Parameters from (linear) mixed models.

## Usage

# S3 method for cpglmm
model_parameters(
model,
ci = 0.95,
ci_method = NULL,
ci_random = NULL,
bootstrap = FALSE,
iterations = 1000,
standardize = NULL,
effects = "all",
group_level = FALSE,
exponentiate = FALSE,
include_sigma = FALSE,
verbose = TRUE,
df_method = ci_method,
...
)

# S3 method for glmmTMB
model_parameters(
model,
ci = 0.95,
ci_method = "wald",
ci_random = NULL,
bootstrap = FALSE,
iterations = 1000,
standardize = NULL,
effects = "all",
component = "all",
group_level = FALSE,
exponentiate = FALSE,
wb_component = TRUE,
summary = getOption("parameters_mixed_summary", FALSE),
keep = NULL,
drop = NULL,
parameters = keep,
verbose = TRUE,
df_method = ci_method,
include_sigma = FALSE,
...
)

# S3 method for merMod
model_parameters(
model,
ci = 0.95,
ci_method = NULL,
ci_random = NULL,
bootstrap = FALSE,
iterations = 1000,
standardize = NULL,
effects = "all",
group_level = FALSE,
exponentiate = FALSE,
wb_component = TRUE,
summary = getOption("parameters_mixed_summary", FALSE),
keep = NULL,
drop = NULL,
parameters = keep,
verbose = TRUE,
df_method = ci_method,
include_sigma = FALSE,
vcov = NULL,
vcov_args = NULL,
...
)

# S3 method for merModList
model_parameters(
model,
ci = 0.95,
exponentiate = FALSE,
verbose = TRUE,
...
)

# S3 method for mixed
model_parameters(
model,
ci = 0.95,
ci_method = "wald",
ci_random = NULL,
bootstrap = FALSE,
iterations = 1000,
standardize = NULL,
effects = "all",
component = "all",
group_level = FALSE,
exponentiate = FALSE,
wb_component = TRUE,
summary = getOption("parameters_mixed_summary", FALSE),
keep = NULL,
drop = NULL,
parameters = keep,
verbose = TRUE,
df_method = ci_method,
include_sigma = FALSE,
...
)

# S3 method for MixMod
model_parameters(
model,
ci = 0.95,
ci_method = "wald",
ci_random = NULL,
bootstrap = FALSE,
iterations = 1000,
standardize = NULL,
effects = "all",
component = "all",
group_level = FALSE,
exponentiate = FALSE,
wb_component = TRUE,
summary = getOption("parameters_mixed_summary", FALSE),
keep = NULL,
drop = NULL,
parameters = keep,
verbose = TRUE,
df_method = ci_method,
include_sigma = FALSE,
...
)

# S3 method for mixor
model_parameters(
model,
ci = 0.95,
effects = "all",
bootstrap = FALSE,
iterations = 1000,
standardize = NULL,
exponentiate = FALSE,
verbose = TRUE,
include_sigma = FALSE,
...
)

# S3 method for lme
model_parameters(
model,
ci = 0.95,
ci_method = NULL,
ci_random = NULL,
bootstrap = FALSE,
iterations = 1000,
standardize = NULL,
effects = "all",
group_level = FALSE,
exponentiate = FALSE,
wb_component = TRUE,
summary = getOption("parameters_mixed_summary", FALSE),
keep = NULL,
drop = NULL,
parameters = keep,
verbose = TRUE,
df_method = ci_method,
include_sigma = FALSE,
vcov = NULL,
vcov_args = NULL,
...
)

# S3 method for clmm2
model_parameters(
model,
ci = 0.95,
bootstrap = FALSE,
iterations = 1000,
component = c("all", "conditional", "scale"),
standardize = NULL,
exponentiate = FALSE,
verbose = TRUE,
...
)

# S3 method for clmm
model_parameters(
model,
ci = 0.95,
ci_method = NULL,
ci_random = NULL,
bootstrap = FALSE,
iterations = 1000,
standardize = NULL,
effects = "all",
group_level = FALSE,
exponentiate = FALSE,
include_sigma = FALSE,
verbose = TRUE,
df_method = ci_method,
...
)

# S3 method for rlmerMod
model_parameters(
model,
ci = 0.95,
ci_method = NULL,
ci_random = NULL,
bootstrap = FALSE,
iterations = 1000,
standardize = NULL,
effects = "all",
group_level = FALSE,
exponentiate = FALSE,
include_sigma = FALSE,
verbose = TRUE,
df_method = ci_method,
...
)

# S3 method for HLfit
model_parameters(
model,
ci = 0.95,
ci_method = NULL,
bootstrap = FALSE,
iterations = 1000,
standardize = NULL,
exponentiate = FALSE,
summary = getOption("parameters_summary", FALSE),
keep = NULL,
drop = NULL,
parameters = keep,
verbose = TRUE,
vcov = NULL,
vcov_args = NULL,
...
)

## Arguments

model

A mixed model.

ci

Confidence Interval (CI) level. Default to 0.95 (95%).

ci_method

Method for computing degrees of freedom for confidence intervals (CI) and the related p-values. Allowed are following options (which vary depending on the model class): "residual", "normal", "likelihood", "satterthwaite", "kenward", "wald", "profile", "boot", "uniroot", "ml1", "betwithin", "hdi", "quantile", "ci", "eti", "si", "bci", or "bcai". See section Confidence intervals and approximation of degrees of freedom in model_parameters() for further details. When ci_method=NULL, in most cases "wald" is used then.

ci_random

Logical, if TRUE, includes the confidence intervals for random effects parameters. Only applies if effects is not "fixed" and if ci is not NULL. Set ci_random = FALSE if computation of the model summary is too much time consuming. By default, ci_random = NULL, which uses a heuristic to guess if computation of confidence intervals for random effects is fast enough or not. For models with larger sample size and/or more complex random effects structures, confidence intervals will not be computed by default, for simpler models or fewer observations, confidence intervals will be included. Set explicitly to TRUE or FALSE to enforce or omit calculation of confidence intervals.

bootstrap

Should estimates be based on bootstrapped model? If TRUE, then arguments of Bayesian regressions apply (see also bootstrap_parameters()).

iterations

The number of draws to simulate/bootstrap.

standardize

The method used for standardizing the parameters. Can be NULL (default; no standardization), "refit" (for re-fitting the model on standardized data) or one of "basic", "posthoc", "smart", "pseudo". See 'Details' in standardize_parameters(). Important:

• The "refit" method does not standardized categorical predictors (i.e. factors), which may be a different behaviour compared to other R packages (such as lm.beta) or other software packages (like SPSS). to mimic such behaviours, either use standardize="basic" or standardize the data with datawizard::standardize(force=TRUE) before fitting the model.

• For mixed models, when using methods other than "refit", only the fixed effects will be returned.

• Robust estimation (i.e., vcov set to a value other than NULL) of standardized parameters only works when standardize="refit".

effects

Should parameters for fixed effects ("fixed"), random effects ("random"), or both ("all") be returned? Only applies to mixed models. May be abbreviated. If the calculation of random effects parameters takes too long, you may use effects = "fixed".

group_level

Logical, for multilevel models (i.e. models with random effects) and when effects = "all" or effects = "random", include the parameters for each group level from random effects. If group_level = FALSE (the default), only information on SD and COR are shown.

exponentiate

Logical, indicating whether or not to exponentiate the the coefficients (and related confidence intervals). This is typical for logistic regression, or more generally speaking, for models with log or logit links. Note: Delta-method standard errors are also computed (by multiplying the standard errors by the transformed coefficients). This is to mimic behaviour of other software packages, such as Stata, but these standard errors poorly estimate uncertainty for the transformed coefficient. The transformed confidence interval more clearly captures this uncertainty. For compare_parameters(), exponentiate = "nongaussian" will only exponentiate coefficients from non-Gaussian families.

Character vector, if not NULL, indicates the method to adjust p-values. See stats::p.adjust() for details. Further possible adjustment methods are "tukey", "scheffe", "sidak" and "none" to explicitly disable adjustment for emmGrid objects (from emmeans).

include_sigma

Logical, if TRUE, includes the residual standard deviation. For mixed models, this is defined as the sum of the distribution-specific variance and the variance for the additive overdispersion term (see insight::get_variance() for details). Defaults to FALSE for mixed models due to the longer computation time.

verbose

Toggle warnings and messages.

df_method

Deprecated. Please use ci_method.

...

Arguments passed to or from other methods.

component

Should all parameters, parameters for the conditional model, for the zero-inflated part of the model, or the dispersion model be returned? Applies to models with zero-inflated and/or dispersion component. component may be one of "conditional", "zi", "zero-inflated", "dispersion" or "all" (default). May be abbreviated.

wb_component

Logical, if TRUE and models contains within- and between-effects (see datawizard::demean()), the Component column will indicate which variables belong to the within-effects, between-effects, and cross-level interactions. By default, the Component column indicates, which parameters belong to the conditional or zero-inflated component of the model.

summary

Logical, if TRUE, prints summary information about the model (model formula, number of observations, residual standard deviation and more).

keep

Character containing a regular expression pattern that describes the parameters that should be included (for keep) or excluded (for drop) in the returned data frame. keep may also be a named list of regular expressions. All non-matching parameters will be removed from the output. If keep is a character vector, every parameter name in the "Parameter" column that matches the regular expression in keep will be selected from the returned data frame (and vice versa, all parameter names matching drop will be excluded). Furthermore, if keep has more than one element, these will be merged with an OR operator into a regular expression pattern like this: "(one|two|three)". If keep is a named list of regular expression patterns, the names of the list-element should equal the column name where selection should be applied. This is useful for model objects where model_parameters() returns multiple columns with parameter components, like in model_parameters.lavaan(). Note that the regular expression pattern should match the parameter names as they are stored in the returned data frame, which can be different from how they are printed. Inspect the $Parameter column of the parameters table to get the exact parameter names. drop See keep. parameters Deprecated, alias for keep. vcov Variance-covariance matrix used to compute uncertainty estimates (e.g., for robust standard errors). This argument accepts a covariance matrix, a function which returns a covariance matrix, or a string which identifies the function to be used to compute the covariance matrix. • A covariance matrix • A function which returns a covariance matrix (e.g., stats::vcov()) • A string which indicates the kind of uncertainty estimates to return. • Heteroskedasticity-consistent: "vcovHC", "HC", "HC0", "HC1", "HC2", "HC3", "HC4", "HC4m", "HC5". See ?sandwich::vcovHC. • Cluster-robust: "vcovCR", "CR0", "CR1", "CR1p", "CR1S", "CR2", "CR3". See ?clubSandwich::vcovCR. • Bootstrap: "vcovBS", "xy", "residual", "wild", "mammen", "webb". See ?sandwich::vcovBS. • Other sandwich package functions: "vcovHAC", "vcovPC", "vcovCL", "vcovPL". vcov_args List of arguments to be passed to the function identified by the vcov argument. This function is typically supplied by the sandwich or clubSandwich packages. Please refer to their documentation (e.g., ?sandwich::vcovHAC) to see the list of available arguments. ## Value A data frame of indices related to the model's parameters. ## Note If the calculation of random effects parameters takes too long, you may use effects = "fixed". There is also a plot()-method implemented in the see-package. ## Confidence intervals for random effect variances For models of class merMod and glmmTMB, confidence intervals for random effect variances can be calculated. • For models of from package lme4, when ci_method is either "profile" or "boot", and effects is either "random" or "all", profiled resp. bootstrapped confidence intervals are computed for the random effects. • For all other options of ci_method, and only when the merDeriv package is installed, confidence intervals for random effects are based on normal-distribution approximation, using the delta-method to transform standard errors for constructing the intervals around the log-transformed SD parameters. These are than back-transformed, so that random effect variances, standard errors and confidence intervals are shown on the original scale. Due to the transformation, the intervals are asymmetrical, however, they are within the correct bounds (i.e. no negative interval for the SD, and the interval for the correlations is within the range from -1 to +1). • For models of class glmmTMB, confidence intervals for random effect variances always use a Wald t-distribution approximation. ## Dispersion parameters in glmmTMB For some models from package glmmTMB, both the dispersion parameter and the residual variance from the random effects parameters are shown. Usually, these are the same but presented on different scales, e.g. model <- glmmTMB(Sepal.Width ~ Petal.Length + (1|Species), data = iris) exp(fixef(model)$disp) # 0.09902987
sigma(model)^2         # 0.09902987

For models where the dispersion parameter and the residual variance are the same, only the residual variance is shown in the output.

## Confidence intervals and approximation of degrees of freedom

There are different ways of approximating the degrees of freedom depending on different assumptions about the nature of the model and its sampling distribution. The ci_method argument modulates the method for computing degrees of freedom (df) that are used to calculate confidence intervals (CI) and the related p-values. Following options are allowed, depending on the model class:

Classical methods:

Classical inference is generally based on the Wald method. The Wald approach to inference computes a test statistic by dividing the parameter estimate by its standard error (Coefficient / SE), then comparing this statistic against a t- or normal distribution. This approach can be used to compute CIs and p-values.

"wald":

• Applies to non-Bayesian models. For linear models, CIs computed using the Wald method (SE and a t-distribution with residual df); p-values computed using the Wald method with a t-distribution with residual df. For other models, CIs computed using the Wald method (SE and a normal distribution); p-values computed using the Wald method with a normal distribution.

"normal"

• Applies to non-Bayesian models. Compute Wald CIs and p-values, but always use a normal distribution.

"residual"

• Applies to non-Bayesian models. Compute Wald CIs and p-values, but always use a t-distribution with residual df when possible. If the residual df for a model cannot be determined, a normal distribution is used instead.

Methods for mixed models:

Compared to fixed effects (or single-level) models, determining appropriate df for Wald-based inference in mixed models is more difficult. See the R GLMM FAQ for a discussion.

Several approximate methods for computing df are available, but you should also consider instead using profile likelihood ("profile") or bootstrap ("boot") CIs and p-values instead.

"satterthwaite"

• Applies to linear mixed models. CIs computed using the Wald method (SE and a t-distribution with Satterthwaite df); p-values computed using the Wald method with a t-distribution with Satterthwaite df.

"kenward"

• Applies to linear mixed models. CIs computed using the Wald method (Kenward-Roger SE and a t-distribution with Kenward-Roger df); p-values computed using the Wald method with Kenward-Roger SE and t-distribution with Kenward-Roger df.

"ml1"

• Applies to linear mixed models. CIs computed using the Wald method (SE and a t-distribution with m-l-1 approximated df); p-values computed using the Wald method with a t-distribution with m-l-1 approximated df. See ci_ml1().

"betwithin"

• Applies to linear mixed models and generalized linear mixed models. CIs computed using the Wald method (SE and a t-distribution with between-within df); p-values computed using the Wald method with a t-distribution with between-within df. See ci_betwithin().

Likelihood-based methods:

Likelihood-based inference is based on comparing the likelihood for the maximum-likelihood estimate to the the likelihood for models with one or more parameter values changed (e.g., set to zero or a range of alternative values). Likelihood ratios for the maximum-likelihood and alternative models are compared to a $$\chi$$-squared distribution to compute CIs and p-values.

"profile"

• Applies to non-Bayesian models of class glm, polr or glmmTMB. CIs computed by profiling the likelihood curve for a parameter, using linear interpolation to find where likelihood ratio equals a critical value; p-values computed using the Wald method with a normal-distribution (note: this might change in a future update!)

"uniroot"

• Applies to non-Bayesian models of class glmmTMB. CIs computed by profiling the likelihood curve for a parameter, using root finding to find where likelihood ratio equals a critical value; p-values computed using the Wald method with a normal-distribution (note: this might change in a future update!)

Methods for bootstrapped or Bayesian models:

Bootstrap-based inference is based on resampling and refitting the model to the resampled datasets. The distribution of parameter estimates across resampled datasets is used to approximate the parameter's sampling distribution. Depending on the type of model, several different methods for bootstrapping and constructing CIs and p-values from the bootstrap distribution are available.

For Bayesian models, inference is based on drawing samples from the model posterior distribution.

"quantile" (or "eti")

• Applies to all models (including Bayesian models). For non-Bayesian models, only applies if bootstrap = TRUE. CIs computed as equal tailed intervals using the quantiles of the bootstrap or posterior samples; p-values are based on the probability of direction. See bayestestR::eti().

"hdi"

• Applies to all models (including Bayesian models). For non-Bayesian models, only applies if bootstrap = TRUE. CIs computed as highest density intervals for the bootstrap or posterior samples; p-values are based on the probability of direction. See bayestestR::hdi().

"bci" (or "bcai")

• Applies to all models (including Bayesian models). For non-Bayesian models, only applies if bootstrap = TRUE. CIs computed as bias corrected and accelerated intervals for the bootstrap or posterior samples; p-values are based on the probability of direction. See bayestestR::bci().

"si"

• Applies to Bayesian models with proper priors. CIs computed as support intervals comparing the posterior samples against the prior samples; p-values are based on the probability of direction. See bayestestR::si().

"boot"

• Applies to non-Bayesian models of class merMod. CIs computed using parametric bootstrapping (simulating data from the fitted model); p-values computed using the Wald method with a normal-distribution) (note: this might change in a future update!).

For all iteration-based methods other than "boot" ("hdi", "quantile", "ci", "eti", "si", "bci", "bcai"), p-values are based on the probability of direction (bayestestR::p_direction()), which is converted into a p-value using bayestestR::pd_to_p().

insight::standardize_names() to rename columns into a consistent, standardized naming scheme.

## Examples

library(parameters)
if (require("lme4")) {
data(mtcars)
model <- lmer(mpg ~ wt + (1 | gear), data = mtcars)
model_parameters(model)
}
#>
#> Attaching package: ‘lme4’
#> The following object is masked from ‘package:nlme’:
#>
#>     lmList
#> # Fixed Effects
#>
#> Parameter   | Coefficient |   SE |         95% CI | t(28) |      p
#> ------------------------------------------------------------------
#> (Intercept) |       36.19 | 2.19 | [31.70, 40.68] | 16.52 | < .001
#> wt          |       -5.05 | 0.64 | [-6.36, -3.73] | -7.89 | < .001
#>
#> # Random Effects
#>
#> Parameter            | Coefficient |   SE |       95% CI
#> --------------------------------------------------------
#> SD (Intercept: gear) |        1.26 | 1.12 | [0.22, 7.17]
#> SD (Residual)        |        2.91 | 0.39 | [2.24, 3.78]
#>
#> Uncertainty intervals (equal-tailed) and p-values (two-tailed) computed
#>   using a Wald t-distribution approximation.
# \donttest{
if (require("glmmTMB")) {
data(Salamanders)
model <- glmmTMB(
count ~ spp + mined + (1 | site),
ziformula = ~mined,
family = poisson(),
data = Salamanders
)
model_parameters(model, effects = "all")
}
#> # 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
#> 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
#>
#> # Fixed Effects (Zero-Inflated Model)
#>
#> Parameter   | Log-Odds |   SE |         95% CI |     z |      p
#> ---------------------------------------------------------------
#> (Intercept) |     0.79 | 0.27 | [ 0.26,  1.32] |  2.90 | 0.004
#> mined [no]  |    -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.

if (require("lme4")) {
model <- lmer(mpg ~ wt + (1 | gear), data = mtcars)
model_parameters(model, bootstrap = TRUE, iterations = 50)
}
#> Warning: Bootstrapping only returns fixed effects of the mixed model.
#> # Fixed Effects
#>
#> Parameter   | Coefficient |         95% CI |      p
#> ---------------------------------------------------
#> (Intercept) |       36.26 | [32.08, 40.38] | < .001
#> wt          |       -5.05 | [-6.46, -3.95] | < .001
#>
#> Uncertainty intervals (equal-tailed) are naıve bootstrap intervals.
# }