Summary of Model Parameters
model_parameters.Rmd
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 dataframe 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.
Correlations and t-tests
Frequentist
> Parameter1 | Parameter2 | r | t | df | p | 95% CI | Method
> --------------------------------------------------------------------------------------------
> iris$Sepal.Length | iris$Sepal.Width | -0.12 | -1.44 | 148 | 0.152 | [-0.27, 0.04] | Pearson> Parameter | Group | Mean_Group1 | Mean_Group2 | Difference | t | df | p | 95% CI | Method
> -------------------------------------------------------------------------------------------------------------------------------
> mpg | vs | 16.62 | 24.56 | 7.94 | -4.67 | 22.72 | < .001 | [-11.46, -4.42] | Welch Two Sample t-testBayesian
library(BayesFactor)
BayesFactor::correlationBF(iris$Sepal.Length, iris$Sepal.Width) %>%
parameters()> Parameter | Median | 89% CI | pd | % in ROPE | Prior | Effects | Component | BF
> -----------------------------------------------------------------------------------------------------------
> rho | -0.11 | [-0.23, 0.02] | 92.90% | 43.13% | Cauchy (0 +- 0.33) | fixed | conditional | 0.51> Parameter | Median | 89% CI | pd | % in ROPE | Prior | Effects | Component | BF
> ----------------------------------------------------------------------------------------------------------------
> Difference | -7.30 | [-10.15, -4.58] | 99.98% | 0% | Cauchy (0 +- 0.71) | fixed | conditional | 529.27ANOVAs
Indices of effect size for ANOVAs, such as partial and non-partial versions of eta_squared(), epsilon_sqared() or omega_squared(), were moved to the effectsize-package. However, parameters uses these function to compute such indices for parameters summaries.
Simple
aov(Sepal.Length ~ Species, data = iris) %>%
parameters(omega_squared = "partial", eta_squared = "partial", epsilon_squared = TRUE)> Parameter | Sum_Squares | df | Mean_Square | F | p | Omega_Sq (partial) | Eta_Sq (partial) | Epsilon_sq
> ------------------------------------------------------------------------------------------------------------------
> Species | 63.21 | 2 | 31.61 | 119.26 | < .001 | 0.61 | 0.62 | 0.61
> Residuals | 38.96 | 147 | 0.27 | | | | |Repeated measures
parameters() (resp. its alias model_parameters()) also works on repeated measures ANOVAs, whether computed from aov() or from a mixed model.
> Group | Parameter | Sum_Squares | df | Mean_Square | F | p
> ------------------------------------------------------------------
> gear | am | 259.75 | 1 | 259.75 | |
> Within | am | 145.45 | 1 | 145.45 | 5.85 | 0.022
> Within | Residuals | 720.85 | 29 | 24.86 | |Regressions (GLMs, Mixed Models, GAMs, …)
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.
GLMs
> Parameter | Coefficient | SE | 95% CI | t | df | p
> ----------------------------------------------------------------------------
> (Intercept) | 2.04 | 0.39 | [ 1.27, 2.80] | 5.22 | 28 | < .001
> mpg [1st degree] | -0.33 | 0.61 | [-1.53, 0.87] | -0.53 | 28 | 0.599
> mpg [2nd degree] | 0.10 | 0.32 | [-0.54, 0.74] | 0.31 | 28 | 0.762
> cyl | -0.26 | 0.06 | [-0.38, -0.14] | -4.14 | 28 | < .001Mixed Models
> Parameter | Coefficient | SE | 95% CI | t | df | p
> ----------------------------------------------------------------------
> (Intercept) | 2.00 | 0.56 | [0.90, 3.10] | 3.56 | 146 | < .001
> Petal.Length | 0.28 | 0.06 | [0.17, 0.40] | 4.75 | 146 | < .001Bayesian Models
model_parameters() works fine with Bayesian models from the rstanarm package…
> Parameter | Median | 89% CI | pd | % in ROPE | Rhat | ESS | Prior
> -----------------------------------------------------------------------------------------------
> (Intercept) | 53.16 | [ 42.36, 61.52] | 100% | 0% | 1.002 | 188 | Normal (0 +- 60.27)
> wt | -8.19 | [-11.59, -4.40] | 100% | 0.20% | 1.006 | 184 | Normal (0 +- 15.40)
> cyl | -3.71 | [ -4.88, -1.77] | 100% | 0.20% | 1.000 | 206 | Normal (0 +- 8.44)
> wt * cyl | 0.76 | [ 0.19, 1.25] | 98.40% | 32.00% | 1.004 | 179 | Normal (0 +- 1.36)… as well as for (more complex) models from the brms package. For more complex models, other model components can be printed using the arguments effects and component arguments.
# We download the model to save computation time. Here is the code
# to refit the exact model used below...
# zinb <- read.csv("http://stats.idre.ucla.edu/stat/data/fish.csv")
# set.seed(123)
# model <- brm(bf(
# count ~ persons + child + camper + (1 | persons),
# zi ~ child + camper + (1 | persons)
# ),
# data = zinb,
# family = zero_inflated_poisson()
# )
model <- insight::download_model("brms_zi_2")
parameters(model, component = "conditional")> Parameter | Median | 89% CI | pd | % in ROPE | ESS | Rhat
> -------------------------------------------------------------------------
> b_Intercept | -0.84 | [-1.44, -0.29] | 96.43% | 2.77% | 562 | 1.009
> b_persons | 0.84 | [ 0.66, 1.06] | 100% | 0% | 382 | 1.010
> b_child | -1.15 | [-1.29, -0.98] | 100% | 0% | 1089 | 1.002
> b_camper | 0.73 | [ 0.58, 0.89] | 100% | 0% | 2724 | 1.000> # Fixed Effects (Count Model)
>
> Parameter | Median | 89% CI | pd | % in ROPE | ESS | Rhat
> -------------------------------------------------------------------------
> (Intercept) | -0.84 | [-1.44, -0.29] | 96.43% | 2.77% | 562 | 1.009
> persons | 0.84 | [ 0.66, 1.06] | 100% | 0% | 382 | 1.010
> child | -1.15 | [-1.29, -0.98] | 100% | 0% | 1089 | 1.002
> camper | 0.73 | [ 0.58, 0.89] | 100% | 0% | 2724 | 1.000
>
> # Fixed Effects (Zero-Inflated Model)
>
> Parameter | Median | 89% CI | pd | % in ROPE | ESS | Rhat
> -------------------------------------------------------------------------
> (Intercept) | -0.64 | [-1.93, 0.52] | 83.15% | 6.95% | 845 | 1.001
> child | 1.88 | [ 1.40, 2.43] | 100% | 0% | 2322 | 1.001
> camper | -0.83 | [-1.41, -0.24] | 98.95% | 1.70% | 2277 | 1.001
>
> # Random Effects (Count Model)
>
> Parameter | Median | 89% CI | pd | % in ROPE | ESS | Rhat
> ---------------------------------------------------------------------
> persons.1 | -0.01 | [-0.38, 0.28] | 55.33% | 60.50% | 572 | 1.009
> persons.2 | 0.02 | [-0.17, 0.30] | 61.88% | 65.62% | 691 | 1.008
> persons.3 | -0.02 | [-0.26, 0.18] | 61.27% | 67.90% | 340 | 1.011
> persons.4 | 0.00 | [-0.32, 0.33] | 51.38% | 62.12% | 287 | 1.011
>
> # Random Effects (Zero-Inflated Model)
>
> Parameter | Median | 89% CI | pd | % in ROPE | ESS | Rhat
> ----------------------------------------------------------------------
> persons.1 | 1.28 | [ 0.08, 2.70] | 95.73% | 2.15% | 811 | 1.001
> persons.2 | 0.25 | [-0.90, 1.57] | 66.45% | 12.72% | 759 | 1.001
> persons.3 | -0.18 | [-1.51, 1.01] | 59.67% | 11.28% | 871 | 1.001
> persons.4 | -1.29 | [-2.62, -0.01] | 94.85% | 1.85% | 912 | 1.000Structural Models (PCA, EFA, CFA, SEM…)
The parameters package extends the support to structural models.
Principal Component Analysis (PCA) and Exploratory Factor Analysis (EFA)
> # 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%).> # Loadings from Principal Component 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 | 0.00 | 0.00 | 1.00
> Petal.Width | 0.94 | 0.01 | 0.00 | 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%).Confirmatory Factor Analysis (CFA) and Structural Equation Models (SEM)
Frequentist
library(lavaan)
model <- lavaan::cfa(' visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9 ',
data = HolzingerSwineford1939)
model_parameters(model)> # Correlation type
>
> Link | Coefficient | SE | 95% CI | p
> --------------------------------------------------------------
> visual ~~ textual | 0.41 | 0.07 | [0.26, 0.55] | < .001
> visual ~~ speed | 0.26 | 0.06 | [0.15, 0.37] | < .001
> textual ~~ speed | 0.17 | 0.05 | [0.08, 0.27] | < .001
>
> # Loading type
>
> Link | Coefficient | SE | 95% CI | p
> ----------------------------------------------------------
> visual =~ x1 | 1.00 | 0.00 | [1.00, 1.00] | < .001
> visual =~ x2 | 0.55 | 0.10 | [0.36, 0.75] | < .001
> visual =~ x3 | 0.73 | 0.11 | [0.52, 0.94] | < .001
> textual =~ x4 | 1.00 | 0.00 | [1.00, 1.00] | < .001
> textual =~ x5 | 1.11 | 0.07 | [0.98, 1.24] | < .001
> textual =~ x6 | 0.93 | 0.06 | [0.82, 1.03] | < .001
> speed =~ x7 | 1.00 | 0.00 | [1.00, 1.00] | < .001
> speed =~ x8 | 1.18 | 0.16 | [0.86, 1.50] | < .001
> speed =~ x9 | 1.08 | 0.15 | [0.79, 1.38] | < .001Meta-Analysis
parameters() 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()> 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 |