A print()-method for objects from model_parameters().
Usage
# S3 method for 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 parameters_model
summary(object, ...)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. IfFALSE, model parameters are printed in a single table and aComponentcolumn 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
selectcan be a character vector (or numeric index) of column names that should be printed. There are two pre-defined options for selecting columns:select = "minimal"prints coefficients, confidence intervals and p-values, whileselect = "short"prints coefficients, standard errors and p-values.A string expression with layout pattern
selectis 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. However, it is possible to create multiple columns as well. 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}. Furthermore, a|separates values into new cells/columns. Ifformat = "html", a<br>inserts a line break inside a cell. See 'Examples'.A string indicating a pre-defined layout
selectcan 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 toselect = "{estimate} ({ci})"."se": Estimates and standard errors, no asterisks for p-values. This is equivalent toselect = "{estimate} ({se})"."ci_p": Estimates, confidence intervals and asterisks for p-values. This is equivalent toselect = "{estimate}{stars} ({ci})"."se_p": Estimates, standard errors and asterisks for p-values. This is equivalent toselect = "{estimate}{stars} ({se})".."ci_p2": Estimates, confidence intervals and numeric p-values, in two columns. This is equivalent toselect = "{estimate} ({ci})|{p}"."se_p2": Estimate, standard errors and numeric p-values, in two columns. This is equivalent toselect = "{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.- caption
Table caption as string. If
NULL, depending on the model, either a default caption or no table caption is printed. Usecaption = ""to suppress the table caption.- footer
Can either be
FALSEor an empty string (i.e."") to suppress the footer,NULLto print the default footer, or a string. The latter will combine the string value with the default footer.- 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, ordigits = "signif5"for 5 significant figures (see alsosignif()).- 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.- zap_small
Logical, if
TRUE, small values are rounded afterdigitsdecimal places. IfFALSE, values with more decimal places thandigitsare printed in scientific notation.- 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.- column_width
Width of table columns. Can be either
NULL, a named numeric vector, or"fixed". IfNULL, 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.- ci_brackets
Logical, if
TRUE(default), CI-values are encompassed in square brackets (else in parentheses).- 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 always0(except whenexponentiate = TRUE, then the coefficient will be1), so this is just for completeness.- ...
Arguments passed to or from other methods.
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_summary:options(parameters_summary = TRUE)will override thesummaryargument inmodel_parameters()and always show the model summary for non-mixed models.parameters_mixed_summary:options(parameters_mixed_summary = TRUE)will override thesummaryargument inmodel_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 toFALSEto hide this message when printingmodel_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 theexponentiateargument inmodel_parameters()is notTRUE. Set this option toFALSEto hide this message when printingmodel_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 theselectargument. See argument's documentation for available options.
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.
See also
There is a dedicated method to use inside rmarkdown files,
print_md(). See also
display().
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 | Effects | Component
#> -----------------------------------------------------------------------------------------------------
#> (Intercept) | -0.36 | 0.28 | [-0.90, 0.18] | -1.30 | 0.194 | fixed | conditional
#> spp [PR] | -1.27 | 0.24 | [-1.74, -0.80] | -5.27 | < .001 | fixed | conditional
#> spp [DM] | 0.27 | 0.14 | [ 0.00, 0.54] | 1.95 | 0.051 | fixed | conditional
#> spp [EC-A] | -0.57 | 0.21 | [-0.97, -0.16] | -2.75 | 0.006 | fixed | conditional
#> spp [EC-L] | 0.67 | 0.13 | [ 0.41, 0.92] | 5.20 | < .001 | fixed | conditional
#> spp [DES-L] | 0.63 | 0.13 | [ 0.38, 0.87] | 4.96 | < .001 | fixed | conditional
#> spp [DF] | 0.12 | 0.15 | [-0.17, 0.40] | 0.78 | 0.435 | fixed | conditional
#> mined [no] | 1.27 | 0.27 | [ 0.74, 1.80] | 4.72 | < .001 | fixed | conditional
#> (Intercept) | 0.79 | 0.27 | [ 0.26, 1.32] | 2.90 | 0.004 | fixed | zero_inflated
#> minedno | -1.84 | 0.31 | [-2.46, -1.23] | -5.87 | < .001 | fixed | zero_inflated
#> SD (Intercept: site) | 0.33 | | [ 0.18, 0.63] | | | 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)
#> <div id="moojjreqbz" style="padding-left:0px;padding-right:0px;padding-top:10px;padding-bottom:10px;overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
#> <style>#moojjreqbz table {
#> font-family: system-ui, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol', 'Noto Color Emoji';
#> -webkit-font-smoothing: antialiased;
#> -moz-osx-font-smoothing: grayscale;
#> }
#>
#> #moojjreqbz thead, #moojjreqbz tbody, #moojjreqbz tfoot, #moojjreqbz tr, #moojjreqbz td, #moojjreqbz th {
#> border-style: none;
#> }
#>
#> #moojjreqbz p {
#> margin: 0;
#> padding: 0;
#> }
#>
#> #moojjreqbz .gt_table {
#> display: table;
#> border-collapse: collapse;
#> line-height: normal;
#> margin-left: auto;
#> margin-right: auto;
#> color: #333333;
#> font-size: 100%;
#> font-weight: normal;
#> font-style: normal;
#> background-color: #FFFFFF;
#> width: auto;
#> border-top-style: solid;
#> border-top-width: 2px;
#> border-top-color: #A8A8A8;
#> border-right-style: none;
#> border-right-width: 2px;
#> border-right-color: #D3D3D3;
#> border-bottom-style: solid;
#> border-bottom-width: 2px;
#> border-bottom-color: #A8A8A8;
#> border-left-style: none;
#> border-left-width: 2px;
#> border-left-color: #D3D3D3;
#> }
#>
#> #moojjreqbz .gt_caption {
#> padding-top: 4px;
#> padding-bottom: 4px;
#> }
#>
#> #moojjreqbz .gt_title {
#> color: #333333;
#> font-size: 125%;
#> font-weight: initial;
#> padding-top: 4px;
#> padding-bottom: 4px;
#> padding-left: 5px;
#> padding-right: 5px;
#> border-bottom-color: #FFFFFF;
#> border-bottom-width: 0;
#> }
#>
#> #moojjreqbz .gt_subtitle {
#> color: #333333;
#> font-size: 85%;
#> font-weight: initial;
#> padding-top: 3px;
#> padding-bottom: 5px;
#> padding-left: 5px;
#> padding-right: 5px;
#> border-top-color: #FFFFFF;
#> border-top-width: 0;
#> }
#>
#> #moojjreqbz .gt_heading {
#> background-color: #FFFFFF;
#> text-align: center;
#> border-bottom-color: #FFFFFF;
#> border-left-style: none;
#> border-left-width: 1px;
#> border-left-color: #D3D3D3;
#> border-right-style: none;
#> border-right-width: 1px;
#> border-right-color: #D3D3D3;
#> }
#>
#> #moojjreqbz .gt_bottom_border {
#> border-bottom-style: solid;
#> border-bottom-width: 2px;
#> border-bottom-color: #D3D3D3;
#> }
#>
#> #moojjreqbz .gt_col_headings {
#> border-top-style: solid;
#> border-top-width: 2px;
#> border-top-color: #D3D3D3;
#> border-bottom-style: solid;
#> border-bottom-width: 2px;
#> border-bottom-color: #D3D3D3;
#> border-left-style: none;
#> border-left-width: 1px;
#> border-left-color: #D3D3D3;
#> border-right-style: none;
#> border-right-width: 1px;
#> border-right-color: #D3D3D3;
#> }
#>
#> #moojjreqbz .gt_col_heading {
#> color: #333333;
#> background-color: #FFFFFF;
#> font-size: 100%;
#> font-weight: normal;
#> text-transform: inherit;
#> border-left-style: none;
#> border-left-width: 1px;
#> border-left-color: #D3D3D3;
#> border-right-style: none;
#> border-right-width: 1px;
#> border-right-color: #D3D3D3;
#> vertical-align: bottom;
#> padding-top: 5px;
#> padding-bottom: 6px;
#> padding-left: 5px;
#> padding-right: 5px;
#> overflow-x: hidden;
#> }
#>
#> #moojjreqbz .gt_column_spanner_outer {
#> color: #333333;
#> background-color: #FFFFFF;
#> font-size: 100%;
#> font-weight: normal;
#> text-transform: inherit;
#> padding-top: 0;
#> padding-bottom: 0;
#> padding-left: 4px;
#> padding-right: 4px;
#> }
#>
#> #moojjreqbz .gt_column_spanner_outer:first-child {
#> padding-left: 0;
#> }
#>
#> #moojjreqbz .gt_column_spanner_outer:last-child {
#> padding-right: 0;
#> }
#>
#> #moojjreqbz .gt_column_spanner {
#> border-bottom-style: solid;
#> border-bottom-width: 2px;
#> border-bottom-color: #D3D3D3;
#> vertical-align: bottom;
#> padding-top: 5px;
#> padding-bottom: 5px;
#> overflow-x: hidden;
#> display: inline-block;
#> width: 100%;
#> }
#>
#> #moojjreqbz .gt_spanner_row {
#> border-bottom-style: hidden;
#> }
#>
#> #moojjreqbz .gt_group_heading {
#> padding-top: 8px;
#> padding-bottom: 8px;
#> padding-left: 5px;
#> padding-right: 5px;
#> color: #333333;
#> background-color: #FFFFFF;
#> font-size: 100%;
#> font-weight: initial;
#> text-transform: inherit;
#> border-top-style: solid;
#> border-top-width: 2px;
#> border-top-color: #D3D3D3;
#> border-bottom-style: solid;
#> border-bottom-width: 2px;
#> border-bottom-color: #D3D3D3;
#> border-left-style: none;
#> border-left-width: 1px;
#> border-left-color: #D3D3D3;
#> border-right-style: none;
#> border-right-width: 1px;
#> border-right-color: #D3D3D3;
#> vertical-align: middle;
#> text-align: left;
#> }
#>
#> #moojjreqbz .gt_empty_group_heading {
#> padding: 0.5px;
#> color: #333333;
#> background-color: #FFFFFF;
#> font-size: 100%;
#> font-weight: initial;
#> border-top-style: solid;
#> border-top-width: 2px;
#> border-top-color: #D3D3D3;
#> border-bottom-style: solid;
#> border-bottom-width: 2px;
#> border-bottom-color: #D3D3D3;
#> vertical-align: middle;
#> }
#>
#> #moojjreqbz .gt_from_md > :first-child {
#> margin-top: 0;
#> }
#>
#> #moojjreqbz .gt_from_md > :last-child {
#> margin-bottom: 0;
#> }
#>
#> #moojjreqbz .gt_row {
#> padding-top: 4px;
#> padding-bottom: 4px;
#> padding-left: 5px;
#> padding-right: 5px;
#> margin: 10px;
#> border-top-style: solid;
#> border-top-width: 1px;
#> border-top-color: #D3D3D3;
#> border-left-style: none;
#> border-left-width: 1px;
#> border-left-color: #D3D3D3;
#> border-right-style: none;
#> border-right-width: 1px;
#> border-right-color: #D3D3D3;
#> vertical-align: middle;
#> overflow-x: hidden;
#> }
#>
#> #moojjreqbz .gt_stub {
#> color: #333333;
#> background-color: #FFFFFF;
#> font-size: 100%;
#> font-weight: initial;
#> text-transform: inherit;
#> border-right-style: solid;
#> border-right-width: 2px;
#> border-right-color: #D3D3D3;
#> padding-left: 5px;
#> padding-right: 5px;
#> }
#>
#> #moojjreqbz .gt_stub_row_group {
#> color: #333333;
#> background-color: #FFFFFF;
#> font-size: 100%;
#> font-weight: initial;
#> text-transform: inherit;
#> border-right-style: solid;
#> border-right-width: 2px;
#> border-right-color: #D3D3D3;
#> padding-left: 5px;
#> padding-right: 5px;
#> vertical-align: top;
#> }
#>
#> #moojjreqbz .gt_row_group_first td {
#> border-top-width: 2px;
#> }
#>
#> #moojjreqbz .gt_row_group_first th {
#> border-top-width: 2px;
#> }
#>
#> #moojjreqbz .gt_summary_row {
#> color: #333333;
#> background-color: #FFFFFF;
#> text-transform: inherit;
#> padding-top: 8px;
#> padding-bottom: 8px;
#> padding-left: 5px;
#> padding-right: 5px;
#> }
#>
#> #moojjreqbz .gt_first_summary_row {
#> border-top-style: solid;
#> border-top-color: #D3D3D3;
#> }
#>
#> #moojjreqbz .gt_first_summary_row.thick {
#> border-top-width: 2px;
#> }
#>
#> #moojjreqbz .gt_last_summary_row {
#> padding-top: 8px;
#> padding-bottom: 8px;
#> padding-left: 5px;
#> padding-right: 5px;
#> border-bottom-style: solid;
#> border-bottom-width: 2px;
#> border-bottom-color: #D3D3D3;
#> }
#>
#> #moojjreqbz .gt_grand_summary_row {
#> color: #333333;
#> background-color: #FFFFFF;
#> text-transform: inherit;
#> padding-top: 8px;
#> padding-bottom: 8px;
#> padding-left: 5px;
#> padding-right: 5px;
#> }
#>
#> #moojjreqbz .gt_first_grand_summary_row {
#> padding-top: 8px;
#> padding-bottom: 8px;
#> padding-left: 5px;
#> padding-right: 5px;
#> border-top-style: double;
#> border-top-width: 6px;
#> border-top-color: #D3D3D3;
#> }
#>
#> #moojjreqbz .gt_last_grand_summary_row_top {
#> padding-top: 8px;
#> padding-bottom: 8px;
#> padding-left: 5px;
#> padding-right: 5px;
#> border-bottom-style: double;
#> border-bottom-width: 6px;
#> border-bottom-color: #D3D3D3;
#> }
#>
#> #moojjreqbz .gt_striped {
#> background-color: rgba(128, 128, 128, 0.05);
#> }
#>
#> #moojjreqbz .gt_table_body {
#> border-top-style: solid;
#> border-top-width: 2px;
#> border-top-color: #D3D3D3;
#> border-bottom-style: solid;
#> border-bottom-width: 2px;
#> border-bottom-color: #D3D3D3;
#> }
#>
#> #moojjreqbz .gt_footnotes {
#> color: #333333;
#> background-color: #FFFFFF;
#> border-bottom-style: none;
#> border-bottom-width: 2px;
#> border-bottom-color: #D3D3D3;
#> border-left-style: none;
#> border-left-width: 2px;
#> border-left-color: #D3D3D3;
#> border-right-style: none;
#> border-right-width: 2px;
#> border-right-color: #D3D3D3;
#> }
#>
#> #moojjreqbz .gt_footnote {
#> margin: 0px;
#> font-size: 90%;
#> padding-top: 4px;
#> padding-bottom: 4px;
#> padding-left: 5px;
#> padding-right: 5px;
#> }
#>
#> #moojjreqbz .gt_sourcenotes {
#> color: #333333;
#> background-color: #FFFFFF;
#> border-bottom-style: none;
#> border-bottom-width: 2px;
#> border-bottom-color: #D3D3D3;
#> border-left-style: none;
#> border-left-width: 2px;
#> border-left-color: #D3D3D3;
#> border-right-style: none;
#> border-right-width: 2px;
#> border-right-color: #D3D3D3;
#> }
#>
#> #moojjreqbz .gt_sourcenote {
#> font-size: 90%;
#> padding-top: 4px;
#> padding-bottom: 4px;
#> padding-left: 5px;
#> padding-right: 5px;
#> }
#>
#> #moojjreqbz .gt_left {
#> text-align: left;
#> }
#>
#> #moojjreqbz .gt_center {
#> text-align: center;
#> }
#>
#> #moojjreqbz .gt_right {
#> text-align: right;
#> font-variant-numeric: tabular-nums;
#> }
#>
#> #moojjreqbz .gt_font_normal {
#> font-weight: normal;
#> }
#>
#> #moojjreqbz .gt_font_bold {
#> font-weight: bold;
#> }
#>
#> #moojjreqbz .gt_font_italic {
#> font-style: italic;
#> }
#>
#> #moojjreqbz .gt_super {
#> font-size: 65%;
#> }
#>
#> #moojjreqbz .gt_footnote_marks {
#> font-size: 75%;
#> vertical-align: 0.4em;
#> position: initial;
#> }
#>
#> #moojjreqbz .gt_asterisk {
#> font-size: 100%;
#> vertical-align: 0;
#> }
#>
#> #moojjreqbz .gt_indent_1 {
#> text-indent: 5px;
#> }
#>
#> #moojjreqbz .gt_indent_2 {
#> text-indent: 10px;
#> }
#>
#> #moojjreqbz .gt_indent_3 {
#> text-indent: 15px;
#> }
#>
#> #moojjreqbz .gt_indent_4 {
#> text-indent: 20px;
#> }
#>
#> #moojjreqbz .gt_indent_5 {
#> text-indent: 25px;
#> }
#> </style>
#> <table class="gt_table" data-quarto-disable-processing="false" data-quarto-bootstrap="false">
#> <thead>
#>
#> <tr class="gt_col_headings gt_spanner_row">
#> <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="2" colspan="1" scope="col" id="Parameter">Parameter</th>
#> <th class="gt_center gt_columns_top_border gt_column_spanner_outer" rowspan="1" colspan="2" scope="colgroup" id="lm1">
#> <span class="gt_column_spanner">lm1</span>
#> </th>
#> <th class="gt_center gt_columns_top_border gt_column_spanner_outer" rowspan="1" colspan="2" scope="colgroup" id="lm2">
#> <span class="gt_column_spanner">lm2</span>
#> </th>
#> </tr>
#> <tr class="gt_col_headings">
#> <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="Estimate(SE)">Estimate(SE)</th>
#> <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="p">p</th>
#> <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="Estimate(SE)">Estimate(SE)</th>
#> <th class="gt_col_heading gt_columns_bottom_border gt_center" rowspan="1" colspan="1" scope="col" id="p">p</th>
#> </tr>
#> </thead>
#> <tbody class="gt_table_body">
#> <tr><td headers="Parameter" class="gt_row gt_left" style="border-right-width: 1px; border-right-style: solid; border-right-color: #d3d3d3;"><div class='gt_from_md'><p>(Intercept)</p>
#> </div></td>
#> <td headers="Estimate(SE) (lm1)" class="gt_row gt_center"><div class='gt_from_md'><p>5.01<br>(0.07)</p>
#> </div></td>
#> <td headers="p (lm1)" class="gt_row gt_center"><div class='gt_from_md'><p><0.001</p>
#> </div></td>
#> <td headers="Estimate(SE) (lm2)" class="gt_row gt_center"><div class='gt_from_md'><p>3.68<br>(0.11)</p>
#> </div></td>
#> <td headers="p (lm2)" class="gt_row gt_center"><div class='gt_from_md'><p><0.001</p>
#> </div></td></tr>
#> <tr><td headers="Parameter" class="gt_row gt_left" style="border-right-width: 1px; border-right-style: solid; border-right-color: #d3d3d3;"><div class='gt_from_md'><p>Species (versicolor)</p>
#> </div></td>
#> <td headers="Estimate(SE) (lm1)" class="gt_row gt_center"><div class='gt_from_md'><p>0.93<br>(0.10)</p>
#> </div></td>
#> <td headers="p (lm1)" class="gt_row gt_center"><div class='gt_from_md'><p><0.001</p>
#> </div></td>
#> <td headers="Estimate(SE) (lm2)" class="gt_row gt_center"><div class='gt_from_md'><p>-1.60<br>(0.19)</p>
#> </div></td>
#> <td headers="p (lm2)" class="gt_row gt_center"><div class='gt_from_md'><p><0.001</p>
#> </div></td></tr>
#> <tr><td headers="Parameter" class="gt_row gt_left" style="border-right-width: 1px; border-right-style: solid; border-right-color: #d3d3d3;"><div class='gt_from_md'><p>Species (virginica)</p>
#> </div></td>
#> <td headers="Estimate(SE) (lm1)" class="gt_row gt_center"><div class='gt_from_md'><p>1.58<br>(0.10)</p>
#> </div></td>
#> <td headers="p (lm1)" class="gt_row gt_center"><div class='gt_from_md'><p><0.001</p>
#> </div></td>
#> <td headers="Estimate(SE) (lm2)" class="gt_row gt_center"><div class='gt_from_md'><p>-2.12<br>(0.27)</p>
#> </div></td>
#> <td headers="p (lm2)" class="gt_row gt_center"><div class='gt_from_md'><p><0.001</p>
#> </div></td></tr>
#> <tr><td headers="Parameter" class="gt_row gt_left" style="border-right-width: 1px; border-right-style: solid; border-right-color: #d3d3d3;"><div class='gt_from_md'><p>Petal Length</p>
#> </div></td>
#> <td headers="Estimate(SE) (lm1)" class="gt_row gt_center"><div class='gt_from_md'></div></td>
#> <td headers="p (lm1)" class="gt_row gt_center"><div class='gt_from_md'></div></td>
#> <td headers="Estimate(SE) (lm2)" class="gt_row gt_center"><div class='gt_from_md'><p>0.90<br>(0.06)</p>
#> </div></td>
#> <td headers="p (lm2)" class="gt_row gt_center"><div class='gt_from_md'><p><0.001</p>
#> </div></td></tr>
#> <tr><td headers="Parameter" class="gt_row gt_left"><div class='gt_from_md'></div></td>
#> <td headers="Estimate(SE) (lm1)" class="gt_row gt_center"><div class='gt_from_md'></div></td>
#> <td headers="p (lm1)" class="gt_row gt_center"><div class='gt_from_md'></div></td>
#> <td headers="Estimate(SE) (lm2)" class="gt_row gt_center"><div class='gt_from_md'></div></td>
#> <td headers="p (lm2)" class="gt_row gt_center"><div class='gt_from_md'></div></td></tr>
#> <tr><td headers="Parameter" class="gt_row gt_left"><div class='gt_from_md'><p>Observations</p>
#> </div></td>
#> <td headers="Estimate(SE) (lm1)" class="gt_row gt_center"><div class='gt_from_md'><p>150</p>
#> </div></td>
#> <td headers="p (lm1)" class="gt_row gt_center"><div class='gt_from_md'></div></td>
#> <td headers="Estimate(SE) (lm2)" class="gt_row gt_center"><div class='gt_from_md'><p>150</p>
#> </div></td>
#> <td headers="p (lm2)" class="gt_row gt_center"><div class='gt_from_md'></div></td></tr>
#> </tbody>
#> <tfoot class="gt_sourcenotes">
#> <tr>
#> <td class="gt_sourcenote" colspan="5"></td>
#> </tr>
#> </tfoot>
#>
#> </table>
#> </div>
# }