parameters

Describe and understand your model’s parameters!

parameters’s primary goal is to provide utilities for processing the parameters of various statistical models. Beyond computing p-values, CIs, Bayesian indices and other measures for a wide variety of models, this package implements features like standardization or bootstrapping of parameters and models, feature reduction (feature extraction and variable selection) as well as conversion between indices of effect size.

Installation

Run the following:

install.packages("devtools")
devtools::install_github("easystats/parameters")

library("parameters")

Documentation

Click on the buttons above to access the package documentation and the easystats blog, and check-out these vignettes:

Parameters Engineering

Variable/Feature Reduction

Features

Model’s parameters description

The model_parameters function 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.
It is able to compute or extract indices not available by default, such as p values, CIs, etc.
It includes feature engineering capabilities, including bootstrapping and standardization of parameters.

Correlations

Frequentist

model <- cor.test(iris$Sepal.Length, iris$Sepal.Width)
model_parameters(model)

# Parameter1        |       Parameter2 |     r |     t |  df |    p |        95% CI |  Method
# -------------------------------------------------------------------------------------------
# iris$Sepal.Length | iris$Sepal.Width | -0.12 | -1.44 | 148 | > .1 | [-0.27, 0.04] | Pearson

Bayesian

library(BayesFactor)

model <- BayesFactor::correlationBF(iris$Sepal.Length, iris$Sepal.Width)
model_parameters(model)

# Parameter | Median |        89% CI |     pd | % in ROPE |              Prior |   BF
# -----------------------------------------------------------------------------------
# rho       |  -0.11 | [-0.23, 0.02] | 92.90% |    43.13% | Cauchy (0 +- 0.33) | 0.51

t-tests

Frequentist

df <- iris
df$Sepal.Big <- ifelse(df$Sepal.Width >= 3, "Yes", "No")

model <- t.test(Sepal.Length ~ Sepal.Big, data = df)
model_parameters(model)

# Parameter    |     Group | Mean_Group1 | Mean_Group2 | Difference |    t |     df |    p |        95% CI |                  Method
# ----------------------------------------------------------------------------------------------------------------------------------
# Sepal.Length | Sepal.Big |        5.95 |        5.78 |      -0.18 | 1.36 | 142.15 | > .1 | [-0.08, 0.43] | Welch Two Sample t-test

Bayesian

model <- BayesFactor::ttestBF(formula = Sepal.Length ~ Sepal.Big, 
    data = df)
model_parameters(model)

# Parameter  | Median |        89% CI |     pd | % in ROPE |              Prior |   BF
# ------------------------------------------------------------------------------------
# Difference |   0.16 | [-0.05, 0.37] | 88.85% |    26.79% | Cauchy (0 +- 0.71) | 0.38

ANOVAs

Simple

model <- aov(Sepal.Length ~ Sepal.Big, data = df)
model_parameters(model, 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
# --------------------------------------------------------------------------------------------------------------
# Sepal.Big |        1.10 |   1 |        1.10 | 1.61 | > .1 |               0.00 |             0.01 |       0.00
# Residuals |      101.07 | 148 |        0.68 |      |   NA |                    |                  |

Repeated measures

model <- aov(Sepal.Length ~ Sepal.Big + Error(Species), data = df)
model_parameters(model)

# Group   | Parameter | Sum_Squares |  df | Mean_Square |     F |      p
# ----------------------------------------------------------------------
# Species | Sepal.Big |       28.27 |   1 |       28.27 |  0.81 |   > .1
# Species | Residuals |       34.94 |   1 |       34.94 |       |     NA
# Within  | Sepal.Big |        4.74 |   1 |        4.74 | 20.24 | < .001
# Within  | Residuals |       34.21 | 146 |        0.23 |       |     NA

library(lme4)
model <- anova(lmer(Sepal.Length ~ Sepal.Big + (1 | Species), 
    data = df))
model_parameters(model)

# Parameter | Sum_Squares | df | Mean_Square |     F
# --------------------------------------------------
# Sepal.Big |        4.64 |  1 |        4.64 | 19.82

General Linear Models (GLM)

model <- glm(vs ~ wt + cyl, data = mtcars, family = "binomial")
model_parameters(model, standardize = "refit")

# Parameter   | Coefficient |   SE |         95% CI |     z | df |     p | Coefficient (std.)
# -------------------------------------------------------------------------------------------
# (Intercept) |       10.62 | 4.17 |  [4.79, 22.66] |  2.55 | 29 | < .05 |              -0.76
# wt          |        2.10 | 1.55 |  [-0.53, 6.24] |  1.36 | 29 |  > .1 |               2.05
# cyl         |       -2.93 | 1.38 | [-6.92, -1.07] | -2.12 | 29 | < .05 |              -5.23

Bootstrapped models

model <- lm(mpg ~ drat * cyl, data = mtcars)
model_parameters(model, bootstrap = TRUE, iterations = 500)

# Parameter   | Coefficient |          95% CI |     p | Coefficient (std.)
# ------------------------------------------------------------------------
# (Intercept) |       -0.94 | [-45.58, 32.09] |  > .1 |              -0.13
# drat        |        9.55 |   [0.55, 21.32] | < .05 |               0.16
# cyl         |        2.18 |   [-2.50, 8.41] |  > .1 |              -0.71
# drat * cyl  |       -1.25 |   [-2.92, 0.12] |  0.06 |              -0.19

Mixed models

library(lme4)

model <- lmer(Sepal.Width ~ Petal.Length + (1 | Species), data = iris)
model_parameters(model, standardize = "refit")

# Parameter    | Coefficient |   SE |        95% CI |    t |      p | Coefficient (std.)
# --------------------------------------------------------------------------------------
# (Intercept)  |        2.00 | 0.56 | [-1.92, 5.92] | 3.56 | < .001 |               0.00
# Petal.Length |        0.28 | 0.06 | [-0.27, 0.83] | 4.75 | < .001 |               1.14

Bayesian models

library(rstanarm)

model <- stan_glm(mpg ~ wt + cyl, data = mtcars)
model_parameters(model)

# Parameter   | Median |         89% CI |     pd | % in ROPE |  ESS |  Rhat |               Prior
# -----------------------------------------------------------------------------------------------
# (Intercept) |  39.65 | [36.79, 42.34] |   100% |        0% | 4833 | 1.000 | Normal (0 +- 60.27)
# wt          |  -3.17 | [-4.39, -1.93] |   100% |     0.02% | 2206 | 1.001 | Normal (0 +- 15.40)
# cyl         |  -1.52 | [-2.24, -0.89] | 99.95% |     1.90% | 2209 | 1.001 |  Normal (0 +- 8.44)

Exploratory Factor Analysis (EFA) and Principal Component Analysis (PCA)

library(psych)

model <- psych::fa(attitude, nfactors = 3)
model_parameters(model)

# # Rotated loadings from Principal Component Analysis (oblimin-rotation)
# 
# Variable   |   MR1 |   MR2 |   MR3 | Complexity | Uniqueness
# ------------------------------------------------------------
# rating     |  0.90 | -0.07 | -0.05 |       1.02 |       0.23
# complaints |  0.97 | -0.06 |  0.04 |       1.01 |       0.10
# privileges |  0.44 |  0.25 | -0.05 |       1.64 |       0.65
# learning   |  0.47 |  0.54 | -0.28 |       2.51 |       0.24
# raises     |  0.55 |  0.43 |  0.25 |       2.35 |       0.23
# critical   |  0.16 |  0.17 |  0.48 |       1.46 |       0.67
# advance    | -0.11 |  0.91 |  0.07 |       1.04 |       0.22
# 
# The 3 latent factors (oblimin rotation) accounted for 66.60% of the total variance of the original data (MR1 = 38.19%, MR2 = 22.69%, MR3 = 5.72%).

Confirmatory Factor Analysis (CFA) and Structural Equation Models (SEM)

library(lavaan)

model <- lavaan::cfa(" visual  =~ x1 + x2 + x3
                       textual =~ x4 + x5 + x6
                       speed   =~ x7 + x8 + x9 ", 
    data = HolzingerSwineford1939)
model_parameters(model)

# Link              | Coefficient |   SE |       95% CI |      p |        Type
# ----------------------------------------------------------------------------
# visual =~ x1      |        1.00 | 0.00 | [1.00, 1.00] | < .001 |     Loading
# visual =~ x2      |        0.55 | 0.10 | [0.36, 0.75] | < .001 |     Loading
# visual =~ x3      |        0.73 | 0.11 | [0.52, 0.94] | < .001 |     Loading
# textual =~ x4     |        1.00 | 0.00 | [1.00, 1.00] | < .001 |     Loading
# textual =~ x5     |        1.11 | 0.07 | [0.98, 1.24] | < .001 |     Loading
# textual =~ x6     |        0.93 | 0.06 | [0.82, 1.03] | < .001 |     Loading
# speed =~ x7       |        1.00 | 0.00 | [1.00, 1.00] | < .001 |     Loading
# speed =~ x8       |        1.18 | 0.16 | [0.86, 1.50] | < .001 |     Loading
# speed =~ x9       |        1.08 | 0.15 | [0.79, 1.38] | < .001 |     Loading
# visual ~~ textual |        0.41 | 0.07 | [0.26, 0.55] | < .001 | Correlation
# visual ~~ speed   |        0.26 | 0.06 | [0.15, 0.37] | < .001 | Correlation
# textual ~~ speed  |        0.17 | 0.05 | [0.08, 0.27] | < .001 | Correlation

Variable and parameters selection

General Linear Models (GLM)

library(dplyr)

lm(disp ~ ., data = mtcars) %>% parameters_selection() %>% model_parameters()

# Parameter   | Coefficient |     SE |            95% CI |     t | df |      p | Coefficient (std.)
# -------------------------------------------------------------------------------------------------
# (Intercept) |      141.70 | 125.67 | [-116.62, 400.02] |  1.13 | 26 |   > .1 |              -0.00
# cyl         |       13.14 |   7.90 |    [-3.10, 29.38] |  1.66 | 26 |   > .1 |               0.19
# hp          |        0.63 |   0.20 |      [0.22, 1.03] |  3.18 | 26 |  < .01 |               0.35
# wt          |       80.45 |  12.22 |   [55.33, 105.57] |  6.58 | 26 | < .001 |               0.64
# qsec        |      -14.68 |   6.14 |   [-27.31, -2.05] | -2.39 | 26 |  < .05 |              -0.21
# carb        |      -28.75 |   5.60 |  [-40.28, -17.23] | -5.13 | 26 | < .001 |              -0.37

Mixed models

library(lme4)

lmer(Sepal.Length ~ Sepal.Width * Petal.Length * Petal.Width + 
    (1 | Species), data = iris) %>% parameters_selection() %>% 
    model_parameters()

# Parameter                                  | Coefficient |   SE |        95% CI |     t |     p | Coefficient (std.)
# --------------------------------------------------------------------------------------------------------------------
# (Intercept)                                |        1.78 | 0.91 | [-1.71, 5.26] |  1.95 |  0.05 |              -0.24
# Sepal.Width                                |        0.88 | 0.50 | [-0.84, 2.60] |  1.77 |  0.08 |               0.30
# Petal.Length                               |        0.28 | 0.24 | [-0.27, 0.83] |  1.16 |  > .1 |               1.57
# Petal.Width                                |       -2.04 | 1.52 | [1.96, -6.03] | -1.34 |  > .1 |              -0.43
# Sepal.Width * Petal.Length                 |        0.75 | 0.27 | [-0.72, 2.22] |  2.80 | < .01 |              -0.15
# Sepal.Width * Petal.Width                  |       -0.10 | 0.16 | [0.10, -0.30] | -0.63 |  > .1 |               0.07
# Petal.Length * Petal.Width                 |       -0.05 | 0.08 | [0.04, -0.14] | -0.61 |  > .1 |               0.22
# (Sepal.Width * Petal.Length) * Petal.Width |        0.34 | 0.49 | [-0.33, 1.02] |  0.70 |  > .1 |              -0.03

Bayesian models

library(rstanarm)

model <- stan_glm(mpg ~ ., data = mtcars) %>% parameters_selection() %>% 
    model_parameters()

# Parameter   | Median |         89% CI |     pd | % in ROPE |  ESS |  Rhat |               Prior
# -----------------------------------------------------------------------------------------------
# (Intercept) |  19.82 | [-1.20, 41.01] | 93.90% |     1.30% | 1254 | 0.999 | Normal (0 +- 60.27)
# wt          |  -3.96 | [-6.01, -1.79] | 99.65% |     0.60% | 1249 | 0.999 | Normal (0 +- 15.40)
# cyl         |  -0.50 |  [-1.85, 0.74] | 72.90% |    45.90% | 1472 | 1.000 |  Normal (0 +- 8.44)
# hp          |  -0.02 |  [-0.04, 0.01] | 88.20% |      100% | 1813 | 0.999 |  Normal (0 +- 0.22)
# am          |   2.93 |   [0.24, 5.80] | 94.85% |     6.85% | 1500 | 1.000 | Normal (0 +- 15.07)
# qsec        |   0.80 |  [-0.04, 1.79] | 92.15% |    35.40% | 1237 | 0.999 |  Normal (0 +- 8.43)
# disp        |   0.01 |  [-0.01, 0.03] | 86.10% |      100% | 1409 | 1.000 |  Normal (0 +- 0.12)

Variable and features extraction

How many factors to retain in Factor Analysis (FA)

n_factors(mtcars)

# # Method Agreement Procedure:
# 
# The choice of 2 dimensions is supported by 2 (40.00%) methods out of 5 (EGA (glasso), EGA (TMFG)).

Miscellaneous

Describe a Distribution

x <- rnorm(300)
describe_distribution(x)

knitr::kable(describe_distribution(rnorm(300)), digits = 1)

Mean	SD	Min	Max	Skewness	Kurtosis	n	n_Missing
0	1	-2	3	0	-0.4	300	0

Standardization and normalization

df <- standardize(iris)
summary(df$Sepal.Length)
#    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#    -1.9    -0.9    -0.1     0.0     0.7     2.5

df <- normalize(iris)
summary(df$Sepal.Length)
#    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#     0.0     0.2     0.4     0.4     0.6     1.0

parameters

Installation

Documentation

Parameters Engineering

Variable/Feature Reduction

Features

Model’s parameters description

Correlations

Frequentist

Bayesian

t-tests

Frequentist

Bayesian

ANOVAs

Simple

Repeated measures

General Linear Models (GLM)

Bootstrapped models

Mixed models

Bayesian models

Exploratory Factor Analysis (EFA) and Principal Component Analysis (PCA)

Confirmatory Factor Analysis (CFA) and Structural Equation Models (SEM)

Variable and parameters selection

General Linear Models (GLM)

Mixed models

Bayesian models

Variable and features extraction

How many factors to retain in Factor Analysis (FA)

Miscellaneous

Describe a Distribution

Standardization and normalization

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Functions in parameters (0.1.0)