: treated as categorical. Level order is preserved as declared; the first level is the reference for the displayed contrast (R's default treatment-contrast convention).
character: coerced to factor with factor(by), which orders the levels alphabetically. To control the reference level, supply by as an explicit factor with the desired level ordering (e.g. via forcats::fct_relevel() or factor(..., levels = ...)).
logical: coerced to factor with levels "FALSE", "TRUE" (in that order, since FALSE < TRUE). The reference level is "FALSE", so a binary contrast displays as Delta (TRUE - FALSE).

Rows with NA in by are excluded from the analytic sample for each outcome (NAs in y and weights are also excluded; see Details).

covariates

Optional additive covariates to adjust each per-outcome linear model for. Accepts a tidyselect expression (e.g. covariates = c(age, sex), covariates = tidyselect::all_of(cov_vec), covariates = tidyselect::starts_with("control_")) or a literal character vector of column names. Each covariate must be numeric, integer, logical, factor, or character; covariates that also appear in select are silently auto-excluded from the outcome list (a variable cannot be both outcome and adjustment), and a covariate that equals by raises an error (a variable cannot be both predictor and adjustment).

When non-empty, each model is fitted as lm(y ~ by + cov1 + cov2 + ...) and the reported estimate / SE / p-value / CI on by are covariate-adjusted via the focal coefficient. For categorical by, the displayed emmean is the covariate-adjusted estimated marginal mean – see adjustment for the choice of estimand (G-computation by default vs. equal-weight averaging). The omnibus test of by is the Wald F restricted to the focal coefficients (computed via sandwich / clubSandwich for HC* / CR* mode), so adding covariates does not contaminate the omnibus statistic with covariate contributions. Effect sizes adapt automatically – see effect_size.

v1 supports additive covariates only. Formula syntax with interactions or transforms (covariates = ~ age * sex, covariates = ~ I(age^2)) is reserved for a future release; passing a formula raises a spicy_unsupported error with a migration hint.

Rows with NA in any covariate are dropped from the analytic sample for each outcome (complete-cases per outcome, matching the existing by / weights NA handling).

adjustment

How the covariate-adjusted estimated marginal means (the emmean / emmean_se / emmean_ci_* columns) are computed when covariates is non-empty. One of:

"proportional" (the default; matches Stata margins and marginaleffects::avg_predictions()): G-computation on the observed sample. For each focal level of by, the model predicts at every observation with by set to that level (covariates kept at their observed values), and the predictions are averaged. Population-weighted by construction – the empirical joint distribution of covariates is the reference. Best when the goal is "what is the predicted mean in this population if everyone had by = lvl".
"balanced" (matches emmeans::emmeans() default and the SPSS UNIANOVA EMMEANS / SAS LSMEANS conventions): synthetic grid of factor-covariate level combinations x numeric covariates fixed at their sample mean, with each grid cell weighted equally. Treats the design as if covariates were balanced – the "marginal mean assuming a balanced design" estimand. Best when the goal is to report a covariate-purified comparison independent of the empirical covariate distribution.

Both methods reduce to the same linear-contrast formula emmean = avg_row %*% beta and inherit the spicy variance pipeline (HC* / CR* / bootstrap / jackknife). They give the same answer when there are no covariates, and also when all covariates are numeric / logical (no factor levels to expand over). The two estimands diverge only when at least one factor / character covariate has non-uniform observed proportions.

exclude

Columns to exclude from select. Supports tidyselect syntax and character vectors of column names.

regex

Logical. If FALSE (the default), uses tidyselect helpers. If TRUE, the select argument is treated as a regular expression.

weights

Optional case weights. Accepts:

NULL (default): an ordinary unweighted lm() is fit.
an unquoted numeric column name present in data.
a single character column name present in data.
a numeric vector of length nrow(data) evaluated in the calling environment.

Validation: weights must be finite, non-negative, and contain at least one positive value (otherwise the function errors). Rows with NA in weights are excluded from the analytic sample for each outcome, alongside rows with NA in y or by. When supplied, weights are passed to lm(..., weights = ...), so coefficients become weighted least-squares estimates and \eqn{R^2}{R^2}, adjusted \eqn{R^2}{R^2}, and the four effect sizes are computed from the corresponding weighted sums of squares (see the Weights section in Details).

vcov

Variance estimator used for standard errors, confidence intervals, and Wald test statistics. One of:

"classical" (default): the ordinary OLS/WLS variance from vcov(lm), which assumes homoscedastic errors.
"HC0": the original Eicker–White heteroskedasticity-consistent sandwich estimator (White 1980), with no finite-sample correction.
"HC1": HC0 multiplied by n / (n - p) (MacKinnon and White 1985). Matches Stata's , robust default.
"HC2": residuals divided by sqrt(1 - h_ii) (MacKinnon and White 1985).
"HC3": residuals divided by (1 - h_ii) (MacKinnon and White 1985). A common default for small to moderate samples (Long and Ervin 2000).
"HC4": leverage-adaptive variant designed for influential observations (Cribari-Neto 2004).
"HC4m": refinement of HC4 with a modified leverage exponent (Cribari-Neto and da Silva 2011).
"HC5": alternative leverage-adaptive variant designed for leveraged data (Cribari-Neto, Souza and Vasconcellos 2007).
"CR0", "CR1", "CR2", "CR3": cluster-robust sandwich estimators for non-independent observations (Liang and Zeger 1986); requires cluster. "CR2" is the modern default (Bell and McCaffrey 2002; Pustejovsky and Tipton 2018), with Satterthwaite degrees of freedom for inference; the fractional df is reported in the df2 column and in the t(df) / F(df1, df2) test header. "CR1" corresponds to Stata's , vce(cluster id) default. Cluster-robust variants are dispatched to clubSandwich::vcovCR() and inference uses clubSandwich::coef_test() / clubSandwich::Wald_test(); install clubSandwich to use them.
"bootstrap": nonparametric (resampling cases) or cluster bootstrap variance, depending on whether cluster is supplied (Davison and Hinkley 1997; Cameron, Gelbach and Miller 2008). The number of replicates is set by boot_n. Inference is asymptotic (z for single contrasts, chi^2(q) for the global Wald test); CIs are Wald-type around the point estimate.
"jackknife": leave-one-out variance, or leave-one-cluster-out when cluster is supplied (Quenouille 1956; MacKinnon and White 1985). Inference is asymptotic (z / chi^2(q)).

The HC* variants are computed via sandwich::vcovHC(). Coefficients (means, contrasts, slopes), \eqn{R^2}{R^2}, and the standardized effect sizes (f2, d, g, omega2) are point estimates from the OLS/WLS fit and are not affected by vcov; only their standard errors, CIs, and the test statistic of the contrast change.

cluster

Cluster identifier for cluster-aware variance estimators. Required when vcov is one of the CR* variants; optional and triggers a cluster bootstrap or leave-one-cluster-out jackknife when vcov is "bootstrap" / "jackknife"; forbidden for the other (independent-observation) variants. Accepts:

NULL (default): no cluster structure.
an unquoted column name in data.
a single character column name in data.
an atomic vector of length nrow(data) evaluated in the calling environment (factor, character, integer, etc.).

Rows with NA in cluster are excluded from the analytic sample for each outcome (alongside rows with NA in y, by, or weights). At least two distinct non-missing cluster values are required. Multi-way clustering (a list / data.frame of multiple cluster vectors) is not supported; use sandwich::vcovCL() or clubSandwich::vcovCR() directly on the fitted model for that case.

boot_n

Integer. Number of bootstrap replicates used when vcov = "bootstrap". Defaults to 1000. Ignored otherwise. Larger values reduce Monte-Carlo error in the bootstrap variance; typical values for inference are 500-2000.

contrast

Contrast display for categorical predictors. One of:

"auto" (default): show a single reference contrast Delta (level2 - level1) only when by has exactly two non-empty levels. The reference level is the first level of the factor (R's default treatment-contrast convention, getOption("contrasts")[1]). To change which level acts as the reference, re-level by upstream (for example with forcats::fct_relevel() or stats::relevel()).
"none": suppress the contrast column for categorical predictors. Level-specific means are still displayed.

statistic

Logical. If TRUE, includes a test-statistic column in the wide and rendered outputs. Defaults to FALSE.

p_value

Logical. If TRUE, includes a p column in the wide and rendered outputs. Defaults to TRUE.

show_n

Logical. If TRUE, includes an unweighted n column in the wide and rendered outputs. Defaults to TRUE.

show_weighted_n

Logical. If TRUE and weights is supplied, includes a Weighted n column equal to the sum of case weights in the analytic sample. Defaults to FALSE.

effect_size

Character. Effect-size column to include in the wide and rendered outputs. One of:

"none" (the default): no effect-size column.
"f2": Cohen's \eqn{f^2}{f^2} = \eqn{R^2}{R^2} / (1 - \eqn{R^2}{R^2}). Defined for any predictor type. Familiar from Cohen (1988); standard input for a-priori power analysis. Note that for a single-predictor model, \eqn{f^2}{f^2} is a monotone transform of \eqn{R^2}{R^2} and adds no information beyond it.
"d": Cohen's d = beta_hat / sigma_hat, where beta_hat is the model coefficient (the displayed difference) and sigma_hat is the residual standard deviation from the fitted model. Defined only when by has exactly two non-empty levels; otherwise the function errors. The sign matches the displayed Delta (level2 - level1).
"g": Hedges' g = J * d with the small-sample correction J = 1 - 3 / (4 * df_resid - 1). Same domain as "d".
"omega2": Hays' omega-squared, a bias-corrected estimator of the population variance explained, less optimistic than \eqn{R^2}{R^2} for small samples. Defined for any predictor type and truncated at 0.

When weights is supplied, "d", "g", and "omega2" are derived from the weighted least-squares fit (using weighted sums of squares and the model's weighted residual standard deviation), keeping them consistent with the weighted contrast and its CI shown in the table. All effect sizes are point estimates derived from the OLS/WLS fit and are not affected by vcov.

Under covariate adjustment (covariates non-empty):

"f2" and "omega2" become the partial $f^2$ / partial $\omega^2$, derived from the partial F of by via stats::drop1() – the correctly-defined effect size when the model is adjusted. For numeric by, partial $f^2$ equals the squared partial correlation of by with the outcome, divided by (1 - r^2_partial).
"d" and "g" raise a spicy_unsupported error: Cohen's d and Hedges' g have no canonical extension to adjusted models (the pooled SD is undefined under adjustment). Use "f2" or "omega2" instead – both generalise via partial F.

effect_size_ci

Logical. If TRUE and effect_size != "none", adds a confidence interval for the effect size derived from inversion of the appropriate noncentral distribution (noncentral t for "d" / "g"; noncentral F for "omega2" / "f2"). The CI level is taken from ci_level. In the long output (output = "long"), the bounds are always present in es_ci_lower / es_ci_upper (numeric). In the wide raw output (output = "data.frame"), the bounds appear as numeric columns effect_size_ci_lower / effect_size_ci_upper. In the printed ASCII table and rendered outputs ("tinytable", "gt", "flextable", "word", "excel", "clipboard"), the effect-size column shows the value followed by the CI in brackets (e.g. 0.18 [0.07, 0.30]). Defaults to FALSE. When effect_size = "none", this argument is ignored with a warning.

r2

Character. Fit statistic to include in the wide and rendered outputs. One of:

"r2" (default): the model \eqn{R^2}{R^2} (summary(lm)$r.squared).
"adj_r2": adjusted \eqn{R^2}{R^2}, penalising for df_effect relative to the residual degrees of freedom.
"none": omit the fit-statistic column.

When weights is supplied, \eqn{R^2}{R^2} and adjusted \eqn{R^2}{R^2} are the weighted least-squares versions reported by summary(lm(..., weights = ...)).

ci

Logical. If TRUE, includes contrast confidence-interval columns in the wide and rendered outputs when a single contrast is shown. Defaults to TRUE.

labels

An optional named character vector of outcome labels. Names must match column names in data. When NULL (the default), labels are auto-detected from variable attributes; if none are found, the column name is used.

ci_level

Confidence level for coefficient and model-based mean intervals (default: 0.95). Must be between 0 and 1 exclusive.

digits

Number of decimal places for descriptive values, regression coefficients, and test statistics (default: 2).

fit_digits

Number of decimal places for model-fit columns (\eqn{R^2}{R^2} or adjusted \eqn{R^2}{R^2}) in wide and rendered outputs (default: 2).

effect_size_digits

Number of decimal places for the effect-size column (f2, d, g, or omega2) in wide and rendered outputs (default: 2).

p_digits

Integer >= 1. Number of decimal places used to render p-values in the p column (default: 3, the APA Publication Manual standard). Both the displayed precision and the small-p threshold derive from this argument: p_digits = 3 prints .045 and <.001; p_digits = 4 prints .0451 and <.0001; p_digits = 2 prints .05 and <.01. Useful for genomics / GWAS contexts where adjusted p-values can be very small, or for journals using a coarser convention. Leading zeros are always stripped, following APA convention.

decimal_mark

Character used as decimal separator. Either "." (default) or ",".

align

Horizontal alignment of numeric columns in the printed ASCII table and in the tinytable, gt, flextable, word, and clipboard outputs. The first column (Variable) is always left-aligned. One of:

"decimal" (default): align numeric columns on the decimal mark, the standard scientific-publication convention used by SPSS, SAS, and LaTeX siunitx. Numeric cells are pre-padded with figure-spaces (U+2007, digit-width) so every string in a column has the same width with the decimal mark at the same internal position; centring those uniform-width strings then stacks the decimal points vertically. The same pad-then-centre strategy is applied on every engine (gt, tinytable, flextable, word, clipboard, ASCII print) for a homogeneous rendering, matching table_regression().
"center": center-align all numeric columns.
"right": right-align all numeric columns.

The excel output uses the engine's default alignment in any case: cell-string padding does not align decimals under proportional fonts, and writing raw numbers with a numeric format would require a separate refactor.

output

Output format. One of:

"default": a printed ASCII table, returned invisibly
"data.frame": a plain wide data.frame
"long": a raw long data.frame
"tinytable" (requires tinytable)
"gt" (requires gt)
"flextable" (requires flextable)
"excel" (requires openxlsx2)
"clipboard" (requires clipr)
"word" (requires flextable and officer)

excel_path

File path for output = "excel".

excel_sheet

Sheet name for output = "excel" (default: "Linear models").

clipboard_delim

Delimiter for output = "clipboard" (default: "\t").

word_path

File path for output = "word".

verbose

Logical. If TRUE, prints messages about ignored non-numeric selected outcomes (default: FALSE).

Value

Depends on output:

"default": prints a styled ASCII table and invisibly returns the underlying long data.frame with class "spicy_continuous_lm_table" / "spicy_table".
"data.frame": a plain wide data.frame with one row per outcome and numeric columns for means (categorical by) or slope (numeric by), optional contrast and CI, optional test statistic, p, fit statistic (\eqn{R^2}{R^2} or adjusted \eqn{R^2}{R^2}), effect size, optional effect_size_ci_lower / effect_size_ci_upper (when effect_size_ci = TRUE), n, and Weighted n.
"long": a raw data.frame with one block per outcome and 28 columns covering identification (variable, label, predictor_type, predictor_label, level, reference), fitted means and their CI (emmean, emmean_se, emmean_ci_lower, emmean_ci_upper), contrast or slope estimates and CI (estimate_type, estimate, estimate_se, estimate_ci_lower, estimate_ci_upper), inferential output (test_type, statistic, df1, df2, p.value), effect size with its CI (es_type, es_value, es_ci_lower, es_ci_upper), fit (r2, adj_r2), and sample size (n, weighted_n).
"tinytable": a tinytable object.
"gt": a gt_tbl object.
"flextable": a flextable object.
"excel" / "word": writes to disk and returns the file path.
"clipboard": copies the wide table and returns it invisibly.

If no numeric outcome columns remain after applying select, exclude, and regex, the function emits a warning and returns an empty data.frame() regardless of output.

Model and outputs

table_continuous_lm() is designed for article-style reporting around a single focal predictor: one model per selected continuous outcome, fitted as lm(outcome ~ by, ...) and optionally extended with case weights and additive covariates (lm(outcome ~ by + cov1 + ...)). For categorical by, the reported means are model-based fitted means (or covariate-adjusted estimated marginal means; see adjustment) for each level, and contrasts come from the same fitted linear model. For an unweighted lm(y ~ factor) with classical variance and no covariates, the fitted means coincide numerically with empirical subgroup means; the model-based qualifier matters because (a) under weights the means become weighted least-squares estimates, (b) their CIs derive from the model vcov (classical, HC*, CR*, bootstrap or jackknife), (c) under covariates they become adjusted marginal means, and (d) tests, p-values and effect sizes all come from the same fitted model, keeping the table internally consistent.

Compared with table_continuous(), this function is the model-based companion: choose it when you want heteroskedasticity-consistent standard errors (vcov = "HC*"), model fit statistics, or case weights via lm(..., weights = ...). Because the function exists to report a fitted model, its inferential output is on by default: p_value = TRUE and r2 = "r2" are the defaults; set p_value = FALSE or r2 = "none" to suppress them.

Effect sizes

Effect size is selected explicitly via effect_size (defaults to "none"). All variants are derived from the same fitted model as the displayed coefficients, \eqn{R^2}{R^2}, and CIs, so the effect size stays internally consistent with the rest of the table.

"f2": Cohen's \eqn{f^2}{f^2} = \eqn{R^2}{R^2} / (1 - \eqn{R^2}{R^2}) (Cohen 1988). Defined for any predictor type. For a single-predictor model, \eqn{f^2}{f^2} is a monotone transform of \eqn{R^2}{R^2} and adds no information beyond it; its primary use is in a priori power analysis (e.g. G*Power).
"d", "g": standardized mean difference (Cohen's d or Hedges' g), defined only when by has exactly two non-empty levels. d = beta_hat / sigma_hat with sigma_hat = summary(fit)$sigma (the pooled within-group SD for the unweighted two-group case); g = J * d with J = 1 - 3 / (4 * df_resid - 1) (Hedges and Olkin 1985). The sign matches the displayed Delta (level2 - level1). For published reports of two-group comparisons, g is the convention recommended by Hedges and Olkin (1985).
"omega2": Hays' $\omega^2$, computed from weighted sums of squares as (SS_effect - df_effect * MSE) / (SS_total + MSE) and truncated at 0 for small or null effects (Hays 1963; Olejnik and Algina 2003). Less biased than $\eta^2$ (which equals R^2 in this single-predictor design) and recommended for reporting variance explained in ANOVA-style designs (Olejnik and Algina 2003).

All four effect sizes are point estimates derived from the OLS/WLS fit and are invariant to vcov: choosing HC* changes the SE, CI, and test statistic of the contrast but not the standardized magnitude itself.

Under covariate adjustment (covariates non-empty), "f2" and "omega2" become the partial $f^2$ / partial $\omega^2$ of by, derived from the partial F via stats::drop1() restricted to the focal term. "d" and "g" raise a spicy_unsupported error: the pooled standard deviation has no canonical extension under adjustment, so Cohen's d and Hedges' g are undefined for adjusted models. See effect_size for the full dispatch.

Confidence intervals for the effect size are available via effect_size_ci = TRUE and use the modern noncentral-distribution inversion approach, the consensus standard in commercial statistical software (Stata esize / estat esize, SAS PROC TTEST and PROC GLM EFFECTSIZE 14.2+) and in mainstream R packages (effectsize, MOTE, TOSTER, effsize):

"d", "g": noncentral t inversion (Steiger and Fouladi 1997; Goulet-Pelletier and Cousineau 2018). Empirical coverage is nominal across sample sizes (Cousineau and Goulet-Pelletier 2021), unlike the older Hedges-Olkin normal approximation which is biased for small samples. For Hedges' g the bounds inherit the J small-sample correction.
"omega2", "f2": noncentral F inversion (Steiger 2004). Bounds are converted from the noncentrality parameter using omega^2 = ncp / (ncp + N) and \eqn{f^2}{f^2} = ncp / N respectively, with N = df1 + df2 + 1 (total sample size).

For the weighted case, the CI uses raw (unweighted) group counts and df.residual(fit) = n - p, consistent with the WLS reporting convention (DuMouchel and Duncan 1983). For propensity-score balance assessment or complex-survey designs, dedicated packages (cobalt::bal.tab() for the Austin and Stuart 2015 formulation; survey for design-based effect sizes) are more appropriate.

Robust standard errors

When vcov is one of the HC* variants, the standard errors, CIs, and Wald test statistics use a heteroskedasticity-consistent sandwich estimator computed via sandwich::vcovHC() (Zeileis 2004), the canonical R implementation. For a brief guide:

"HC0" is the original White (1980) form; "HC1" adds the n / (n - p) correction (MacKinnon and White 1985), Stata's , robust default.
"HC2" and "HC3" use leverage-based residual rescalings (MacKinnon and White 1985); "HC3" is the sandwich::vcovHC() default for small to moderate samples (Long and Ervin 2000).
"HC4" adapts the leverage exponent for influential observations (Cribari-Neto 2004); "HC4m" is a modified-exponent refinement (Cribari-Neto and da Silva 2011); "HC5" is an alternative leverage-adaptive variant (Cribari-Neto, Souza and Vasconcellos 2007).

When observations are not independent (repeated measurements per individual, students nested in classes, patients in hospitals, country-year panels), classical and HC* standard errors are biased downward. Use the CR* variants together with cluster = id_var to get cluster-robust inference (Liang and Zeger 1986). The implementation dispatches to clubSandwich::vcovCR() for the variance and to clubSandwich::coef_test() (single-coefficient, Satterthwaite t) and clubSandwich::Wald_test() (multi-coefficient Hotelling-T-squared with Satterthwaite df, "HTZ") for inference. "CR2" (Bell and McCaffrey 2002; Pustejovsky and Tipton 2018) is the modern recommended default; it generally produces fractional Satterthwaite degrees of freedom in df2, which the displayed t(df) / F(df1, df2) header renders to one decimal. "CR1" matches Stata's , vce(cluster id). Effect sizes remain invariant to vcov (including CR*); only the SE, CI, test statistic, and df2 of the contrast change.

Two resampling-based estimators are also available without adding any dependency: vcov = "bootstrap" (nonparametric resampling-cases bootstrap; Davison and Hinkley 1997) and vcov = "jackknife" (leave-one-out delete-1; Quenouille 1956; MacKinnon and White 1985). Supplying cluster switches both to their cluster-aware variants (cluster bootstrap, Cameron, Gelbach and Miller 2008; leave-one-cluster-out jackknife). The number of bootstrap replicates is controlled by boot_n (default 1000); replicates that fail to fit on rank-deficient resamples are dropped, with an explicit warning if more than half fail and a fallback to the classical OLS variance below 10 valid replicates. Inference for both estimators is asymptotic (z for single-coefficient contrasts, chi^2(q) for the multi-coefficient global Wald test on k > 2 categorical predictors), reflected in the displayed test header. Use the bootstrap when the residual distribution is non-standard or the sample is small; use the jackknife as a closed-form, deterministic alternative.

\eqn{R^2}{R^2}, adjusted \eqn{R^2}{R^2}, and the effect sizes remain ordinary least-squares (or weighted least-squares) statistics regardless of vcov.

Weights

When weights is supplied, table_continuous_lm() fits weighted linear models via lm(..., weights = ...). Means become weighted least-squares estimates and contrasts and slopes are weighted. The fit statistics \eqn{R^2}{R^2} and adjusted \eqn{R^2}{R^2}, as well as Hays' omega^2 and Cohen's \eqn{f^2}{f^2}, use the corresponding weighted sums of squares from the WLS fit. Cohen's d and Hedges' g use the WLS coefficient and the model's weighted residual standard deviation (summary(fit)$sigma), which is the standard convention for case-weighted regression-style reporting (DuMouchel and Duncan 1983); the noncentral t CI for d / g uses the raw (unweighted) group counts and the residual degrees of freedom of the WLS fit (n - p). This case-weighted workflow is appropriate for weighted article tables, but is not a substitute for a full complex-survey design (see e.g. the survey package), nor for propensity-score balance assessment under the Austin and Stuart (2015) convention (see e.g. cobalt::bal.tab()).

The n column always reports the unweighted analytic sample size for each outcome. When show_weighted_n = TRUE, an additional Weighted n column reports the sum of case weights in the same analytic sample.

Display conventions

For dichotomous categorical predictors, the wide outputs report fitted means in reference-level order and label the contrast column explicitly as Delta (level2 - level1). For categorical predictors with more than two levels, no single contrast or contrast CI is shown in the wide outputs; instead, the table reports level-specific means plus the overall F test when statistic = TRUE (or F(df1, df2) when the degrees of freedom are constant across outcomes).

When covariates is non-empty, the printed ASCII table appends an APA-style footer naming the covariates and the chosen estimand, e.g. Note. Adjusted for age, education (proportional).

Optional output engines require the corresponding suggested packages:

tinytable for output = "tinytable"
gt for output = "gt"
flextable for output = "flextable"
flextable + officer for output = "word"
openxlsx2 for output = "excel"
clipr for output = "clipboard"

References

Austin, P. C., & Stuart, E. A. (2015). Moving towards best practice when using inverse probability of treatment weighting (IPTW) using the propensity score to estimate causal treatment effects in observational studies. Statistics in Medicine, 34(28), 3661–3679. doi:10.1002/sim.6607

Bell, R. M., & McCaffrey, D. F. (2002). Bias reduction in standard errors for linear regression with multi-stage samples. Survey Methodology, 28(2), 169–181.

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Examples

# --- Basic usage ---------------------------------------------------------

# Default: ASCII table with model-based means, p, and \eqn{R^2}{R^2}.
table_continuous_lm(
  sochealth,
  select = c(wellbeing_score, bmi),
  by = sex
)
#> Continuous outcomes by Sex
#> 
#>  Variable                      │ M (Female)  M (Male)  Δ (Male - Female) 
#> ───────────────────────────────┼─────────────────────────────────────────
#>  WHO-5 wellbeing index (0-100) │   67.16      71.05          3.89        
#>  Body mass index               │   25.69      26.20          0.51        
#> 
#>  Variable                      │ 95% CI LL  95% CI UL    p     R²    n   
#> ───────────────────────────────┼─────────────────────────────────────────
#>  WHO-5 wellbeing index (0-100) │   2.13       5.64     <.001  0.02  1200 
#>  Body mass index               │   0.09       0.93      .018  0.00  1188 

# --- Effect sizes -------------------------------------------------------

# Cohen's d (binary by required).
table_continuous_lm(
  sochealth,
  select = c(wellbeing_score, bmi),
  by = sex,
  effect_size = "d"
)
#> Continuous outcomes by Sex
#> 
#>  Variable                      │ M (Female)  M (Male)  Δ (Male - Female) 
#> ───────────────────────────────┼─────────────────────────────────────────
#>  WHO-5 wellbeing index (0-100) │   67.16      71.05          3.89        
#>  Body mass index               │   25.69      26.20          0.51        
#> 
#>  Variable                      │ 95% CI LL  95% CI UL    p     R²    d     n   
#> ───────────────────────────────┼───────────────────────────────────────────────
#>  WHO-5 wellbeing index (0-100) │   2.13       5.64     <.001  0.02  0.25  1200 
#>  Body mass index               │   0.09       0.93      .018  0.00  0.14  1188 

# Hedges' g with weighted analysis and weighted n column.
table_continuous_lm(
  sochealth,
  select = c(wellbeing_score, bmi),
  by = sex,
  weights = weight,
  statistic = TRUE,
  effect_size = "g",
  show_weighted_n = TRUE
)
#> Continuous outcomes by Sex
#> 
#>  Variable                      │ M (Female)  M (Male)  Δ (Male - Female) 
#> ───────────────────────────────┼─────────────────────────────────────────
#>  WHO-5 wellbeing index (0-100) │   67.01      70.88          3.87        
#>  Body mass index               │   25.51      25.98          0.47        
#> 
#>  Variable                      │ 95% CI LL  95% CI UL   t      p     R²    g   
#> ───────────────────────────────┼───────────────────────────────────────────────
#>  WHO-5 wellbeing index (0-100) │   2.11       5.62     4.33  <.001  0.02  0.25 
#>  Body mass index               │   0.05       0.89     2.18   .030  0.00  0.13 
#> 
#>  Variable                      │  n    Weighted n 
#> ───────────────────────────────┼──────────────────
#>  WHO-5 wellbeing index (0-100) │ 1200   1196.47   
#>  Body mass index               │ 1188   1183.32   

# Hedges' g with noncentral t confidence interval (bracket notation).
table_continuous_lm(
  sochealth,
  select = c(wellbeing_score, bmi),
  by = sex,
  effect_size = "g",
  effect_size_ci = TRUE
)
#> Continuous outcomes by Sex
#> 
#>  Variable                      │ M (Female)  M (Male)  Δ (Male - Female) 
#> ───────────────────────────────┼─────────────────────────────────────────
#>  WHO-5 wellbeing index (0-100) │   67.16      71.05          3.89        
#>  Body mass index               │   25.69      26.20          0.51        
#> 
#>  Variable                      │ 95% CI LL  95% CI UL    p     R²  
#> ───────────────────────────────┼───────────────────────────────────
#>  WHO-5 wellbeing index (0-100) │   2.13       5.64     <.001  0.02 
#>  Body mass index               │   0.09       0.93      .018  0.00 
#> 
#>  Variable                      │         g           n   
#> ───────────────────────────────┼─────────────────────────
#>  WHO-5 wellbeing index (0-100) │ 0.25 [0.14, 0.36]  1200 
#>  Body mass index               │ 0.14 [0.02, 0.25]  1188 

# Cohen's \eqn{f^2}{f^2} alongside \eqn{R^2}{R^2} (familiar power-analysis effect size).
table_continuous_lm(
  sochealth,
  select = c(wellbeing_score, bmi),
  by = sex,
  effect_size = "f2"
)
#> Continuous outcomes by Sex
#> 
#>  Variable                      │ M (Female)  M (Male)  Δ (Male - Female) 
#> ───────────────────────────────┼─────────────────────────────────────────
#>  WHO-5 wellbeing index (0-100) │   67.16      71.05          3.89        
#>  Body mass index               │   25.69      26.20          0.51        
#> 
#>  Variable                      │ 95% CI LL  95% CI UL    p     R²    f²    n   
#> ───────────────────────────────┼───────────────────────────────────────────────
#>  WHO-5 wellbeing index (0-100) │   2.13       5.64     <.001  0.02  0.02  1200 
#>  Body mass index               │   0.09       0.93      .018  0.00  0.00  1188 

# Hays' omega-squared for a 3-level predictor (d / g would error here).
table_continuous_lm(
  sochealth,
  select = c(wellbeing_score, bmi),
  by = education,
  effect_size = "omega2"
)
#> Continuous outcomes by Highest education level
#> 
#>  Variable                      │ M (Lower secondary)  M (Upper secondary) 
#> ───────────────────────────────┼──────────────────────────────────────────
#>  WHO-5 wellbeing index (0-100) │        67.68                81.56        
#>  Body mass index               │        26.17                23.55        
#> 
#>  Variable                      │ M (Tertiary)    p     R²    ω²    n   
#> ───────────────────────────────┼───────────────────────────────────────
#>  WHO-5 wellbeing index (0-100) │    66.10      <.001  0.21  0.21  1200 
#>  Body mass index               │    26.35      <.001  0.13  0.13  1188 

# --- Robust SE for a numeric predictor ----------------------------------

# HC3 standard errors for the slope of a continuous predictor.
table_continuous_lm(
  sochealth,
  select = c(wellbeing_score, bmi),
  by = age,
  vcov = "HC3",
  ci = FALSE
)
#> Continuous outcomes by Age (years)
#> 
#>  Variable                        │   B        p       R²      n    
#> ─────────────────────────────────┼─────────────────────────────────
#>  WHO-5 wellbeing index (0-100)   │  0.04     .176    0.00    1200  
#>  Body mass index                 │  0.04    <.001    0.02    1188  

# Cluster-robust SE for repeated-measures data: the `sleep` dataset
# has 10 subjects measured twice (one observation per group).
table_continuous_lm(
  sleep,
  select = extra,
  by = group,
  cluster = ID,
  vcov = "CR2"
)
#> Registered S3 method overwritten by 'clubSandwich':
#>   method    from    
#>   bread.mlm sandwich
#> Continuous outcomes by group
#> 
#>  Variable │ M (1)  M (2)  Δ (2 - 1)  95% CI LL  95% CI UL   p     R²   n  
#> ──────────┼───────────────────────────────────────────────────────────────
#>  extra    │ 0.75   2.33     1.58       0.70       2.46     .003  0.16  20 

# --- Covariate adjustment ----------------------------------------------

# Adjust the comparison of `wellbeing_score` and `bmi` by `sex` for `age`
# and `education`. The footer surfaces the adjustment estimand
# ("proportional" by default = G-computation, matching Stata `margins`).
table_continuous_lm(
  sochealth,
  select = c(wellbeing_score, bmi),
  by = sex,
  covariates = c(age, education),
  vcov = "HC3"
)
#> Continuous outcomes by Sex
#> 
#>  Variable                      │ M (Female)  M (Male)  Δ (Male - Female) 
#> ───────────────────────────────┼─────────────────────────────────────────
#>  WHO-5 wellbeing index (0-100) │   67.27      70.93          3.65        
#>  Body mass index               │   25.65      26.23          0.58        
#> 
#>  Variable                      │ 95% CI LL  95% CI UL    p     R²    n   
#> ───────────────────────────────┼─────────────────────────────────────────
#>  WHO-5 wellbeing index (0-100) │   2.08       5.23     <.001  0.22  1200 
#>  Body mass index               │   0.19       0.97      .004  0.16  1188 
#> 
#> Note. Adjusted for age, education (proportional).

# Same model with the emmeans / SPSS UNIANOVA convention (equal-weight
# marginal means on a synthetic covariate grid).
table_continuous_lm(
  sochealth,
  select = c(wellbeing_score, bmi),
  by = sex,
  covariates = c(age, education),
  adjustment = "balanced",
  vcov = "HC3"
)
#> Continuous outcomes by Sex
#> 
#>  Variable                      │ M (Female)  M (Male)  Δ (Male - Female) 
#> ───────────────────────────────┼─────────────────────────────────────────
#>  WHO-5 wellbeing index (0-100) │   69.93      73.59          3.65        
#>  Body mass index               │   25.04      25.62          0.58        
#> 
#>  Variable                      │ 95% CI LL  95% CI UL    p     R²    n   
#> ───────────────────────────────┼─────────────────────────────────────────
#>  WHO-5 wellbeing index (0-100) │   2.08       5.23     <.001  0.22  1200 
#>  Body mass index               │   0.19       0.97      .004  0.16  1188 
#> 
#> Note. Adjusted for age, education (balanced).

# Effect sizes adjust automatically: f2 / omega2 become partial
# effect sizes via partial F (drop1) restricted to the focal `by`.
# d / g are undefined under adjustment and raise spicy_unsupported.
table_continuous_lm(
  sochealth,
  select = c(wellbeing_score, bmi),
  by = sex,
  covariates = c(age, education),
  effect_size = "f2",
  effect_size_ci = TRUE
)
#> Continuous outcomes by Sex
#> 
#>  Variable                      │ M (Female)  M (Male)  Δ (Male - Female) 
#> ───────────────────────────────┼─────────────────────────────────────────
#>  WHO-5 wellbeing index (0-100) │   67.27      70.93          3.65        
#>  Body mass index               │   25.65      26.23          0.58        
#> 
#>  Variable                      │ 95% CI LL  95% CI UL    p     R²  
#> ───────────────────────────────┼───────────────────────────────────
#>  WHO-5 wellbeing index (0-100) │   2.09       5.22     <.001  0.22 
#>  Body mass index               │   0.19       0.97      .004  0.16 
#> 
#>  Variable                      │        f²           n   
#> ───────────────────────────────┼─────────────────────────
#>  WHO-5 wellbeing index (0-100) │ 0.02 [0.01, 0.04]  1200 
#>  Body mass index               │ 0.01 [0.00, 0.02]  1188 
#> 
#> Note. Adjusted for age, education (proportional).

# --- Article-style polish -----------------------------------------------

# Pretty outcome labels and adjusted \eqn{R^2}{R^2}.
table_continuous_lm(
  sochealth,
  select = c(wellbeing_score, bmi),
  by = sex,
  labels = c(
    wellbeing_score = "WHO-5 wellbeing (0-100)",
    bmi = "Body-mass index (kg/m^2)"
  ),
  r2 = "adj_r2"
)
#> Continuous outcomes by Sex
#> 
#>  Variable                 │ M (Female)  M (Male)  Δ (Male - Female)  95% CI LL 
#> ──────────────────────────┼────────────────────────────────────────────────────
#>  WHO-5 wellbeing (0-100)  │   67.16      71.05          3.89           2.13    
#>  Body-mass index (kg/m^2) │   25.69      26.20          0.51           0.09    
#> 
#>  Variable                 │ 95% CI UL    p    Adj. R²   n   
#> ──────────────────────────┼─────────────────────────────────
#>  WHO-5 wellbeing (0-100)  │   5.64     <.001   0.01    1200 
#>  Body-mass index (kg/m^2) │   0.93      .018   0.00    1188 

# European decimal comma.
table_continuous_lm(
  sochealth,
  select = c(wellbeing_score, bmi),
  by = sex,
  decimal_mark = ","
)
#> Continuous outcomes by Sex
#> 
#>  Variable                      │ M (Female)  M (Male)  Δ (Male - Female) 
#> ───────────────────────────────┼─────────────────────────────────────────
#>  WHO-5 wellbeing index (0-100) │   67,16      71,05          3,89        
#>  Body mass index               │   25,69      26,20          0,51        
#> 
#>  Variable                      │ 95% CI LL  95% CI UL    p     R²    n   
#> ───────────────────────────────┼─────────────────────────────────────────
#>  WHO-5 wellbeing index (0-100) │   2,13       5,64     <,001  0,02  1200 
#>  Body mass index               │   0,09       0,93      ,018  0,00  1188 

# Regex selection of all columns starting with "life_sat".
table_continuous_lm(
  sochealth,
  select = "^life_sat",
  by = sex,
  regex = TRUE
)
#> Continuous outcomes by Sex
#> 
#>  Variable                                   │ M (Female)  M (Male) 
#> ────────────────────────────────────────────┼──────────────────────
#>  Satisfaction with health (1-5)             │    3.51       3.59   
#>  Satisfaction with work (1-5)               │    3.32       3.44   
#>  Satisfaction with relationships (1-5)      │    3.71       3.74   
#>  Satisfaction with standard of living (1-5) │    3.37       3.42   
#> 
#>  Variable                                   │ Δ (Male - Female)  95% CI LL 
#> ────────────────────────────────────────────┼──────────────────────────────
#>  Satisfaction with health (1-5)             │       0.08           -0.06   
#>  Satisfaction with work (1-5)               │       0.12           -0.01   
#>  Satisfaction with relationships (1-5)      │       0.04           -0.09   
#>  Satisfaction with standard of living (1-5) │       0.05           -0.08   
#> 
#>  Variable                                   │ 95% CI UL   p     R²    n   
#> ────────────────────────────────────────────┼─────────────────────────────
#>  Satisfaction with health (1-5)             │   0.22     .267  0.00  1192 
#>  Satisfaction with work (1-5)               │   0.26     .073  0.00  1192 
#>  Satisfaction with relationships (1-5)      │   0.16     .570  0.00  1192 
#>  Satisfaction with standard of living (1-5) │   0.18     .453  0.00  1192 

# --- Output formats -----------------------------------------------------

# The rendered outputs below all wrap the same call:
#   table_continuous_lm(sochealth,
#                       select = c(wellbeing_score, bmi),
#                       by = sex)
# only `output` changes. Assign to a variable to avoid the
# console-friendly text fallback that some engines fall back to
# when printed directly in `?` help.

# Wide data.frame (one row per outcome).
table_continuous_lm(
  sochealth,
  select = c(wellbeing_score, bmi),
  by = sex,
  output = "data.frame"
)
#>                                      Variable M (Female) M (Male)
#> wellbeing_score WHO-5 wellbeing index (0-100)   67.16194 71.04879
#> bmi                           Body mass index   25.68506 26.19685
#>                 Δ (Male - Female)  95% CI LL 95% CI UL            p          R²
#> wellbeing_score         3.8868576 2.12952733 5.6441879 1.548898e-05 0.015475137
#> bmi                     0.5117882 0.08879857 0.9347778 1.776254e-02 0.004728908
#>                    n
#> wellbeing_score 1200
#> bmi             1188

# Raw long data.frame (one block per outcome).
table_continuous_lm(
  sochealth,
  select = c(wellbeing_score, bmi),
  by = sex,
  output = "long"
)
#>          variable                         label predictor_type predictor_label
#> 1 wellbeing_score WHO-5 wellbeing index (0-100)    categorical             Sex
#> 2 wellbeing_score WHO-5 wellbeing index (0-100)    categorical             Sex
#> 3             bmi               Body mass index    categorical             Sex
#> 4             bmi               Body mass index    categorical             Sex
#>    level reference estimate_type   emmean emmean_se emmean_ci_lower
#> 1 Female    Female          <NA> 67.16194 0.6227155        65.94020
#> 2   Male    Female    difference 71.04879 0.6438305        69.78563
#> 3 Female    Female          <NA> 25.68506 0.1495988        25.39156
#> 4   Male    Female    difference 26.19685 0.1552460        25.89227
#>   emmean_ci_upper  estimate estimate_se estimate_ci_lower estimate_ci_upper
#> 1        68.38367        NA          NA                NA                NA
#> 2        72.31195 3.8868576   0.8957077        2.12952733         5.6441879
#> 3        25.97857        NA          NA                NA                NA
#> 4        26.50144 0.5117882   0.2155948        0.08879857         0.9347778
#>   test_type statistic df1  df2      p.value es_type es_value es_ci_lower
#> 1         F 18.830621   1 1198 1.548898e-05    <NA>       NA          NA
#> 2         t  4.339426   1 1198 1.548898e-05    <NA>       NA          NA
#> 3         F  5.635133   1 1186 1.776254e-02    <NA>       NA          NA
#> 4         t  2.373843   1 1186 1.776254e-02    <NA>       NA          NA
#>   es_ci_upper          r2      adj_r2    n weighted_n
#> 1          NA 0.015475137 0.014653330 1200         NA
#> 2          NA          NA          NA 1200         NA
#> 3          NA 0.004728908 0.003889725 1188         NA
#> 4          NA          NA          NA 1188         NA

# \donttest{
# Rendered HTML / docx objects -- best viewed inside a
# Quarto / R Markdown document or a pkgdown article.
if (requireNamespace("tinytable", quietly = TRUE)) {
  tt <- table_continuous_lm(
    sochealth, select = c(wellbeing_score, bmi), by = sex,
    output = "tinytable"
  )
}
if (requireNamespace("gt", quietly = TRUE)) {
  tbl <- table_continuous_lm(
    sochealth, select = c(wellbeing_score, bmi), by = sex,
    output = "gt"
  )
}
if (requireNamespace("flextable", quietly = TRUE)) {
  ft <- table_continuous_lm(
    sochealth, select = c(wellbeing_score, bmi), by = sex,
    output = "flextable"
  )
}

# Excel and Word: write to a temporary file.
if (requireNamespace("openxlsx2", quietly = TRUE)) {
  tmp <- tempfile(fileext = ".xlsx")
  table_continuous_lm(
    sochealth, select = c(wellbeing_score, bmi), by = sex,
    output = "excel", excel_path = tmp
  )
  unlink(tmp)
}
if (
  requireNamespace("flextable", quietly = TRUE) &&
    requireNamespace("officer", quietly = TRUE)
) {
  tmp <- tempfile(fileext = ".docx")
  table_continuous_lm(
    sochealth, select = c(wellbeing_score, bmi), by = sex,
    output = "word", word_path = tmp
  )
  unlink(tmp)
}
# }

if (FALSE) { # \dontrun{
# Clipboard: writes to the system clipboard.
table_continuous_lm(
  sochealth, select = c(wellbeing_score, bmi), by = sex,
  output = "clipboard"
)
} # }