Prepare CRAN release

DESCRIPTION

@@ -1,7 +1,7 @@
 Type: Package
 Package: parameters
 Title: Processing of Model Parameters
-Version: 0.22.1.9
+Version: 0.22.1.99
 Authors@R:
     c(person(given = "Daniel",
              family = "Lüdecke",
@@ -221,4 +221,3 @@ Config/testthat/edition: 3
 Config/testthat/parallel: true
 Config/Needs/website: easystats/easystatstemplate
 Config/rcmdcheck/ignore-inconsequential-notes: true
-Remotes: easystats/insight

NAMESPACE

@@ -350,6 +350,22 @@ S3method(model_parameters,zeroinfl)
 S3method(model_parameters,zoo)
 S3method(p_calibrate,default)
 S3method(p_calibrate,numeric)
+S3method(p_significance,coxph)
+S3method(p_significance,feis)
+S3method(p_significance,felm)
+S3method(p_significance,gee)
+S3method(p_significance,glm)
+S3method(p_significance,glmmTMB)
+S3method(p_significance,gls)
+S3method(p_significance,hurdle)
+S3method(p_significance,lm)
+S3method(p_significance,lme)
+S3method(p_significance,merMod)
+S3method(p_significance,mixed)
+S3method(p_significance,rma)
+S3method(p_significance,svyglm)
+S3method(p_significance,wbm)
+S3method(p_significance,zeroinfl)
 S3method(p_value,BBmm)
 S3method(p_value,BBreg)
 S3method(p_value,BFBayesFactor)
@@ -547,6 +563,7 @@ S3method(print,n_clusters_hclust)
 S3method(print,n_clusters_silhouette)
 S3method(print,n_factors)
 S3method(print,p_calibrate)
+S3method(print,p_significance_lm)
 S3method(print,parameters_brms_meta)
 S3method(print,parameters_clusters)
 S3method(print,parameters_da)
@@ -914,6 +931,7 @@ export(n_factors)
 export(n_parameters)
 export(p_calibrate)
 export(p_function)
+export(p_significance)
 export(p_value)
 export(p_value_betwithin)
 export(p_value_kenward)
@@ -951,6 +969,7 @@ export(supported_models)
 export(visualisation_recipe)
 importFrom(bayestestR,ci)
 importFrom(bayestestR,equivalence_test)
+importFrom(bayestestR,p_significance)
 importFrom(datawizard,demean)
 importFrom(datawizard,describe_distribution)
 importFrom(datawizard,kurtosis)

NEWS.md

@@ -7,6 +7,8 @@
 
 ## Changes
 
+* Added `p_significance()` methods for frequentist models.
+
 * Methods for `degrees_of_freedom()` have been removed. `degrees_of_freedom()`
   now calls `insight::get_df()`.
 

R/1_model_parameters.R

@@ -74,10 +74,7 @@
 #' packages or other software packages (like SPSS). To mimic behaviour of SPSS
 #' or packages such as **lm.beta**, use `standardize = "basic"`.
 #'
-#' @section
-#'
-#' Standardization Methods:
-#'
+#' @section Standardization Methods:
 #' - **refit**: This method is based on a complete model re-fit with a
 #' standardized version of the data. Hence, this method is equal to
 #' standardizing the variables before fitting the model. It is the "purest" and
@@ -280,21 +277,98 @@
 #' p-values are based on the probability of direction ([`bayestestR::p_direction()`]),
 #' which is converted into a p-value using [`bayestestR::pd_to_p()`].
 #'
+#' @section Statistical inference - how to quantify evidence:
+#' There is no standardized approach to drawing conclusions based on the
+#' available data and statistical models. A frequently chosen but also much
+#' criticized approach is to evaluate results based on their statistical
+#' significance (*Amrhein et al. 2017*).
+#'
+#' A more sophisticated way would be to test whether estimated effects exceed
+#' the "smallest effect size of interest", to avoid even the smallest effects
+#' being considered relevant simply because they are statistically significant,
+#' but clinically or practically irrelevant (*Lakens et al. 2018, Lakens 2024*).
+#'
+#' A rather unconventional approach, which is nevertheless advocated by various
+#' authors, is to interpret results from classical regression models in terms of
+#' probabilities, similar to the usual approach in Bayesian statistics
+#' (*Greenland et al. 2022; Rafi and Greenland 2020; Schweder 2018; Schweder and
+#' Hjort 2003; Vos 2022*).
+#'
+#' The _parameters_ package provides several options or functions to aid
+#' statistical inference. These are, for example:
+#' - [`equivalence_test()`], to compute the (conditional) equivalence test for
+#'   frequentist models
+#' - [`p_significance()`], to compute the probability of *practical significance*,
+#'   which can be conceptualized as a unidirectional equivalence test
+#' - [`p_function()`], or _consonance function_, to compute p-values and
+#'   compatibility (confidence) intervals for statistical models
+#' - the `pd` argument (setting `pd = TRUE`) in `model_parameters()` includes
+#'   a column with the *probability of direction*, i.e. the probability that a
+#'   parameter is strictly positive or negative. See [`bayestestR::p_direction()`]
+#'   for details.
+#' - the `s_value` argument (setting `s_value = TRUE`) in `model_parameters()`
+#'   replaces the p-values with their related _S_-values (*Rafi and Greenland 2020*)
+#' - finally, it is possible to generate distributions of model coefficients by
+#'   generating bootstrap-samples (setting `bootstrap = TRUE`) or simulating
+#'   draws from model coefficients using [`simulate_model()`]. These samples
+#'   can then be treated as "posterior samples" and used in many functions from
+#'   the **bayestestR** package.
+#'
+#' Most of the above shown options or functions derive from methods originally
+#' implemented for Bayesian models (*Makowski et al. 2019*). However, assuming
+#' that model assumptions are met (which means, the model fits well to the data,
+#' the correct model is chosen that reflectsa the data generating process
+#' (distributional model family) etc.), it seems appropriate to interpret
+#' results from classical frequentist models in a "Bayesian way" (more details:
+#' documentation in [`p_function()`]).
+#'
 #' @inheritSection format_parameters Interpretation of Interaction Terms
 #' @inheritSection print.parameters_model Global Options to Customize Messages and Tables when Printing
 #'
 #' @references
 #'
+#'   - Amrhein, V., Korner-Nievergelt, F., and Roth, T. (2017). The earth is
+#'     flat (p > 0.05): Significance thresholds and the crisis of unreplicable
+#'     research. PeerJ, 5, e3544. \doi{10.7717/peerj.3544}
+#'
+#'   - Greenland S, Rafi Z, Matthews R, Higgs M. To Aid Scientific Inference,
+#'     Emphasize Unconditional Compatibility Descriptions of Statistics. (2022)
+#'     https://arxiv.org/abs/1909.08583v7 (Accessed November 10, 2022)
+#'
 #'   - Hoffman, L. (2015). Longitudinal analysis: Modeling within-person
-#'   fluctuation and change. Routledge.
+#'     fluctuation and change. Routledge.
+#'
+#'   - Lakens, D. (2024). Improving Your Statistical Inferences (Version v1.5.1).
+#'     Retrieved from https://lakens.github.io/statistical_inferences/.
+#'     \doi{10.5281/ZENODO.6409077}
+#'
+#'   - Lakens, D., Scheel, A. M., and Isager, P. M. (2018). Equivalence Testing
+#'     for Psychological Research: A Tutorial. Advances in Methods and Practices
+#'     in Psychological Science, 1(2), 259–269. \doi{10.1177/2515245918770963}
+#'
+#'   - Makowski, D., Ben-Shachar, M. S., Chen, S. H. A., and Lüdecke, D. (2019).
+#'     Indices of Effect Existence and Significance in the Bayesian Framework.
+#'     Frontiers in Psychology, 10, 2767. \doi{10.3389/fpsyg.2019.02767}
 #'
 #'   - Neter, J., Wasserman, W., & Kutner, M. H. (1989). Applied linear
-#'   regression models.
+#'     regression models.
 #'
 #'   - Rafi Z, Greenland S. Semantic and cognitive tools to aid statistical
-#'   science: replace confidence and significance by compatibility and surprise.
-#'   BMC Medical Research Methodology (2020) 20:244.
-
+#'     science: replace confidence and significance by compatibility and surprise.
+#'     BMC Medical Research Methodology (2020) 20:244.
+#'
+#'   - Schweder T. Confidence is epistemic probability for empirical science.
+#'     Journal of Statistical Planning and Inference (2018) 195:116–125.
+#'     \doi{10.1016/j.jspi.2017.09.016}
+#'
+#'   - Schweder T, Hjort NL. Frequentist analogues of priors and posteriors.
+#'     In Stigum, B. (ed.), Econometrics and the Philosophy of Economics: Theory
+#'     Data Confrontation in Economics, pp. 285-217. Princeton University Press,
+#'     Princeton, NJ, 2003
+#'
+#'   - Vos P, Holbert D. Frequentist statistical inference without repeated sampling.
+#'     Synthese 200, 89 (2022). \doi{10.1007/s11229-022-03560-x}
+#'
 #' @return A data frame of indices related to the model's parameters.
 #' @export
 model_parameters <- function(model, ...) {

R/equivalence_test.R

@@ -24,8 +24,9 @@ bayestestR::equivalence_test
 #' @inheritParams model_parameters.merMod
 #' @inheritParams p_value
 #'
-#' @seealso For more details, see [bayestestR::equivalence_test()].
-#'   Further readings can be found in the references.
+#' @seealso For more details, see [bayestestR::equivalence_test()]. Further
+#' readings can be found in the references. See also [`p_significance()`] for
+#' a unidirectional equivalence test.
 #'
 #' @details
 #' In classical null hypothesis significance testing (NHST) within a frequentist
@@ -111,6 +112,8 @@ bayestestR::equivalence_test
 #' (argument `range`). See 'Details' in [bayestestR::rope_range()]
 #' for further information.
 #'
+#' @inheritSection model_parameters Statistical inference - how to quantify evidence
+#'
 #' @note There is also a [`plot()`-method](https://easystats.github.io/see/articles/parameters.html)
 #' implemented in the [**see**-package](https://easystats.github.io/see/).
 #'
@@ -339,6 +342,7 @@ equivalence_test.ggeffects <- function(x,
   l <- Map(
     function(ci_wide, ci_narrow) {
       .equivalence_test_numeric(
+        ci = ci,
         ci_wide,
         ci_narrow,
         range_rope = range,
@@ -432,11 +436,11 @@ equivalence_test.ggeffects <- function(x,
   l <- Map(
     function(ci_wide, ci_narrow) {
       .equivalence_test_numeric(
+        ci = ci,
         ci_wide,
         ci_narrow,
         range_rope = range,
         rule = rule,
-        ci = ci,
         verbose = verbose
       )
     }, conf_int, conf_int2
@@ -520,11 +524,11 @@ equivalence_test.ggeffects <- function(x,
     l <- Map(
       function(ci_wide, ci_narrow) {
         .equivalence_test_numeric(
+          ci = ci,
           ci_wide,
           ci_narrow,
           range_rope = range,
           rule = rule,
-          ci = ci,
           verbose = verbose
         )
       }, conf_int, conf_int2
@@ -542,7 +546,12 @@ equivalence_test.ggeffects <- function(x,
 
 
 #' @keywords internal
-.equivalence_test_numeric <- function(ci_wide, ci_narrow, range_rope, rule, ci = 0.95, verbose) {
+.equivalence_test_numeric <- function(ci = 0.95,
+                                      ci_wide,
+                                      ci_narrow,
+                                      range_rope,
+                                      rule,
+                                      verbose) {
   final_ci <- NULL
 
   # ==== HDI+ROPE decision rule, by Kruschke ====
@@ -593,7 +602,7 @@ equivalence_test.ggeffects <- function(x,
   data.frame(
     CI_low = final_ci[1],
     CI_high = final_ci[2],
-    SGPV = .rope_coverage(range_rope, final_ci),
+    SGPV = .rope_coverage(ci = ci, range_rope, ci_range = final_ci),
     ROPE_low = range_rope[1],
     ROPE_high = range_rope[2],
     ROPE_Equivalence = decision,
@@ -645,29 +654,66 @@ equivalence_test.ggeffects <- function(x,
 # same range / limits as the confidence interval, thus indeed representing a
 # normally distributed confidence interval. We then calculate the probability
 # mass of this interval that is inside the ROPE.
-.rope_coverage <- function(range_rope, ci_range) {
-  diff_ci <- abs(diff(ci_range))
-  out <- bayestestR::distribution_normal(
-    n = 1000,
-    mean = ci_range[2] - (diff_ci / 2),
-    # we divide the complete range by 2, the one-directional range for the SD
-    # then, the range from mean value to lower/upper limit, for a normal
-    # distribution is approximately 3.3 SD (3 SD cover 99.7% of the probability
-    # mass of the normal distribution). Thus, assuming that half of the ci_range
-    # refers to ~ 3.3 SD, we "normalize" the value (i.e. divide by 3.290525) to
-    # get the value for one SD, which we need to build the normal distribution.
-    sd = (diff_ci / 2) / 3.290525
-  )
-
+.rope_coverage <- function(ci = 0.95, range_rope, ci_range) {
+  out <- .generate_posterior_from_ci(ci, ci_range)
   # compare: ci_range and range(out)
-
   # The SGPV refers to the proportion of the confidence interval inside the
   # full ROPE - thus, we set ci = 1 here
   rc <- bayestestR::rope(out, range = range_rope, ci = 1)
   rc$ROPE_Percentage
 }
 
 
+.generate_posterior_from_ci <- function(ci = 0.95, ci_range, precision = 10000) {
+  # this function creates an approximate normal distribution that covers
+  # the CI-range, i.e. we "simulate" a posterior distribution of a
+  # frequentist CI
+  diff_ci <- abs(diff(ci_range))
+  bayestestR::distribution_normal(
+    n = precision,
+    mean = ci_range[2] - (diff_ci / 2),
+    # we divide the complete range by 2, the one-directional range for the SD.
+    # then, the range from mean value to lower/upper limit, for a normal
+    # distribution is approximately 3.3 SD (3 SD cover 99.7% of the probability
+    # mass of the normal distribution, `1 - ((1 - pnorm(3)) * 2)`). Thus,
+    # assuming that half of the ci_range refers to ~ 3.3 SD, we "normalize" the
+    # value (i.e. divide by 3.3) to get the value for one SD, which we need
+    # to build the normal distribution. The SD itself varies by confidence level,
+    # therefore we have a multiplier based on the confidence level. I agree this
+    # looks *very* hacky, but it is tested against following code, which used
+    # this code to create a normal distribution with "full" coverage, based on
+    # the approximation of the SD related to the CI-level. From this normal-
+    # distribution, the CI-level % interval is drawn and the range of the
+    # simulated normal distribution equals the desired range.
+    # -------------------------------------------------------------------------
+    # m <- lm(mpg ~ gear + hp + wt + cyl + am, data = mtcars)
+    # ci <- 0.75
+    # mp <- model_parameters(m, ci = ci)
+    # ci_range <- c(mp$CI_low[2], mp$CI_high[2])
+    # diff_ci <- abs(diff(ci_range))
+    # out <- bayestestR::distribution_normal(
+    #   n = 10000,
+    #   mean = ci_range[2] - (diff_ci / 2),
+    #   sd = diff_ci / ((stats::qnorm((1+ci)/2) * (stats::qnorm(0.999975) / 2)))
+    # )
+    # # these to ranges are roughly the same
+    # ci(out, ci = ci)
+    # ci_range
+    # -------------------------------------------------------------------------
+    # furthermore, using this approximation, following three approaches yield
+    # similar results:
+    # -------------------------------------------------------------------------
+    # m <- lm(mpg ~ gear + wt + cyl + hp, data = mtcars)
+    # m2 <- brm(mpg ~ gear + wt + cyl + hp, data = mtcars)
+    # p_significance(m, threshold = 0.6) # the default for "mpg" as response
+    # p_significance(m2)
+    # p_significance(simulate_model(m))
+    # -------------------------------------------------------------------------
+    sd = diff_ci / ((stats::qnorm((1 + ci) / 2) * (stats::qnorm(0.999975) / 2)))
+  )
+}
+
+
 .add_p_to_equitest <- function(model, ci, range) {
   tryCatch(
     {