Print model parameters — format.parameters

A print()-method for objects from model_parameters().

Usage

# S3 method for class 'parameters_model'
format(
  x,
  pretty_names = TRUE,
  split_components = TRUE,
  select = NULL,
  digits = 2,
  ci_digits = digits,
  p_digits = 3,
  ci_width = NULL,
  ci_brackets = NULL,
  zap_small = FALSE,
  format = NULL,
  groups = NULL,
  include_reference = FALSE,
  ...
)

# S3 method for class 'parameters_model'
print(
  x,
  pretty_names = TRUE,
  split_components = TRUE,
  select = NULL,
  caption = NULL,
  footer = NULL,
  digits = 2,
  ci_digits = digits,
  p_digits = 3,
  footer_digits = 3,
  show_sigma = FALSE,
  show_formula = FALSE,
  zap_small = FALSE,
  groups = NULL,
  column_width = NULL,
  ci_brackets = c("[", "]"),
  include_reference = FALSE,
  ...
)

# S3 method for class 'parameters_model'
summary(object, ...)

# S3 method for class 'parameters_model'
print_html(
  x,
  pretty_names = TRUE,
  split_components = TRUE,
  select = NULL,
  caption = NULL,
  subtitle = NULL,
  footer = NULL,
  align = NULL,
  digits = 2,
  ci_digits = digits,
  p_digits = 3,
  footer_digits = 3,
  ci_brackets = c("(", ")"),
  show_sigma = FALSE,
  show_formula = FALSE,
  zap_small = FALSE,
  groups = NULL,
  font_size = "100%",
  line_padding = 4,
  column_labels = NULL,
  include_reference = FALSE,
  verbose = TRUE,
  ...
)

# S3 method for class 'parameters_model'
print_md(
  x,
  pretty_names = TRUE,
  split_components = TRUE,
  select = NULL,
  caption = NULL,
  subtitle = NULL,
  footer = NULL,
  align = NULL,
  digits = 2,
  ci_digits = digits,
  p_digits = 3,
  footer_digits = 3,
  ci_brackets = c("(", ")"),
  show_sigma = FALSE,
  show_formula = FALSE,
  zap_small = FALSE,
  groups = NULL,
  include_reference = FALSE,
  verbose = TRUE,
  ...
)

Arguments

x, object

An object returned by model_parameters().

pretty_names

Can be TRUE, which will return "pretty" (i.e. more human readable) parameter names. Or "labels", in which case value and variable labels will be used as parameters names. The latter only works for "labelled" data, i.e. if the data used to fit the model had "label" and "labels" attributes. See also section Global Options to Customize Messages when Printing.

split_components

Logical, if TRUE (default), For models with multiple components (zero-inflation, smooth terms, ...), each component is printed in a separate table. If FALSE, model parameters are printed in a single table and a Component column is added to the output.

select

Determines which columns and and which layout columns are printed. There are three options for this argument:

Selecting columns by name or index

select can be a character vector (or numeric index) of column names that should be printed, where columns are extracted from the data frame returned by model_parameters() and related functions.

There are two pre-defined options for selecting columns: select = "minimal" prints coefficients, confidence intervals and p-values, while select = "short" prints coefficients, standard errors and p-values.
A string expression with layout pattern

select is a string with "tokens" enclosed in braces. These tokens will be replaced by their associated columns, where the selected columns will be collapsed into one column. Following tokens are replaced by the related coefficients or statistics: {estimate}, {se}, {ci} (or {ci_low} and {ci_high}), {p} and {stars}. The token {ci} will be replaced by {ci_low}, {ci_high}. Example: select = "{estimate}{stars} ({ci})"

It is possible to create multiple columns as well. A | separates values into new cells/columns. Example: select = "{estimate} ({ci})|{p}".

If format = "html", a <br> inserts a line break inside a cell. See 'Examples'.
A string indicating a pre-defined layout

select can be one of the following string values, to create one of the following pre-defined column layouts:
- "ci": Estimates and confidence intervals, no asterisks for p-values. This is equivalent to select = "{estimate} ({ci})".
- "se": Estimates and standard errors, no asterisks for p-values. This is equivalent to select = "{estimate} ({se})".
- "ci_p": Estimates, confidence intervals and asterisks for p-values. This is equivalent to select = "{estimate}{stars} ({ci})".
- "se_p": Estimates, standard errors and asterisks for p-values. This is equivalent to select = "{estimate}{stars} ({se})"..
- "ci_p2": Estimates, confidence intervals and numeric p-values, in two columns. This is equivalent to select = "{estimate} ({ci})|{p}".
- "se_p2": Estimate, standard errors and numeric p-values, in two columns. This is equivalent to select = "{estimate} ({se})|{p}".

For model_parameters(), glue-like syntax is still experimental in the case of more complex models (like mixed models) and may not return expected results.

digits, ci_digits, p_digits

Number of digits for rounding or significant figures. May also be "signif" to return significant figures or "scientific" to return scientific notation. Control the number of digits by adding the value as suffix, e.g. digits = "scientific4" to have scientific notation with 4 decimal places, or digits = "signif5" for 5 significant figures (see also signif()).

ci_width

Minimum width of the returned string for confidence intervals. If not NULL and width is larger than the string's length, leading whitespaces are added to the string. If width="auto", width will be set to the length of the longest string.

ci_brackets

Logical, if TRUE (default), CI-values are encompassed in square brackets (else in parentheses).

zap_small

Logical, if TRUE, small values are rounded after digits decimal places. If FALSE, values with more decimal places than digits are printed in scientific notation.

format

String, indicating the output format. Can be "markdown" or "html".

groups

Named list, can be used to group parameters in the printed output. List elements may either be character vectors that match the name of those parameters that belong to one group, or list elements can be row numbers of those parameter rows that should belong to one group. The names of the list elements will be used as group names, which will be inserted as "header row". A possible use case might be to emphasize focal predictors and control variables, see 'Examples'. Parameters will be re-ordered according to the order used in groups, while all non-matching parameters will be added to the end.

include_reference

Logical, if TRUE, the reference level of factors will be added to the parameters table. This is only relevant for models with categorical predictors. The coefficient for the reference level is always 0 (except when exponentiate = TRUE, then the coefficient will be 1), so this is just for completeness.

...

Arguments passed down to format.parameters_model(), insight::format_table() and insight::export_table()

caption

Table caption as string. If NULL, depending on the model, either a default caption or no table caption is printed. Use caption = "" to suppress the table caption.

footer

Can either be FALSE or an empty string (i.e. "") to suppress the footer, NULL to print the default footer, or a string. The latter will combine the string value with the default footer.

footer_digits

Number of decimal places for values in the footer summary.

show_sigma

Logical, if TRUE, adds information about the residual standard deviation.

show_formula

Logical, if TRUE, adds the model formula to the output.

column_width

Width of table columns. Can be either NULL, a named numeric vector, or "fixed". If NULL, the width for each table column is adjusted to the minimum required width. If a named numeric vector, value names are matched against column names, and for each match, the specified width is used. If "fixed", and table is split into multiple components, columns across all table components are adjusted to have the same width.

subtitle

Table title (same as caption) and subtitle, as strings. If NULL, no title or subtitle is printed, unless it is stored as attributes (table_title, or its alias table_caption, and table_subtitle). If x is a list of data frames, caption may be a list of table captions, one for each table.

align

Only applies to HTML tables. May be one of "left", "right" or "center".

font_size

For HTML tables, the font size.

line_padding

For HTML tables, the distance (in pixel) between lines.

column_labels

Labels of columns for HTML tables. If NULL, automatic column names are generated. See 'Examples'.

verbose

Toggle messages and warnings.

Value

Invisibly returns the original input object.

Details

summary() is a convenient shortcut for print(object, select = "minimal", show_sigma = TRUE, show_formula = TRUE).

Global Options to Customize Messages and Tables when Printing

The verbose argument can be used to display or silence messages and warnings for the different functions in the parameters package. However, some messages providing additional information can be displayed or suppressed using options():

parameters_info: options(parameters_info = TRUE) will override the include_info argument in model_parameters() and always show the model summary for non-mixed models.
parameters_mixed_info: options(parameters_mixed_info = TRUE) will override the include_info argument in model_parameters() for mixed models, and will then always show the model summary.
parameters_cimethod: options(parameters_cimethod = TRUE) will show the additional information about the approximation method used to calculate confidence intervals and p-values. Set to FALSE to hide this message when printing model_parameters() objects.
parameters_exponentiate: options(parameters_exponentiate = TRUE) will show the additional information on how to interpret coefficients of models with log-transformed response variables or with log-/logit-links when the exponentiate argument in model_parameters() is not TRUE. Set this option to FALSE to hide this message when printing model_parameters() objects.

There are further options that can be used to modify the default behaviour for printed outputs:

parameters_labels: options(parameters_labels = TRUE) will use variable and value labels for pretty names, if data is labelled. If no labels available, default pretty names are used.
parameters_interaction: options(parameters_interaction = <character>) will replace the interaction mark (by default, *) with the related character.
parameters_select: options(parameters_select = <value>) will set the default for the select argument. See argument's documentation for available options.
easystats_table_width: options(easystats_table_width = <value>) will set the default width for tables in text-format, i.e. for most of the outputs printed to console. If not specified, tables will be adjusted to the current available width, e.g. of the of the console (or any other source for textual output, like markdown files). The argument table_width can also be used in most print() methods to specify the table width as desired.
easystats_html_engine: options(easystats_html_engine = "gt") will set the default HTML engine for tables to gt, i.e. the gt package is used to create HTML tables. If set to tt, the tinytable package is used.
insight_use_symbols: options(insight_use_symbols = TRUE) will try to print unicode-chars for symbols as column names, wherever possible (e.g., ω instead of Omega).

Interpretation of Interaction Terms

Note that the interpretation of interaction terms depends on many characteristics of the model. The number of parameters, and overall performance of the model, can differ or not between a * b, a : b, and a / b, suggesting that sometimes interaction terms give different parameterizations of the same model, but other times it gives completely different models (depending on a or b being factors of covariates, included as main effects or not, etc.). Their interpretation depends of the full context of the model, which should not be inferred from the parameters table alone - rather, we recommend to use packages that calculate estimated marginal means or marginal effects, such as modelbased, emmeans, ggeffects, or marginaleffects. To raise awareness for this issue, you may use print(...,show_formula=TRUE) to add the model-specification to the output of the print() method for model_parameters().

Labeling the Degrees of Freedom

Throughout the parameters package, we decided to label the residual degrees of freedom df_error. The reason for this is that these degrees of freedom not always refer to the residuals. For certain models, they refer to the estimate error - in a linear model these are the same, but in - for instance - any mixed effects model, this isn't strictly true. Hence, we think that df_error is the most generic label for these degrees of freedom.

Examples

# \donttest{
library(parameters)
model <- glmmTMB::glmmTMB(
  count ~ spp + mined + (1 | site),
  ziformula = ~mined,
  family = poisson(),
  data = Salamanders
)
mp <- model_parameters(model)

print(mp, pretty_names = FALSE)
#> # Fixed Effects (Count Model) 
#> 
#> Parameter   | Log-Mean |   SE |         95% CI |     z |      p
#> ---------------------------------------------------------------
#> (Intercept) |    -0.36 | 0.28 | [-0.90,  0.18] | -1.30 | 0.194 
#> sppPR       |    -1.27 | 0.24 | [-1.74, -0.80] | -5.27 | < .001
#> sppDM       |     0.27 | 0.14 | [ 0.00,  0.54] |  1.95 | 0.051 
#> sppEC-A     |    -0.57 | 0.21 | [-0.97, -0.16] | -2.75 | 0.006 
#> sppEC-L     |     0.67 | 0.13 | [ 0.41,  0.92] |  5.20 | < .001
#> sppDES-L    |     0.63 | 0.13 | [ 0.38,  0.87] |  4.96 | < .001
#> sppDF       |     0.12 | 0.15 | [-0.17,  0.40] |  0.78 | 0.435 
#> minedno     |     1.27 | 0.27 | [ 0.74,  1.80] |  4.72 | < .001
#> 
#> # Fixed Effects (Zero-Inflation Component) 
#> 
#> Parameter   | Log-Odds |   SE |         95% CI |     z |      p
#> ---------------------------------------------------------------
#> (Intercept) |     0.79 | 0.27 | [ 0.26,  1.32] |  2.90 | 0.004 
#> minedno     |    -1.84 | 0.31 | [-2.46, -1.23] | -5.87 | < .001
#> 
#> # Random Effects Variances 
#> 
#> Parameter            | Coefficient |       95% CI
#> -------------------------------------------------
#> SD (Intercept: site) |        0.33 | [0.18, 0.63]
#> 
#> Uncertainty intervals (equal-tailed) and p-values (two-tailed)
#>   computed using a Wald z-distribution approximation.

print(mp, split_components = FALSE)
#> # Fixed Effects
#> 
#> Parameter            | Coefficient |   SE |         95% CI |     z |      p
#> ---------------------------------------------------------------------------
#> (Intercept)          |       -0.36 | 0.28 | [-0.90,  0.18] | -1.30 | 0.194 
#> spp [PR]             |       -1.27 | 0.24 | [-1.74, -0.80] | -5.27 | < .001
#> spp [DM]             |        0.27 | 0.14 | [ 0.00,  0.54] |  1.95 | 0.051 
#> spp [EC-A]           |       -0.57 | 0.21 | [-0.97, -0.16] | -2.75 | 0.006 
#> spp [EC-L]           |        0.67 | 0.13 | [ 0.41,  0.92] |  5.20 | < .001
#> spp [DES-L]          |        0.63 | 0.13 | [ 0.38,  0.87] |  4.96 | < .001
#> spp [DF]             |        0.12 | 0.15 | [-0.17,  0.40] |  0.78 | 0.435 
#> mined [no]           |        1.27 | 0.27 | [ 0.74,  1.80] |  4.72 | < .001
#> (Intercept)          |        0.79 | 0.27 | [ 0.26,  1.32] |  2.90 | 0.004 
#> minedno              |       -1.84 | 0.31 | [-2.46, -1.23] | -5.87 | < .001
#> SD (Intercept: site) |        0.33 |      | [ 0.18,  0.63] |       |       
#> 
#> Parameter            | Effects |     Component
#> ----------------------------------------------
#> (Intercept)          |   fixed |   conditional
#> spp [PR]             |   fixed |   conditional
#> spp [DM]             |   fixed |   conditional
#> spp [EC-A]           |   fixed |   conditional
#> spp [EC-L]           |   fixed |   conditional
#> spp [DES-L]          |   fixed |   conditional
#> spp [DF]             |   fixed |   conditional
#> mined [no]           |   fixed |   conditional
#> (Intercept)          |   fixed | zero_inflated
#> minedno              |   fixed | zero_inflated
#> SD (Intercept: site) |  random |   conditional
#> 
#> Uncertainty intervals (equal-tailed) and p-values (two-tailed)
#>   computed using a Wald z-distribution approximation.

print(mp, select = c("Parameter", "Coefficient", "SE"))
#> # Fixed Effects (Count Model) 
#> 
#> Parameter   | Log-Mean |   SE
#> -----------------------------
#> (Intercept) |    -0.36 | 0.28
#> spp [PR]    |    -1.27 | 0.24
#> spp [DM]    |     0.27 | 0.14
#> spp [EC-A]  |    -0.57 | 0.21
#> spp [EC-L]  |     0.67 | 0.13
#> spp [DES-L] |     0.63 | 0.13
#> spp [DF]    |     0.12 | 0.15
#> mined [no]  |     1.27 | 0.27
#> 
#> # Fixed Effects (Zero-Inflation Component) 
#> 
#> Parameter   | Log-Odds |   SE
#> -----------------------------
#> (Intercept) |     0.79 | 0.27
#> mined [no]  |    -1.84 | 0.31
#> 
#> # Random Effects Variances 
#> 
#> Parameter            | Coefficient
#> ----------------------------------
#> SD (Intercept: site) |        0.33
#> 
#> Uncertainty intervals (equal-tailed) and p-values (two-tailed)
#>   computed using a Wald z-distribution approximation.

print(mp, select = "minimal")
#> # Fixed Effects (Count Model) 
#> 
#> Parameter   | Log-Mean |         95% CI |      p
#> ------------------------------------------------
#> (Intercept) |    -0.36 | [-0.90,  0.18] | 0.194 
#> spp [PR]    |    -1.27 | [-1.74, -0.80] | < .001
#> spp [DM]    |     0.27 | [ 0.00,  0.54] | 0.051 
#> spp [EC-A]  |    -0.57 | [-0.97, -0.16] | 0.006 
#> spp [EC-L]  |     0.67 | [ 0.41,  0.92] | < .001
#> spp [DES-L] |     0.63 | [ 0.38,  0.87] | < .001
#> spp [DF]    |     0.12 | [-0.17,  0.40] | 0.435 
#> mined [no]  |     1.27 | [ 0.74,  1.80] | < .001
#> 
#> # Fixed Effects (Zero-Inflation Component) 
#> 
#> Parameter   | Log-Odds |         95% CI |      p
#> ------------------------------------------------
#> (Intercept) |     0.79 | [ 0.26,  1.32] | 0.004 
#> mined [no]  |    -1.84 | [-2.46, -1.23] | < .001
#> 
#> # Random Effects Variances 
#> 
#> Parameter            | Coefficient |       95% CI
#> -------------------------------------------------
#> SD (Intercept: site) |        0.33 | [0.18, 0.63]
#> 
#> Uncertainty intervals (equal-tailed) and p-values (two-tailed)
#>   computed using a Wald z-distribution approximation.


# group parameters ------

data(iris)
model <- lm(
  Sepal.Width ~ Sepal.Length + Species + Petal.Length,
  data = iris
)
# don't select "Intercept" parameter
mp <- model_parameters(model, parameters = "^(?!\\(Intercept)")
groups <- list(
  "Focal Predictors" = c("Speciesversicolor", "Speciesvirginica"),
  "Controls" = c("Sepal.Length", "Petal.Length")
)
print(mp, groups = groups)
#> Parameter              | Coefficient |   SE |         95% CI | t(145) |      p
#> ------------------------------------------------------------------------------
#> Focal Predictors       |             |      |                |        |       
#>   Species [versicolor] |       -0.89 | 0.20 | [-1.29, -0.49] |  -4.43 | < .001
#>   Species [virginica]  |       -0.88 | 0.28 | [-1.43, -0.33] |  -3.15 | 0.002 
#> Controls               |             |      |                |        |       
#>   Sepal Length         |        0.38 | 0.07 | [ 0.24,  0.52] |   5.31 | < .001
#>   Petal Length         |       -0.04 | 0.08 | [-0.21,  0.13] |  -0.50 | 0.618 
#> (Intercept)            |        1.60 | 0.28 | [ 1.06,  2.15] |   5.80 | < .001
#> 
#> Uncertainty intervals (equal-tailed) and p-values (two-tailed)
#>   computed using a Wald t-distribution approximation.

# or use row indices
print(mp, groups = list(
  "Focal Predictors" = c(1, 4),
  "Controls" = c(2, 3)
))
#> Parameter              | Coefficient |   SE |         95% CI | t(145) |      p
#> ------------------------------------------------------------------------------
#> Focal Predictors       |             |      |                |        |       
#>   (Intercept)          |        1.60 | 0.28 | [ 1.06,  2.15] |   5.80 | < .001
#>   Species [virginica]  |       -0.88 | 0.28 | [-1.43, -0.33] |  -3.15 | 0.002 
#> Controls               |             |      |                |        |       
#>   Sepal Length         |        0.38 | 0.07 | [ 0.24,  0.52] |   5.31 | < .001
#>   Species [versicolor] |       -0.89 | 0.20 | [-1.29, -0.49] |  -4.43 | < .001
#> Petal Length           |       -0.04 | 0.08 | [-0.21,  0.13] |  -0.50 | 0.618 
#> 
#> Uncertainty intervals (equal-tailed) and p-values (two-tailed)
#>   computed using a Wald t-distribution approximation.

# only show coefficients, CI and p,
# put non-matched parameters to the end

data(mtcars)
mtcars$cyl <- as.factor(mtcars$cyl)
mtcars$gear <- as.factor(mtcars$gear)
model <- lm(mpg ~ hp + gear * vs + cyl + drat, data = mtcars)

# don't select "Intercept" parameter
mp <- model_parameters(model, parameters = "^(?!\\(Intercept)")
print(mp, groups = list(
  "Engine" = c("cyl6", "cyl8", "vs", "hp"),
  "Interactions" = c("gear4:vs", "gear5:vs")
))
#> Parameter        | Coefficient |   SE |          95% CI | t(22) |     p
#> -----------------------------------------------------------------------
#> Engine           |             |      |                 |       |      
#>   cyl [6]        |       -2.47 | 2.21 | [ -7.05,  2.12] | -1.12 | 0.276
#>   cyl [8]        |        1.97 | 5.11 | [ -8.63, 12.58] |  0.39 | 0.703
#>   vs             |        3.18 | 3.79 | [ -4.68, 11.04] |  0.84 | 0.410
#>   hp             |       -0.06 | 0.02 | [ -0.11, -0.02] | -2.91 | 0.008
#> Interactions     |             |      |                 |       |      
#>   gear [4] × vs  |       -2.90 | 4.67 | [-12.57,  6.78] | -0.62 | 0.541
#>   gear [5] × vs  |        2.59 | 4.54 | [ -6.82, 12.00] |  0.57 | 0.574
#> (Intercept)      |       16.63 | 7.77 | [  0.53, 32.74] |  2.14 | 0.044
#> gear [4]         |        3.10 | 4.34 | [ -5.90, 12.10] |  0.71 | 0.482
#> gear [5]         |        4.80 | 3.48 | [ -2.42, 12.01] |  1.38 | 0.182
#> drat             |        2.70 | 2.03 | [ -1.52,  6.91] |  1.33 | 0.198
#> 
#> Uncertainty intervals (equal-tailed) and p-values (two-tailed)
#>   computed using a Wald t-distribution approximation.
# }


# custom column layouts ------

data(iris)
lm1 <- lm(Sepal.Length ~ Species, data = iris)
lm2 <- lm(Sepal.Length ~ Species + Petal.Length, data = iris)

# custom style
result <- compare_parameters(lm1, lm2, select = "{estimate}{stars} ({se})")
print(result)
#> Parameter            |            lm1 |             lm2
#> -------------------------------------------------------
#> (Intercept)          | 5.01*** (0.07) |  3.68*** (0.11)
#> Species [versicolor] | 0.93*** (0.10) | -1.60*** (0.19)
#> Species [virginica]  | 1.58*** (0.10) | -2.12*** (0.27)
#> Petal Length         |                |  0.90*** (0.06)
#> -------------------------------------------------------
#> Observations         |            150 |             150

# \donttest{
# custom style, in HTML
result <- compare_parameters(lm1, lm2, select = "{estimate}<br>({se})|{p}")
print_html(result)


  Parameter
      
        lm1
      
      
        lm2
      
    
Estimate(SE)
      p
      Estimate(SE)
      p
    
(Intercept)
5.01
(0.07)
<0.001
3.68
(0.11)
<0.001
Species (versicolor)
0.93
(0.10)
<0.001
-1.60
(0.19)
<0.001
Species (virginica)
1.58
(0.10)
<0.001
-2.12
(0.27)
<0.001
Petal Length


0.90
(0.06)
<0.001




Observations
150

150

    
# }

Parameter	lm1		lm2
Parameter	Estimate(SE)	p	Estimate(SE)	p
(Intercept)	5.01 (0.07)	<0.001	3.68 (0.11)	<0.001
Species (versicolor)	0.93 (0.10)	<0.001	-1.60 (0.19)	<0.001
Species (virginica)	1.58 (0.10)	<0.001	-2.12 (0.27)	<0.001
Petal Length			0.90 (0.06)	<0.001

Observations	150		150