The model_parameters() function (also accessible via the shortcut parameters()) allows you to extract the parameters and their characteristics from various models in a consistent way. It can be considered as a lightweight alternative to broom::tidy(), with some notable differences:
The names of the returned data frame are specific to their content. For instance, the column containing the statistic is named following the statistic name, i.e., t, z, etc., instead of a generic name such as statistic (however, you can get standardized (generic) column names using standardize_names()).
It is able to compute or extract indices not available by default, such as **p*-values, CIs**, etc.
It includes feature engineering capabilities, including parameters bootstrapping.
cor.test(iris$Sepal.Length, iris$Sepal.Width) %>%
parameters()
#> Pearson's product-moment correlation
#>
#> Parameter1 | Parameter2 | r | 95% CI | t(148) | p
#> -----------------------------------------------------------------------------
#> iris$Sepal.Length | iris$Sepal.Width | -0.12 | [-0.27, 0.04] | -1.44 | 0.152
#>
#> Alternative hypothesis: true correlation is not equal to 0
t.test(mpg ~ vs, data = mtcars) %>%
parameters()
#> Welch Two Sample t-test
#>
#> Parameter | Group | vs = 0 | vs = 1 | Difference | 95% CI | t(22.72) | p
#> --------------------------------------------------------------------------------------
#> mpg | vs | 16.62 | 24.56 | -7.94 | [-11.46, -4.42] | -4.67 | < .001
#>
#> Alternative hypothesis: true difference in means between group 0 and group 1 is not equal to 0
library(BayesFactor)
BayesFactor::correlationBF(iris$Sepal.Length, iris$Sepal.Width) %>%
parameters()
#> Bayesian correlation analysis
#>
#> Parameter | Median | 95% CI | pd | % in ROPE | Prior | BF
#> -------------------------------------------------------------------------------
#> rho | -0.11 | [-0.27, 0.04] | 92.25% | 19.65% | Beta (3 +- 3) | 0.509
BayesFactor::ttestBF(formula = mpg ~ vs, data = mtcars) %>%
parameters()
#> Bayesian t-test
#>
#> Parameter | Median | 95% CI | pd | % in ROPE | Prior | BF
#> ----------------------------------------------------------------------------------------
#> Difference | -7.31 | [-10.73, -3.72] | 99.98% | 0% | Cauchy (0 +- 0.71) | 529.27Indices of effect size for ANOVAs, such as partial and non-partial versions of eta_squared(), epsilon_sqared() or omega_squared() are powered by the effectsize-package. However, parameters uses these function to compute such indices for parameters summaries, including confidence intervals
aov(Sepal.Length ~ Species, data = iris) %>%
parameters(
omega_squared = "partial",
eta_squared = "partial",
epsilon_squared = "partial"
)
#> Parameter | Sum_Squares | df | Mean_Square | F | p | Omega2 | Eta2 | Epsilon2
#> ----------------------------------------------------------------------------------------
#> Species | 63.21 | 2 | 31.61 | 119.26 | < .001 | 0.61 | 0.62 | 0.61
#> Residuals | 38.96 | 147 | 0.27 | | | | |
#>
#> Anova Table (Type 1 tests)Let’s complicate things further with an interaction term:
aov(Sepal.Length ~ Species * Sepal.Width, data = iris) %>%
parameters(
omega_squared = "partial",
eta_squared = "partial",
ci = .8
)
#> Parameter | Sum_Squares | df | Mean_Square | F | p | Omega2 (partial) | Omega2 80% CI | Eta2 (partial) | Eta2 80% CI
#> ------------------------------------------------------------------------------------------------------------------------------------------
#> Species | 63.21 | 2 | 31.61 | 163.44 | < .001 | 0.68 | [0.65, 1.00] | 0.69 | [0.66, 1.00]
#> Sepal.Width | 10.95 | 1 | 10.95 | 56.64 | < .001 | 0.27 | [0.22, 1.00] | 0.28 | [0.23, 1.00]
#> Species:Sepal.Width | 0.16 | 2 | 0.08 | 0.41 | 0.667 | -7.98e-03 | [0.00, 1.00] | 5.61e-03 | [0.00, 1.00]
#> Residuals | 27.85 | 144 | 0.19 | | | | | |
#>
#> Anova Table (Type 1 tests)parameters() (resp. its alias model_parameters()) also works on repeated measures ANOVAs, whether computed from aov() or from a mixed model.
aov(mpg ~ am + Error(gear), data = mtcars) %>%
parameters()
#> # gear
#>
#> Parameter | Sum_Squares | df | Mean_Square
#> ------------------------------------------
#> am | 259.75 | 1 | 259.75
#>
#> # Within
#>
#> Parameter | Sum_Squares | df | Mean_Square | F | p
#> ---------------------------------------------------------
#> am | 145.45 | 1 | 145.45 | 5.85 | 0.022
#> Residuals | 720.85 | 29 | 24.86 | |
#>
#> Anova Table (Type 1 tests)parameters() (resp. its alias model_parameters()) was mainly built with regression models in mind. It works for many types of models and packages, including mixed models and Bayesian models.
glm(vs ~ poly(mpg, 2) + cyl, data = mtcars, family = binomial()) %>%
parameters()
#> Parameter | Log-Odds | SE | 95% CI | z | p
#> --------------------------------------------------------------------
#> (Intercept) | 13.51 | 7.20 | [ 2.56, 33.42] | 1.88 | 0.060
#> mpg [1st degree] | -6.64 | 8.99 | [-27.81, 11.13] | -0.74 | 0.461
#> mpg [2nd degree] | 1.16 | 3.59 | [ -7.91, 8.56] | 0.32 | 0.746
#> cyl | -2.28 | 1.18 | [ -5.58, -0.51] | -1.92 | 0.055
# show Odds Ratios and Wald-method for degrees of freedom
glm(vs ~ poly(mpg, 2) + cyl, data = mtcars, family = binomial()) %>%
parameters(exponentiate = TRUE, df_method = "wald")
#> Parameter | Odds Ratio | SE | 95% CI | z | p
#> ---------------------------------------------------------------------------
#> (Intercept) | 7.38e+05 | 5.31e+06 | [0.55, 9.87e+11] | 1.88 | 0.060
#> mpg [1st degree] | 1.31e-03 | 0.01 | [0.00, 59497.56] | -0.74 | 0.461
#> mpg [2nd degree] | 3.20 | 11.49 | [0.00, 3637.30] | 0.32 | 0.746
#> cyl | 0.10 | 0.12 | [0.01, 1.05] | -1.92 | 0.055
# show Odds Ratios and include model summary
glm(vs ~ poly(mpg, 2) + cyl, data = mtcars, family = binomial()) %>%
parameters(exponentiate = TRUE, summary = TRUE)
#> Parameter | Odds Ratio | SE | 95% CI | z | p
#> ----------------------------------------------------------------------------
#> (Intercept) | 7.38e+05 | 5.31e+06 | [12.95, 3.26e+14] | 1.88 | 0.060
#> mpg [1st degree] | 1.31e-03 | 0.01 | [ 0.00, 68459.83] | -0.74 | 0.461
#> mpg [2nd degree] | 3.20 | 11.49 | [ 0.00, 5212.21] | 0.32 | 0.746
#> cyl | 0.10 | 0.12 | [ 0.00, 0.60] | -1.92 | 0.055
#>
#> Model: vs ~ poly(mpg, 2) + cyl (32 Observations)
#> Residual standard deviation: 0.788 (df = 28)
#> Tjur's R2: 0.670
library(lme4)
lmer(Sepal.Width ~ Petal.Length + (1 | Species), data = iris) %>%
parameters()
#> # Fixed Effects
#>
#> Parameter | Coefficient | SE | 95% CI | t(146) | p
#> ------------------------------------------------------------------
#> (Intercept) | 2.00 | 0.56 | [0.89, 3.11] | 3.56 | < .001
#> Petal Length | 0.28 | 0.06 | [0.16, 0.40] | 4.75 | < .001
#>
#> # Random Effects
#>
#> Parameter | Coefficient
#> -------------------------------------
#> SD (Intercept: Species) | 0.89
#> SD (Residual) | 0.32
lmer(Sepal.Width ~ Petal.Length + (1 | Species), data = iris) %>%
parameters(effects = "fixed")
#> # Fixed Effects
#>
#> Parameter | Coefficient | SE | 95% CI | t(146) | p
#> ------------------------------------------------------------------
#> (Intercept) | 2.00 | 0.56 | [0.89, 3.11] | 3.56 | < .001
#> Petal Length | 0.28 | 0.06 | [0.16, 0.40] | 4.75 | < .001
library(GLMMadaptive)
library(glmmTMB)
data("Salamanders")
model <- mixed_model(
count ~ spp + mined,
random = ~ 1 | site,
zi_fixed = ~ spp + mined,
family = zi.negative.binomial(),
data = Salamanders
)
parameters(model)
#> # Fixed Effects (Count Model)
#>
#> Parameter | Log-Mean | SE | 95% CI | z | p
#> --------------------------------------------------------------
#> (Intercept) | -0.63 | 0.40 | [-1.42, 0.16] | -1.56 | 0.118
#> spp [PR] | -0.99 | 0.70 | [-2.35, 0.38] | -1.41 | 0.157
#> spp [DM] | 0.17 | 0.24 | [-0.29, 0.63] | 0.72 | 0.469
#> spp [EC-A] | -0.39 | 0.35 | [-1.07, 0.29] | -1.13 | 0.258
#> spp [EC-L] | 0.49 | 0.24 | [ 0.02, 0.96] | 2.03 | 0.043
#> spp [DES-L] | 0.59 | 0.23 | [ 0.14, 1.04] | 2.57 | 0.010
#> spp [DF] | -0.11 | 0.24 | [-0.59, 0.37] | -0.46 | 0.642
#> mined [no] | 1.45 | 0.37 | [ 0.73, 2.17] | 3.95 | < .001
#>
#> # Fixed Effects (Zero-Inflated Model)
#>
#> Parameter | Log-Odds | SE | 95% CI | z | p
#> ---------------------------------------------------------------
#> (Intercept) | 0.90 | 0.64 | [-0.35, 2.15] | 1.41 | 0.159
#> spp [PR] | 1.12 | 1.50 | [-1.82, 4.06] | 0.74 | 0.456
#> spp [DM] | -0.95 | 0.82 | [-2.56, 0.65] | -1.17 | 0.244
#> spp [EC-A] | 1.04 | 0.72 | [-0.38, 2.46] | 1.44 | 0.150
#> spp [EC-L] | -0.58 | 0.74 | [-2.03, 0.88] | -0.77 | 0.439
#> spp [DES-L] | -0.91 | 0.78 | [-2.43, 0.61] | -1.18 | 0.239
#> spp [DF] | -2.63 | 2.37 | [-7.27, 2.02] | -1.11 | 0.268
#> mined [no] | -2.56 | 0.63 | [-3.80, -1.32] | -4.06 | < .001
#>
#> # Random Effects Variances
#>
#> Parameter | Coefficient
#> ----------------------------------
#> SD (Intercept: site) | 0.39
#> SD (Residual) | 0.00
library(glmmTMB)
sim1 <- function(nfac = 40, nt = 100, facsd = 0.1, tsd = 0.15, mu = 0, residsd = 1) {
dat <- expand.grid(fac = factor(letters[1:nfac]), t = 1:nt)
n <- nrow(dat)
dat$REfac <- rnorm(nfac, sd = facsd)[dat$fac]
dat$REt <- rnorm(nt, sd = tsd)[dat$t]
dat$x <- rnorm(n, mean = mu, sd = residsd) + dat$REfac + dat$REt
dat
}
set.seed(101)
d1 <- sim1(mu = 100, residsd = 10)
d2 <- sim1(mu = 200, residsd = 5)
d1$sd <- "ten"
d2$sd <- "five"
dat <- rbind(d1, d2)
model <- glmmTMB(x ~ sd + (1 | t), dispformula = ~sd, data = dat)
parameters(model)
#> # Fixed Effects
#>
#> Parameter | Coefficient | SE | 95% CI | z | p
#> -----------------------------------------------------------------------
#> (Intercept) | 200.03 | 0.10 | [ 199.84, 200.22] | 2056.35 | < .001
#> sd [ten] | -99.71 | 0.22 | [-100.14, -99.29] | -458.39 | < .001
#>
#> # Dispersion
#>
#> Parameter | Coefficient | SE | 95% CI | z | p
#> -----------------------------------------------------------------
#> (Intercept) | 3.20 | 0.03 | [3.15, 3.26] | 115.48 | < .001
#> sd [ten] | 1.39 | 0.04 | [1.31, 1.46] | 35.35 | < .001
#>
#> # Random Effects Variances
#>
#> Parameter | Coefficient | 95% CI
#> ---------------------------------------------------
#> SD (Intercept: t) | 5.56e-04 | [0.00, 4.36e+290]model_parameters() also works with Bayesian models from the rstanarm package:
library(rstanarm)
# if you are unfamiliar with the `refresh` argument here, it just avoids
# printing few messages to the console
stan_glm(mpg ~ wt * cyl, data = mtcars, refresh = 0) %>%
parameters()
#> Parameter | Median | 95% CI | pd | % in ROPE | Rhat | ESS | Prior
#> -------------------------------------------------------------------------------------------------------
#> (Intercept) | 52.34 | [ 40.92, 64.50] | 100% | 0% | 1.002 | 1154.00 | Normal (20.09 +- 15.07)
#> wt | -7.90 | [-12.79, -3.70] | 99.98% | 0% | 1.002 | 1250.00 | Normal (0.00 +- 15.40)
#> cyl | -3.51 | [ -5.55, -1.63] | 100% | 0% | 1.002 | 1267.00 | Normal (0.00 +- 8.44)
#> wt:cyl | 0.70 | [ 0.12, 1.36] | 98.55% | 37.02% | 1.002 | 1184.00 | Normal (0.00 +- 1.36)Additionally, it also works for models from the brms package.
For more complex models, specific model components can be printed using the arguments effects and component arguments.
library(brms)
data(fish)
set.seed(123)
# fitting a model using `brms`
model <- brm(
bf(
count ~ persons + child + camper + (1 | persons),
zi ~ child + camper + (1 | persons)
),
data = fish,
family = zero_inflated_poisson(),
refresh = 0
)
parameters(model, component = "conditional")
#> Parameter | Median | 95% CI | pd | % in ROPE | Rhat | ESS
#> ----------------------------------------------------------------------------
#> (Intercept) | -0.86 | [-1.46, -0.24] | 99.58% | 0% | 1.004 | 957.00
#> persons | 0.84 | [ 0.66, 1.06] | 100% | 0% | 1.005 | 778.00
#> child | -1.15 | [-1.33, -0.97] | 100% | 0% | 1.001 | 2688.00
#> camper1 | 0.73 | [ 0.55, 0.91] | 100% | 0% | 1.001 | 3045.00
parameters(model, effects = "all", component = "all")
#> # Fixed effects (conditional)
#>
#> Parameter | Median | 95% CI | pd | % in ROPE | Rhat | ESS
#> ----------------------------------------------------------------------------
#> (Intercept) | -0.86 | [-1.46, -0.24] | 99.58% | 0% | 1.004 | 957.00
#> persons | 0.84 | [ 0.66, 1.06] | 100% | 0% | 1.005 | 778.00
#> child | -1.15 | [-1.33, -0.97] | 100% | 0% | 1.001 | 2688.00
#> camper1 | 0.73 | [ 0.55, 0.91] | 100% | 0% | 1.001 | 3045.00
#>
#> # Fixed effects (zero-inflated)
#>
#> Parameter | Median | 95% CI | pd | % in ROPE | Rhat | ESS
#> ----------------------------------------------------------------------------
#> (Intercept) | -0.67 | [-2.02, 0.83] | 84.35% | 7.18% | 1.003 | 1160.00
#> child | 1.86 | [ 1.23, 2.54] | 100% | 0% | 1.000 | 2574.00
#> camper1 | -0.83 | [-1.62, -0.15] | 98.62% | 0% | 1.000 | 2777.00
#>
#> # Random effects (conditional) SD/Cor: persons
#>
#> Parameter | Median | 95% CI | pd | % in ROPE | Rhat | ESS
#> -----------------------------------------------------------------------
#> (Intercept) | 0.11 | [0.00, 0.48] | 100% | 48.80% | 1.003 | 753.00
#>
#> # Random effects (zero-inflated) SD/Cor: persons
#>
#> Parameter | Median | 95% CI | pd | % in ROPE | Rhat | ESS
#> ------------------------------------------------------------------------
#> (Intercept) | 1.32 | [0.37, 3.00] | 100% | 0% | 1.003 | 1183.00To include information about the random effect parameters (group levels), set group_level = TRUE:
parameters(model, effects = "all", component = "conditional", group_level = TRUE)
#> # Fixed effects
#>
#> Parameter | Median | 95% CI | pd | % in ROPE | Rhat | ESS
#> ----------------------------------------------------------------------------
#> (Intercept) | -0.86 | [-1.46, -0.24] | 99.58% | 0% | 1.004 | 957.00
#> persons | 0.84 | [ 0.66, 1.06] | 100% | 0% | 1.005 | 778.00
#> child | -1.15 | [-1.33, -0.97] | 100% | 0% | 1.001 | 2688.00
#> camper1 | 0.73 | [ 0.55, 0.91] | 100% | 0% | 1.001 | 3045.00
#>
#> # Random effects Intercept: persons
#>
#> Parameter | Median | 95% CI | pd | % in ROPE | Rhat | ESS
#> ----------------------------------------------------------------------------
#> persons.1 | -5.23e-03 | [-0.39, 0.33] | 54.77% | 69.40% | 1.003 | 1036.00
#> persons.2 | 0.03 | [-0.21, 0.37] | 65.70% | 69.90% | 1.004 | 827.00
#> persons.3 | -0.01 | [-0.29, 0.21] | 59.13% | 77.11% | 1.004 | 807.00
#> persons.4 | 2.93e-03 | [-0.35, 0.33] | 52.98% | 70.30% | 1.004 | 594.00
#>
#> # Random effects SD/Cor: persons
#>
#> Parameter | Median | 95% CI | pd | % in ROPE | Rhat | ESS
#> -----------------------------------------------------------------------
#> (Intercept) | 0.11 | [0.00, 0.48] | 100% | 48.80% | 1.003 | 753.00The parameters package extends the support to structural models.
library(psych)
psych::pca(mtcars, nfactors = 3) %>%
parameters()
#> # Rotated loadings from Principal Component Analysis (varimax-rotation)
#>
#> Variable | RC2 | RC3 | RC1 | Complexity | Uniqueness
#> ----------------------------------------------------------
#> mpg | 0.66 | -0.41 | -0.54 | 2.63 | 0.10
#> cyl | -0.62 | 0.67 | 0.34 | 2.49 | 0.05
#> disp | -0.72 | 0.52 | 0.35 | 2.33 | 0.10
#> hp | -0.30 | 0.64 | 0.63 | 2.40 | 0.10
#> drat | 0.85 | -0.26 | -0.05 | 1.19 | 0.21
#> wt | -0.78 | 0.21 | 0.51 | 1.90 | 0.08
#> qsec | -0.18 | -0.91 | -0.28 | 1.28 | 0.06
#> vs | 0.28 | -0.86 | -0.23 | 1.36 | 0.12
#> am | 0.92 | 0.14 | -0.11 | 1.08 | 0.12
#> gear | 0.91 | -0.02 | 0.26 | 1.16 | 0.10
#> carb | 0.11 | 0.44 | 0.85 | 1.53 | 0.07
#>
#> The 3 principal components (varimax rotation) accounted for 89.87% of the total variance of the original data (RC2 = 41.43%, RC3 = 29.06%, RC1 = 19.39%).We will avoid displaying a graph while carrying out factor analysis:
library(FactoMineR)
FactoMineR::FAMD(iris, ncp = 3, graph = FALSE) %>%
parameters()
#> # Loadings from Factor Analysis (no rotation)
#>
#> Variable | Dim.1 | Dim.2 | Dim.3 | Complexity
#> -------------------------------------------------------
#> Sepal.Length | 0.75 | 0.07 | 0.10 | 1.05
#> Sepal.Width | 0.23 | 0.51 | 0.23 | 1.86
#> Petal.Length | 0.98 | 1.32e-03 | 1.99e-03 | 1.00
#> Petal.Width | 0.94 | 0.01 | 2.82e-05 | 1.00
#> Species | 0.96 | 0.75 | 0.26 | 2.05
#>
#> The 3 latent factors accounted for 96.73% of the total variance of the original data (Dim.1 = 64.50%, Dim.2 = 22.37%, Dim.3 = 9.86%).
library(lavaan)
model <- lavaan::cfa(" visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9 ",
data = HolzingerSwineford1939
)
model_parameters(model)
#> # Loading
#>
#> Link | Coefficient | SE | 95% CI | z | p
#> ------------------------------------------------------------------
#> visual =~ x1 | 1.00 | 0.00 | [1.00, 1.00] | | < .001
#> visual =~ x2 | 0.55 | 0.10 | [0.36, 0.75] | 5.55 | < .001
#> visual =~ x3 | 0.73 | 0.11 | [0.52, 0.94] | 6.68 | < .001
#> textual =~ x4 | 1.00 | 0.00 | [1.00, 1.00] | | < .001
#> textual =~ x5 | 1.11 | 0.07 | [0.98, 1.24] | 17.01 | < .001
#> textual =~ x6 | 0.93 | 0.06 | [0.82, 1.03] | 16.70 | < .001
#> speed =~ x7 | 1.00 | 0.00 | [1.00, 1.00] | | < .001
#> speed =~ x8 | 1.18 | 0.16 | [0.86, 1.50] | 7.15 | < .001
#> speed =~ x9 | 1.08 | 0.15 | [0.79, 1.38] | 7.15 | < .001
#>
#> # Correlation
#>
#> Link | Coefficient | SE | 95% CI | z | p
#> ---------------------------------------------------------------------
#> visual ~~ textual | 0.41 | 0.07 | [0.26, 0.55] | 5.55 | < .001
#> visual ~~ speed | 0.26 | 0.06 | [0.15, 0.37] | 4.66 | < .001
#> textual ~~ speed | 0.17 | 0.05 | [0.08, 0.27] | 3.52 | < .001parameters() also works for rma-objects from the metafor package.
library(metafor)
mydat <- data.frame(
effectsize = c(-0.393, 0.675, 0.282, -1.398),
standarderror = c(0.317, 0.317, 0.13, 0.36)
)
rma(yi = effectsize, sei = standarderror, method = "REML", data = mydat) %>%
model_parameters()
#> Meta-analysis using 'metafor'
#>
#> Parameter | Coefficient | SE | 95% CI | z | p | Weight
#> -------------------------------------------------------------------------
#> Study 1 | -0.39 | 0.32 | [-1.01, 0.23] | -1.24 | 0.215 | 9.95
#> Study 2 | 0.68 | 0.32 | [ 0.05, 1.30] | 2.13 | 0.033 | 9.95
#> Study 3 | 0.28 | 0.13 | [ 0.03, 0.54] | 2.17 | 0.030 | 59.17
#> Study 4 | -1.40 | 0.36 | [-2.10, -0.69] | -3.88 | < .001 | 7.72
#> Overall | -0.18 | 0.44 | [-1.05, 0.68] | -0.42 | 0.676 |There is a plot()-method implemented in the see-package. Several examples are shown in this vignette.