From 1652e71e073f118f6d66177fe10a6b47b1a52ccb Mon Sep 17 00:00:00 2001 From: wlandau Date: Mon, 25 Sep 2023 11:55:26 -0400 Subject: [PATCH] Elaborate on model matrices --- R/brm_data.R | 9 + R/brm_formula.R | 24 +- R/brm_model.R | 15 + man/brm_data.Rd | 13 +- man/brm_formula.Rd | 27 +- man/brm_model.Rd | 27 + vignettes/usage.Rmd | 1028 ++++++++++-------------------- vignettes/usage.Rmd.upstream | 33 + vignettes/usage/difference-1.png | Bin 19579 -> 18088 bytes vignettes/usage/draws-1.png | Bin 7354 -> 7323 bytes vignettes/usage/response-1.png | Bin 23014 -> 20924 bytes 11 files changed, 472 insertions(+), 704 deletions(-) diff --git a/R/brm_data.R b/R/brm_data.R index 2823172c..401c67c8 100644 --- a/R/brm_data.R +++ b/R/brm_data.R @@ -51,8 +51,17 @@ #' In other words, set `level_baseline` to `NULL` if `role` is `"change"`, #' and set `level_baseline` to a non-null value in `data[[time]]` #' if `role` is `"response"`. +#' +#' Note: `level_baseline` only applies to the post-processing that happens +#' in functions like [brm_marginal_draws()] downstream of the model. +#' It does not control the fixed effect parameterization in the +#' model matrix that `brms` derives from the formula from `brm_formula()`. #' @param level_control Character of length 1, Level of the `group` column #' to indicate the control group. +#' `level_control` only applies to the post-processing that happens +#' in functions like [brm_marginal_draws()] downstream of the model. +#' It does not control the fixed effect parameterization in the +#' model matrix that `brms` derives from the formula from `brm_formula()`. #' @examples #' set.seed(0) #' data <- brm_simulate_simple()$data diff --git a/R/brm_formula.R b/R/brm_formula.R index 8cf10f5a..3c9da11d 100644 --- a/R/brm_formula.R +++ b/R/brm_formula.R @@ -2,6 +2,16 @@ #' @export #' @family models #' @description Build a model formula for an MMRM. +#' @section Parameterization: +#' The formula is not the only factor +#' that determines the fixed effect parameterization. +#' The ordering of the categorical variables in the data, +#' as well as the `contrast` option in R, affect the +#' construction of the model matrix. To see the model +#' matrix that will ultimately be used in [brm_model()], +#' run [brms::make_standata()] and examine the `X` element +#' of the returned list. See the examples below for a +#' demonstration. #' @return An object of class `"brmsformula"` returned from #' `brms::brmsformula()`. It contains the fixed effect parameterization, #' correlation structure, and residual variance structure. @@ -33,12 +43,24 @@ #' ) #' brm_formula(data) #' brm_formula(data = data, intercept = FALSE, effect_baseline = FALSE) -#' brm_formula( +#' formula <- brm_formula( #' data = data, #' intercept = FALSE, #' effect_baseline = FALSE, #' interaction_group = FALSE #' ) +#' formula +#' # Optional: set the contrast option, which determines the model matrix. +#' options(contrasts = c(unordered = "contr.SAS", ordered = "contr.poly")) +#' # See the fixed effect parameterization you get from the data: +#' head(brms::make_standata(formula = formula, data = data)$X) +#' # Specify a different contrast method to use an alternative +#' # parameterization when fitting the model with brm_model(): +#' options( +#' contrasts = c(unordered = "contr.treatment", ordered = "contr.poly") +#' ) +#' # different model matrix than before: +#' head(brms::make_standata(formula = formula, data = data)$X) brm_formula <- function( data, intercept = TRUE, diff --git a/R/brm_model.R b/R/brm_model.R index 82db07d3..52188bf9 100644 --- a/R/brm_model.R +++ b/R/brm_model.R @@ -2,6 +2,7 @@ #' @export #' @family models #' @description Fit a basic MMRM model using `brms`. +#' @inheritSection brm_formula Parameterization #' @return A fitted model object from `brms`. #' @param data A tidy data frame with one row per patient per discrete #' time point. @@ -32,6 +33,17 @@ #' effect_baseline = FALSE, #' interaction_baseline = FALSE #' ) +#' # Optional: set the contrast option, which determines the model matrix. +#' options(contrasts = c(unordered = "contr.SAS", ordered = "contr.poly")) +#' # See the fixed effect parameterization you get from the data: +#' head(brms::make_standata(formula = formula, data = data)$X) +#' # Specify a different contrast method to use an alternative +#' # parameterization when fitting the model with brm_model(): +#' options( +#' contrasts = c(unordered = "contr.treatment", ordered = "contr.poly") +#' ) +#' # different model matrix than before: +#' head(brms::make_standata(formula = formula, data = data)$X) #' tmp <- utils::capture.output( #' suppressMessages( #' suppressWarnings( @@ -45,7 +57,10 @@ #' ) #' ) #' ) +#' # The output model is a brms model fit object. #' model +#' # The `prior_summary()` function shows the full prior specification +#' # which reflects the fully realized fixed effects parameterization. #' brms::prior_summary(model) #' } brm_model <- function( diff --git a/man/brm_data.Rd b/man/brm_data.Rd index 7a55bc9e..48e7879d 100644 --- a/man/brm_data.Rd +++ b/man/brm_data.Rd @@ -48,7 +48,11 @@ in a simulated dataset to indicate which outcome values should be missing. Set to \code{NULL} to omit.} \item{level_control}{Character of length 1, Level of the \code{group} column -to indicate the control group.} +to indicate the control group. +\code{level_control} only applies to the post-processing that happens +in functions like \code{\link[=brm_marginal_draws]{brm_marginal_draws()}} downstream of the model. +It does not control the fixed effect parameterization in the +model matrix that \code{brms} derives from the formula from \code{brm_formula()}.} \item{level_baseline}{Character of length 1 or \code{NULL}, level of the \code{time} column to indicate the baseline time point. @@ -58,7 +62,12 @@ if the outcome variable is the raw response so that \code{brms.mmrm} can produce model-based marginal estimates of change from baseline. In other words, set \code{level_baseline} to \code{NULL} if \code{role} is \code{"change"}, and set \code{level_baseline} to a non-null value in \code{data[[time]]} -if \code{role} is \code{"response"}.} +if \code{role} is \code{"response"}. + +Note: \code{level_baseline} only applies to the post-processing that happens +in functions like \code{\link[=brm_marginal_draws]{brm_marginal_draws()}} downstream of the model. +It does not control the fixed effect parameterization in the +model matrix that \code{brms} derives from the formula from \code{brm_formula()}.} } \value{ A classed tibble with attributes which denote features of diff --git a/man/brm_formula.Rd b/man/brm_formula.Rd index a775122f..4985292f 100644 --- a/man/brm_formula.Rd +++ b/man/brm_formula.Rd @@ -46,6 +46,19 @@ correlation structure, and residual variance structure. \description{ Build a model formula for an MMRM. } +\section{Parameterization}{ + +The formula is not the only factor +that determines the fixed effect parameterization. +The ordering of the categorical variables in the data, +as well as the \code{contrast} option in R, affect the +construction of the model matrix. To see the model +matrix that will ultimately be used in \code{\link[=brm_model]{brm_model()}}, +run \code{\link[brms:make_standata]{brms::make_standata()}} and examine the \code{X} element +of the returned list. See the examples below for a +demonstration. +} + \examples{ set.seed(0) data <- brm_data( @@ -60,12 +73,24 @@ data <- brm_data( ) brm_formula(data) brm_formula(data = data, intercept = FALSE, effect_baseline = FALSE) -brm_formula( +formula <- brm_formula( data = data, intercept = FALSE, effect_baseline = FALSE, interaction_group = FALSE ) +formula +# Optional: set the contrast option, which determines the model matrix. +options(contrasts = c(unordered = "contr.SAS", ordered = "contr.poly")) +# See the fixed effect parameterization you get from the data: +head(brms::make_standata(formula = formula, data = data)$X) +# Specify a different contrast method to use an alternative +# parameterization when fitting the model with brm_model(): +options( + contrasts = c(unordered = "contr.treatment", ordered = "contr.poly") +) +# different model matrix than before: +head(brms::make_standata(formula = formula, data = data)$X) } \seealso{ Other models: diff --git a/man/brm_model.Rd b/man/brm_model.Rd index 9c9117af..b89d7e17 100644 --- a/man/brm_model.Rd +++ b/man/brm_model.Rd @@ -28,6 +28,19 @@ A fitted model object from \code{brms}. \description{ Fit a basic MMRM model using \code{brms}. } +\section{Parameterization}{ + +The formula is not the only factor +that determines the fixed effect parameterization. +The ordering of the categorical variables in the data, +as well as the \code{contrast} option in R, affect the +construction of the model matrix. To see the model +matrix that will ultimately be used in \code{\link[=brm_model]{brm_model()}}, +run \code{\link[brms:make_standata]{brms::make_standata()}} and examine the \code{X} element +of the returned list. See the examples below for a +demonstration. +} + \examples{ if (identical(Sys.getenv("BRM_EXAMPLES", unset = ""), "true")) { set.seed(0L) @@ -46,6 +59,17 @@ formula <- brm_formula( effect_baseline = FALSE, interaction_baseline = FALSE ) +# Optional: set the contrast option, which determines the model matrix. +options(contrasts = c(unordered = "contr.SAS", ordered = "contr.poly")) +# See the fixed effect parameterization you get from the data: +head(brms::make_standata(formula = formula, data = data)$X) +# Specify a different contrast method to use an alternative +# parameterization when fitting the model with brm_model(): +options( + contrasts = c(unordered = "contr.treatment", ordered = "contr.poly") +) +# different model matrix than before: +head(brms::make_standata(formula = formula, data = data)$X) tmp <- utils::capture.output( suppressMessages( suppressWarnings( @@ -59,7 +83,10 @@ tmp <- utils::capture.output( ) ) ) +# The output model is a brms model fit object. model +# The `prior_summary()` function shows the full prior specification +# which reflects the fully realized fixed effects parameterization. brms::prior_summary(model) } } diff --git a/vignettes/usage.Rmd b/vignettes/usage.Rmd index 3bea913f..240809c4 100644 --- a/vignettes/usage.Rmd +++ b/vignettes/usage.Rmd @@ -34,18 +34,18 @@ raw_data <- brm_simulate_simple( raw_data #> # A tibble: 1,200 × 7 -#> response group time patient biomarker1 biomarker2 biomarker3 -#> -#> 1 1.11 grou… time… patien… 1.31 -0.361 1.52 -#> 2 2.15 grou… time… patien… 1.31 -0.361 1.52 -#> 3 2.54 grou… time… patien… 1.31 -0.361 1.52 -#> 4 -1.73 grou… time… patien… 1.31 -0.361 1.52 -#> 5 -0.180 grou… time… patien… 0.107 -2.44 -0.139 -#> 6 0.626 grou… time… patien… 0.107 -2.44 -0.139 -#> 7 -0.221 grou… time… patien… 0.107 -2.44 -0.139 -#> 8 -1.53 grou… time… patien… 0.107 -2.44 -0.139 -#> 9 0.393 grou… time… patien… 1.44 -0.419 -1.54 -#> 10 0.442 grou… time… patien… 1.44 -0.419 -1.54 +#> response group time patient biomarker1 biomarker2 biomarker3 +#> +#> 1 1.11 group_1 time_1 patient_1 1.31 -0.361 1.52 +#> 2 2.15 group_1 time_2 patient_1 1.31 -0.361 1.52 +#> 3 2.54 group_1 time_3 patient_1 1.31 -0.361 1.52 +#> 4 -1.73 group_1 time_4 patient_1 1.31 -0.361 1.52 +#> 5 -0.180 group_1 time_1 patient_10 0.107 -2.44 -0.139 +#> 6 0.626 group_1 time_2 patient_10 0.107 -2.44 -0.139 +#> 7 -0.221 group_1 time_3 patient_10 0.107 -2.44 -0.139 +#> 8 -1.53 group_1 time_4 patient_10 0.107 -2.44 -0.139 +#> 9 0.393 group_1 time_1 patient_100 1.44 -0.419 -1.54 +#> 10 0.442 group_1 time_2 patient_100 1.44 -0.419 -1.54 #> # ℹ 1,190 more rows ``` @@ -142,6 +142,83 @@ formula #> sigma ~ 0 + time ``` +# Parameterization + +The formula is not the only factor +that ultimately determines the fixed effect parameterization. +The ordering of the categorical variables in the data, +as well as the `contrast` option in R, affect the +construction of the model matrix. To see the model +matrix that will ultimately be used in `brm_model()`, +run `brms::make_standata()` and examine the `X` element +of the returned list. + +The `contrast` option accepts a named vector of two character vectors which govern `model.matrix()` contrasts for unordered and ordered variables, respectively. + + +```r +options(contrasts = c(unordered = "contr.SAS", ordered = "contr.poly")) +``` + +The `make_standata()` function lets you see the data that `brms` will generate for Stan. This includes the fixed effects model matrix `X`. Note the differences in the `groupgroup_*` additive terms between the matrix below and the one above. + +```r +head(brms::make_standata(formula = formula, data = data)$X) +#> Intercept timetime_1 timetime_2 timetime_3 groupgroup_1 groupgroup_2 biomarker1 +#> 1 1 1 0 0 1 0 1.3126508 +#> 2 1 0 1 0 1 0 1.3126508 +#> 3 1 0 0 1 1 0 1.3126508 +#> 4 1 0 0 0 1 0 1.3126508 +#> 5 1 1 0 0 1 0 0.1068624 +#> 6 1 0 1 0 1 0 0.1068624 +#> biomarker2 timetime_1:groupgroup_1 timetime_2:groupgroup_1 timetime_3:groupgroup_1 +#> 1 -0.3608809 1 0 0 +#> 2 -0.3608809 0 1 0 +#> 3 -0.3608809 0 0 1 +#> 4 -0.3608809 0 0 0 +#> 5 -2.4441488 1 0 0 +#> 6 -2.4441488 0 1 0 +#> timetime_1:groupgroup_2 timetime_2:groupgroup_2 timetime_3:groupgroup_2 +#> 1 0 0 0 +#> 2 0 0 0 +#> 3 0 0 0 +#> 4 0 0 0 +#> 5 0 0 0 +#> 6 0 0 0 +``` + +If you choose a different contrast method, a different model matrix may result. + + +```r +options( + contrasts = c(unordered = "contr.treatment", ordered = "contr.poly") +) +# different model matrix than before: +head(brms::make_standata(formula = formula, data = data)$X) +#> Intercept timetime_2 timetime_3 timetime_4 groupgroup_2 groupgroup_3 biomarker1 +#> 1 1 0 0 0 0 0 1.3126508 +#> 2 1 1 0 0 0 0 1.3126508 +#> 3 1 0 1 0 0 0 1.3126508 +#> 4 1 0 0 1 0 0 1.3126508 +#> 5 1 0 0 0 0 0 0.1068624 +#> 6 1 1 0 0 0 0 0.1068624 +#> biomarker2 timetime_2:groupgroup_2 timetime_3:groupgroup_2 timetime_4:groupgroup_2 +#> 1 -0.3608809 0 0 0 +#> 2 -0.3608809 0 0 0 +#> 3 -0.3608809 0 0 0 +#> 4 -0.3608809 0 0 0 +#> 5 -2.4441488 0 0 0 +#> 6 -2.4441488 0 0 0 +#> timetime_2:groupgroup_3 timetime_3:groupgroup_3 timetime_4:groupgroup_3 +#> 1 0 0 0 +#> 2 0 0 0 +#> 3 0 0 0 +#> 4 0 0 0 +#> 5 0 0 0 +#> 6 0 0 0 +``` + # Priors Some analyses require informative priors, others require non-informative ones. Please use [`brms`](https://paul-buerkner.github.io/brms/) to construct a prior suitable for your analysis. The [`brms`](https://paul-buerkner.github.io/brms/) package has documentation on how its default priors are constructed and how to set your own priors. Once you have an R object that represents the joint prior distribution of your model, you can pass it to the `brm_model()` function described below. The `get_prior()` function shows the default priors for a given dataset and model formula. @@ -149,50 +226,50 @@ Some analyses require informative priors, others require non-informative ones. P ```r brms::get_prior(data = data, formula = formula) -#> prior class coef group -#> (flat) b -#> (flat) b biomarker1 -#> (flat) b biomarker2 -#> (flat) b groupgroup_2 -#> (flat) b groupgroup_3 -#> (flat) b timetime_2 -#> (flat) b timetime_2:groupgroup_2 -#> (flat) b timetime_2:groupgroup_3 -#> (flat) b timetime_3 -#> (flat) b timetime_3:groupgroup_2 -#> (flat) b timetime_3:groupgroup_3 -#> (flat) b timetime_4 -#> (flat) b timetime_4:groupgroup_2 -#> (flat) b timetime_4:groupgroup_3 -#> lkj(1) cortime -#> student_t(3, 0.9, 2.5) Intercept -#> (flat) b -#> (flat) b timetime_1 -#> (flat) b timetime_2 -#> (flat) b timetime_3 -#> (flat) b timetime_4 -#> resp dpar nlpar lb ub source -#> default -#> (vectorized) -#> (vectorized) -#> (vectorized) -#> (vectorized) -#> (vectorized) -#> (vectorized) -#> (vectorized) -#> (vectorized) -#> (vectorized) -#> (vectorized) -#> (vectorized) -#> (vectorized) -#> (vectorized) -#> default -#> default -#> sigma default -#> sigma (vectorized) -#> sigma (vectorized) -#> sigma (vectorized) -#> sigma (vectorized) +#> prior class coef group resp dpar nlpar lb ub +#> (flat) b +#> (flat) b biomarker1 +#> (flat) b biomarker2 +#> (flat) b groupgroup_2 +#> (flat) b groupgroup_3 +#> (flat) b timetime_2 +#> (flat) b timetime_2:groupgroup_2 +#> (flat) b timetime_2:groupgroup_3 +#> (flat) b timetime_3 +#> (flat) b timetime_3:groupgroup_2 +#> (flat) b timetime_3:groupgroup_3 +#> (flat) b timetime_4 +#> (flat) b timetime_4:groupgroup_2 +#> (flat) b timetime_4:groupgroup_3 +#> lkj(1) cortime +#> student_t(3, 0.9, 2.5) Intercept +#> (flat) b sigma +#> (flat) b timetime_1 sigma +#> (flat) b timetime_2 sigma +#> (flat) b timetime_3 sigma +#> (flat) b timetime_4 sigma +#> source +#> default +#> (vectorized) +#> (vectorized) +#> (vectorized) +#> (vectorized) +#> (vectorized) +#> (vectorized) +#> (vectorized) +#> (vectorized) +#> (vectorized) +#> (vectorized) +#> (vectorized) +#> (vectorized) +#> (vectorized) +#> default +#> default +#> default +#> (vectorized) +#> (vectorized) +#> (vectorized) +#> (vectorized) ``` # Model @@ -220,192 +297,36 @@ model #> total post-warmup draws = 4000 #> #> Correlation Structures: -#> Estimate -#> cortime(time_1,time_2) 0.49 -#> cortime(time_1,time_3) -0.49 -#> cortime(time_2,time_3) -0.26 -#> cortime(time_1,time_4) -0.15 -#> cortime(time_2,time_4) 0.14 -#> cortime(time_3,time_4) 0.08 -#> Est.Error -#> cortime(time_1,time_2) 0.04 -#> cortime(time_1,time_3) 0.04 -#> cortime(time_2,time_3) 0.06 -#> cortime(time_1,time_4) 0.05 -#> cortime(time_2,time_4) 0.06 -#> cortime(time_3,time_4) 0.06 -#> l-95% CI -#> cortime(time_1,time_2) 0.40 -#> cortime(time_1,time_3) -0.57 -#> cortime(time_2,time_3) -0.37 -#> cortime(time_1,time_4) -0.25 -#> cortime(time_2,time_4) 0.03 -#> cortime(time_3,time_4) -0.04 -#> u-95% CI -#> cortime(time_1,time_2) 0.58 -#> cortime(time_1,time_3) -0.40 -#> cortime(time_2,time_3) -0.15 -#> cortime(time_1,time_4) -0.04 -#> cortime(time_2,time_4) 0.25 -#> cortime(time_3,time_4) 0.19 -#> Rhat -#> cortime(time_1,time_2) 1.00 -#> cortime(time_1,time_3) 1.00 -#> cortime(time_2,time_3) 1.00 -#> cortime(time_1,time_4) 1.00 -#> cortime(time_2,time_4) 1.00 -#> cortime(time_3,time_4) 1.00 -#> Bulk_ESS -#> cortime(time_1,time_2) 5073 -#> cortime(time_1,time_3) 5197 -#> cortime(time_2,time_3) 5131 -#> cortime(time_1,time_4) 6564 -#> cortime(time_2,time_4) 5987 -#> cortime(time_3,time_4) 6469 -#> Tail_ESS -#> cortime(time_1,time_2) 3186 -#> cortime(time_1,time_3) 3348 -#> cortime(time_2,time_3) 2786 -#> cortime(time_1,time_4) 3319 -#> cortime(time_2,time_4) 3071 -#> cortime(time_3,time_4) 3246 +#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS +#> cortime(time_1,time_2) 0.50 0.04 0.41 0.57 1.00 4516 3319 +#> cortime(time_1,time_3) -0.49 0.04 -0.57 -0.40 1.00 5194 3374 +#> cortime(time_2,time_3) -0.26 0.05 -0.36 -0.15 1.00 4833 3372 +#> cortime(time_1,time_4) -0.15 0.06 -0.26 -0.03 1.00 5513 2907 +#> cortime(time_2,time_4) 0.14 0.06 0.03 0.25 1.00 5748 2987 +#> cortime(time_3,time_4) 0.07 0.06 -0.04 0.19 1.00 5557 2927 #> #> Population-Level Effects: -#> Estimate -#> Intercept -0.20 -#> timetime_2 1.32 -#> timetime_3 0.51 -#> timetime_4 -1.44 -#> groupgroup_2 1.35 -#> groupgroup_3 1.55 -#> biomarker1 0.02 -#> biomarker2 0.02 -#> timetime_2:groupgroup_2 0.04 -#> timetime_3:groupgroup_2 -0.17 -#> timetime_4:groupgroup_2 -0.08 -#> timetime_2:groupgroup_3 0.02 -#> timetime_3:groupgroup_3 -0.19 -#> timetime_4:groupgroup_3 -0.27 -#> sigma_timetime_1 -0.06 -#> sigma_timetime_2 0.08 -#> sigma_timetime_3 0.09 -#> sigma_timetime_4 0.26 -#> Est.Error -#> Intercept 0.10 -#> timetime_2 0.10 -#> timetime_3 0.18 -#> timetime_4 0.18 -#> groupgroup_2 0.13 -#> groupgroup_3 0.13 -#> biomarker1 0.03 -#> biomarker2 0.03 -#> timetime_2:groupgroup_2 0.14 -#> timetime_3:groupgroup_2 0.25 -#> timetime_4:groupgroup_2 0.25 -#> timetime_2:groupgroup_3 0.14 -#> timetime_3:groupgroup_3 0.25 -#> timetime_4:groupgroup_3 0.25 -#> sigma_timetime_1 0.04 -#> sigma_timetime_2 0.04 -#> sigma_timetime_3 0.04 -#> sigma_timetime_4 0.04 -#> l-95% CI -#> Intercept -0.39 -#> timetime_2 1.12 -#> timetime_3 0.17 -#> timetime_4 -1.79 -#> groupgroup_2 1.09 -#> groupgroup_3 1.28 -#> biomarker1 -0.03 -#> biomarker2 -0.03 -#> timetime_2:groupgroup_2 -0.24 -#> timetime_3:groupgroup_2 -0.65 -#> timetime_4:groupgroup_2 -0.57 -#> timetime_2:groupgroup_3 -0.26 -#> timetime_3:groupgroup_3 -0.68 -#> timetime_4:groupgroup_3 -0.76 -#> sigma_timetime_1 -0.14 -#> sigma_timetime_2 -0.00 -#> sigma_timetime_3 0.01 -#> sigma_timetime_4 0.18 -#> u-95% CI -#> Intercept -0.01 -#> timetime_2 1.52 -#> timetime_3 0.86 -#> timetime_4 -1.10 -#> groupgroup_2 1.62 -#> groupgroup_3 1.81 -#> biomarker1 0.07 -#> biomarker2 0.07 -#> timetime_2:groupgroup_2 0.31 -#> timetime_3:groupgroup_2 0.32 -#> timetime_4:groupgroup_2 0.41 -#> timetime_2:groupgroup_3 0.32 -#> timetime_3:groupgroup_3 0.29 -#> timetime_4:groupgroup_3 0.20 -#> sigma_timetime_1 0.02 -#> sigma_timetime_2 0.16 -#> sigma_timetime_3 0.17 -#> sigma_timetime_4 0.34 -#> Rhat -#> Intercept 1.00 -#> timetime_2 1.00 -#> timetime_3 1.00 -#> timetime_4 1.00 -#> groupgroup_2 1.00 -#> groupgroup_3 1.00 -#> biomarker1 1.00 -#> biomarker2 1.00 -#> timetime_2:groupgroup_2 1.00 -#> timetime_3:groupgroup_2 1.00 -#> timetime_4:groupgroup_2 1.00 -#> timetime_2:groupgroup_3 1.00 -#> timetime_3:groupgroup_3 1.00 -#> timetime_4:groupgroup_3 1.00 -#> sigma_timetime_1 1.00 -#> sigma_timetime_2 1.00 -#> sigma_timetime_3 1.00 -#> sigma_timetime_4 1.00 -#> Bulk_ESS -#> Intercept 1462 -#> timetime_2 1941 -#> timetime_3 1592 -#> timetime_4 1612 -#> groupgroup_2 1514 -#> groupgroup_3 1572 -#> biomarker1 6023 -#> biomarker2 6342 -#> timetime_2:groupgroup_2 2187 -#> timetime_3:groupgroup_2 1692 -#> timetime_4:groupgroup_2 1811 -#> timetime_2:groupgroup_3 2210 -#> timetime_3:groupgroup_3 1531 -#> timetime_4:groupgroup_3 1739 -#> sigma_timetime_1 4527 -#> sigma_timetime_2 4901 -#> sigma_timetime_3 5446 -#> sigma_timetime_4 6614 -#> Tail_ESS -#> Intercept 1836 -#> timetime_2 2866 -#> timetime_3 1970 -#> timetime_4 2118 -#> groupgroup_2 2403 -#> groupgroup_3 2442 -#> biomarker1 2983 -#> biomarker2 2646 -#> timetime_2:groupgroup_2 2723 -#> timetime_3:groupgroup_2 2214 -#> timetime_4:groupgroup_2 2320 -#> timetime_2:groupgroup_3 2913 -#> timetime_3:groupgroup_3 2200 -#> timetime_4:groupgroup_3 2627 -#> sigma_timetime_1 3156 -#> sigma_timetime_2 2810 -#> sigma_timetime_3 3485 -#> sigma_timetime_4 2952 +#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS +#> Intercept -0.20 0.09 -0.38 -0.02 1.00 1213 2044 +#> timetime_2 1.32 0.10 1.12 1.51 1.00 1948 2529 +#> timetime_3 0.51 0.17 0.17 0.85 1.00 1324 2119 +#> timetime_4 -1.44 0.17 -1.78 -1.12 1.00 1285 2264 +#> groupgroup_2 1.35 0.13 1.09 1.61 1.00 1409 2368 +#> groupgroup_3 1.55 0.13 1.29 1.79 1.00 1325 2469 +#> biomarker1 0.02 0.03 -0.03 0.07 1.00 5913 3069 +#> biomarker2 0.02 0.03 -0.03 0.07 1.00 6207 2738 +#> timetime_2:groupgroup_2 0.04 0.14 -0.24 0.33 1.00 2261 2921 +#> timetime_3:groupgroup_2 -0.16 0.24 -0.63 0.31 1.00 1459 2458 +#> timetime_4:groupgroup_2 -0.07 0.24 -0.53 0.41 1.00 1493 2212 +#> timetime_2:groupgroup_3 0.02 0.14 -0.25 0.31 1.00 2131 3201 +#> timetime_3:groupgroup_3 -0.20 0.24 -0.67 0.28 1.00 1453 2171 +#> timetime_4:groupgroup_3 -0.27 0.24 -0.75 0.20 1.00 1393 2081 +#> sigma_timetime_1 -0.06 0.04 -0.14 0.02 1.00 4289 3157 +#> sigma_timetime_2 0.08 0.04 0.00 0.16 1.00 4967 3265 +#> sigma_timetime_3 0.09 0.04 0.01 0.17 1.00 4796 3073 +#> sigma_timetime_4 0.26 0.04 0.18 0.34 1.00 6301 2938 #> -#> Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS +#> Draws were sampled using sample(hmc). For each parameter, Bulk_ESS #> and Tail_ESS are effective sample size measures, and Rhat is the potential #> scale reduction factor on split chains (at convergence, Rhat = 1). ``` @@ -428,329 +349,109 @@ draws <- brm_marginal_draws(model = model, data = data) draws #> $response #> # A draws_df: 1000 iterations, 4 chains, and 12 variables -#> group_1|time_1 -#> 1 -0.206 -#> 2 -0.134 -#> 3 -0.148 -#> 4 -0.132 -#> 5 -0.227 -#> 6 -0.079 -#> 7 -0.235 -#> 8 -0.211 -#> 9 -0.210 -#> 10 -0.263 -#> group_2|time_1 -#> 1 1.12 -#> 2 1.00 -#> 3 1.22 -#> 4 1.13 -#> 5 1.25 -#> 6 1.16 -#> 7 0.96 -#> 8 0.98 -#> 9 1.34 -#> 10 1.02 -#> group_3|time_1 -#> 1 1.4 -#> 2 1.5 -#> 3 1.3 -#> 4 1.3 -#> 5 1.2 -#> 6 1.5 -#> 7 1.3 -#> 8 1.4 -#> 9 1.5 -#> 10 1.3 -#> group_1|time_2 -#> 1 1.07 -#> 2 1.22 -#> 3 1.06 -#> 4 1.25 -#> 5 0.99 -#> 6 1.21 -#> 7 1.16 -#> 8 1.14 -#> 9 1.34 -#> 10 1.22 -#> group_2|time_2 -#> 1 2.3 -#> 2 2.5 -#> 3 2.4 -#> 4 2.8 -#> 5 2.5 -#> 6 2.5 -#> 7 2.4 -#> 8 2.4 -#> 9 2.7 -#> 10 2.3 -#> group_3|time_2 -#> 1 2.7 -#> 2 2.7 -#> 3 2.7 -#> 4 2.7 -#> 5 2.3 -#> 6 2.9 -#> 7 2.8 -#> 8 2.8 -#> 9 2.7 -#> 10 2.8 -#> group_1|time_3 -#> 1 0.24 -#> 2 0.40 -#> 3 0.23 -#> 4 0.47 -#> 5 0.41 -#> 6 0.36 -#> 7 0.48 -#> 8 0.45 -#> 9 0.28 -#> 10 0.44 -#> group_2|time_3 -#> 1 1.4 -#> 2 1.6 -#> 3 1.3 -#> 4 1.5 -#> 5 1.5 -#> 6 1.5 -#> 7 1.7 -#> 8 1.6 -#> 9 1.3 -#> 10 1.5 +#> group_1|time_1 group_2|time_1 group_3|time_1 group_1|time_2 group_2|time_2 +#> 1 -0.256 1.03 1.2 0.94 2.3 +#> 2 -0.207 1.04 1.2 1.01 2.6 +#> 3 -0.090 1.18 1.5 0.94 2.3 +#> 4 -0.011 1.29 1.4 1.36 2.6 +#> 5 -0.070 1.04 1.1 1.09 2.6 +#> 6 -0.032 1.14 1.5 1.23 2.5 +#> 7 -0.093 1.06 1.2 1.13 2.5 +#> 8 -0.034 1.08 1.3 1.26 2.5 +#> 9 -0.167 0.98 1.4 1.09 2.4 +#> 10 -0.204 1.21 1.3 1.07 2.6 +#> group_3|time_2 group_1|time_3 group_2|time_3 +#> 1 2.6 0.338 1.4 +#> 2 2.5 0.474 1.6 +#> 3 2.7 0.055 1.5 +#> 4 2.9 0.234 1.4 +#> 5 2.5 0.260 1.5 +#> 6 2.8 0.194 1.6 +#> 7 2.6 0.335 1.6 +#> 8 2.6 0.077 1.7 +#> 9 2.8 0.252 1.6 +#> 10 2.6 0.288 1.6 #> # ... with 3990 more draws, and 4 more variables #> # ... hidden reserved variables {'.chain', '.iteration', '.draw'} #> #> $change #> # A draws_df: 1000 iterations, 4 chains, and 9 variables -#> group_1|time_2 -#> 1 1.3 -#> 2 1.4 -#> 3 1.2 -#> 4 1.4 -#> 5 1.2 -#> 6 1.3 -#> 7 1.4 -#> 8 1.3 -#> 9 1.6 -#> 10 1.5 -#> group_1|time_3 -#> 1 0.45 -#> 2 0.54 -#> 3 0.37 -#> 4 0.60 -#> 5 0.63 -#> 6 0.44 -#> 7 0.72 -#> 8 0.66 -#> 9 0.49 -#> 10 0.70 -#> group_1|time_4 -#> 1 -1.5 -#> 2 -1.3 -#> 3 -1.6 -#> 4 -1.4 -#> 5 -1.5 -#> 6 -1.3 -#> 7 -1.3 -#> 8 -1.3 -#> 9 -1.4 -#> 10 -1.2 -#> group_2|time_2 -#> 1 1.2 -#> 2 1.5 -#> 3 1.1 -#> 4 1.7 -#> 5 1.2 -#> 6 1.3 -#> 7 1.5 -#> 8 1.4 -#> 9 1.4 -#> 10 1.3 -#> group_2|time_3 -#> 1 0.260 -#> 2 0.569 -#> 3 0.101 -#> 4 0.370 -#> 5 0.230 -#> 6 0.367 -#> 7 0.756 -#> 8 0.644 -#> 9 -0.024 -#> 10 0.492 -#> group_2|time_4 -#> 1 -1.5 -#> 2 -1.4 -#> 3 -1.8 -#> 4 -1.3 -#> 5 -1.8 -#> 6 -1.4 -#> 7 -1.3 -#> 8 -1.4 -#> 9 -1.7 -#> 10 -1.4 -#> group_3|time_2 -#> 1 1.3 -#> 2 1.2 -#> 3 1.3 -#> 4 1.4 -#> 5 1.1 -#> 6 1.4 -#> 7 1.5 -#> 8 1.4 -#> 9 1.2 -#> 10 1.5 -#> group_3|time_3 -#> 1 0.262 -#> 2 0.243 -#> 3 0.355 -#> 4 0.230 -#> 5 0.481 -#> 6 0.096 -#> 7 0.335 -#> 8 0.369 -#> 9 0.227 -#> 10 0.395 +#> group_1|time_2 group_1|time_3 group_1|time_4 group_2|time_2 group_2|time_3 +#> 1 1.2 0.59 -1.4 1.3 0.38 +#> 2 1.2 0.68 -1.4 1.5 0.57 +#> 3 1.0 0.14 -1.6 1.1 0.36 +#> 4 1.4 0.24 -1.7 1.3 0.16 +#> 5 1.2 0.33 -1.4 1.5 0.50 +#> 6 1.3 0.23 -2.0 1.3 0.42 +#> 7 1.2 0.43 -1.6 1.4 0.53 +#> 8 1.3 0.11 -1.7 1.4 0.60 +#> 9 1.3 0.42 -1.5 1.4 0.65 +#> 10 1.3 0.49 -1.5 1.4 0.42 +#> group_2|time_4 group_3|time_2 group_3|time_3 +#> 1 -1.5 1.4 0.6418 +#> 2 -1.4 1.2 0.3158 +#> 3 -1.5 1.3 0.0437 +#> 4 -1.7 1.5 0.1925 +#> 5 -1.2 1.4 0.7741 +#> 6 -1.7 1.3 0.0014 +#> 7 -1.2 1.4 0.5891 +#> 8 -1.5 1.3 0.3694 +#> 9 -1.3 1.4 0.1679 +#> 10 -1.6 1.3 0.4824 #> # ... with 3990 more draws, and 1 more variables #> # ... hidden reserved variables {'.chain', '.iteration', '.draw'} #> #> $difference #> # A draws_df: 1000 iterations, 4 chains, and 6 variables -#> group_2|time_2 -#> 1 -0.059 -#> 2 0.172 -#> 3 -0.076 -#> 4 0.280 -#> 5 -0.013 -#> 6 0.042 -#> 7 0.080 -#> 8 0.035 -#> 9 -0.193 -#> 10 -0.198 -#> group_2|time_3 -#> 1 -0.190 -#> 2 0.033 -#> 3 -0.273 -#> 4 -0.234 -#> 5 -0.404 -#> 6 -0.072 -#> 7 0.040 -#> 8 -0.012 -#> 9 -0.512 -#> 10 -0.208 -#> group_2|time_4 -#> 1 0.019 -#> 2 -0.056 -#> 3 -0.191 -#> 4 0.122 -#> 5 -0.314 -#> 6 -0.098 -#> 7 0.050 -#> 8 -0.031 -#> 9 -0.286 -#> 10 -0.178 -#> group_3|time_2 -#> 1 0.02699 -#> 2 -0.12298 -#> 3 0.13425 -#> 4 -0.01787 -#> 5 -0.08279 -#> 6 0.10895 -#> 7 0.09175 -#> 8 0.07055 -#> 9 -0.31149 -#> 10 -0.00073 -#> group_3|time_3 -#> 1 -0.19 -#> 2 -0.29 -#> 3 -0.02 -#> 4 -0.37 -#> 5 -0.15 -#> 6 -0.34 -#> 7 -0.38 -#> 8 -0.29 -#> 9 -0.26 -#> 10 -0.30 +#> group_2|time_2 group_2|time_3 group_2|time_4 group_3|time_2 group_3|time_3 +#> 1 0.106 -0.216 -0.059 0.233 0.0481 +#> 2 0.335 -0.115 0.015 0.014 -0.3649 +#> 3 0.119 0.213 0.021 0.240 -0.1007 +#> 4 -0.076 -0.085 0.064 0.137 -0.0523 +#> 5 0.363 0.169 0.242 0.277 0.4438 +#> 6 0.051 0.194 0.279 0.026 -0.2247 +#> 7 0.218 0.097 0.453 0.142 0.1610 +#> 8 0.095 0.484 0.251 -0.039 0.2579 +#> 9 0.166 0.233 0.268 0.097 -0.2517 +#> 10 0.165 -0.072 -0.128 0.052 -0.0093 #> group_3|time_4 -#> 1 -0.335 -#> 2 -0.402 -#> 3 -0.099 -#> 4 -0.506 -#> 5 -0.160 -#> 6 -0.370 -#> 7 -0.262 -#> 8 -0.326 -#> 9 -0.400 -#> 10 -0.320 +#> 1 -0.2188 +#> 2 -0.3413 +#> 3 -0.4630 +#> 4 0.1403 +#> 5 -0.0098 +#> 6 0.2332 +#> 7 0.0092 +#> 8 0.0695 +#> 9 -0.1699 +#> 10 -0.2650 #> # ... with 3990 more draws #> # ... hidden reserved variables {'.chain', '.iteration', '.draw'} #> #> $effect #> # A draws_df: 1000 iterations, 4 chains, and 6 variables -#> group_2|time_2 -#> 1 -0.057 -#> 2 0.164 -#> 3 -0.069 -#> 4 0.262 -#> 5 -0.012 -#> 6 0.038 -#> 7 0.071 -#> 8 0.031 -#> 9 -0.174 -#> 10 -0.165 -#> group_2|time_3 -#> 1 -0.177 -#> 2 0.030 -#> 3 -0.246 -#> 4 -0.216 -#> 5 -0.376 -#> 6 -0.066 -#> 7 0.038 -#> 8 -0.012 -#> 9 -0.449 -#> 10 -0.184 -#> group_2|time_4 -#> 1 0.015 -#> 2 -0.045 -#> 3 -0.146 -#> 4 0.092 -#> 5 -0.237 -#> 6 -0.078 -#> 7 0.038 -#> 8 -0.025 -#> 9 -0.208 -#> 10 -0.138 -#> group_3|time_2 -#> 1 0.02600 -#> 2 -0.11734 -#> 3 0.12200 -#> 4 -0.01670 -#> 5 -0.07554 -#> 6 0.09773 -#> 7 0.08133 -#> 8 0.06257 -#> 9 -0.28115 -#> 10 -0.00061 -#> group_3|time_3 -#> 1 -0.175 -#> 2 -0.265 -#> 3 -0.018 -#> 4 -0.345 -#> 5 -0.142 -#> 6 -0.317 -#> 7 -0.362 -#> 8 -0.271 -#> 9 -0.230 -#> 10 -0.269 +#> group_2|time_2 group_2|time_3 group_2|time_4 group_3|time_2 group_3|time_3 +#> 1 0.102 -0.201 -0.047 0.223 0.0448 +#> 2 0.330 -0.106 0.011 0.013 -0.3341 +#> 3 0.109 0.192 0.015 0.220 -0.0908 +#> 4 -0.070 -0.079 0.053 0.125 -0.0485 +#> 5 0.342 0.151 0.177 0.261 0.3973 +#> 6 0.046 0.176 0.211 0.024 -0.2032 +#> 7 0.202 0.085 0.321 0.132 0.1402 +#> 8 0.085 0.448 0.202 -0.035 0.2385 +#> 9 0.157 0.206 0.197 0.092 -0.2224 +#> 10 0.140 -0.069 -0.102 0.044 -0.0089 #> group_3|time_4 -#> 1 -0.261 -#> 2 -0.327 -#> 3 -0.076 -#> 4 -0.381 -#> 5 -0.120 -#> 6 -0.293 -#> 7 -0.201 -#> 8 -0.256 -#> 9 -0.291 -#> 10 -0.247 +#> 1 -0.1748 +#> 2 -0.2589 +#> 3 -0.3365 +#> 4 0.1148 +#> 5 -0.0071 +#> 6 0.1764 +#> 7 0.0065 +#> 8 0.0559 +#> 9 -0.1249 +#> 10 -0.2116 #> # ... with 3990 more draws #> # ... hidden reserved variables {'.chain', '.iteration', '.draw'} ``` @@ -762,131 +463,65 @@ If you need samples from these marginals averaged across time points, e.g. an "o brm_marginal_draws_average(draws = draws, data = data) #> $response #> # A draws_df: 1000 iterations, 4 chains, and 3 variables -#> group_1|average -#> 1 -0.1501 -#> 2 0.0057 -#> 3 -0.1500 -#> 4 0.0159 -#> 5 -0.1307 -#> 6 0.0184 -#> 7 -0.0390 -#> 8 -0.0416 -#> 9 -0.0532 -#> 10 -0.0290 -#> group_2|average -#> 1 1.1 -#> 2 1.2 -#> 3 1.1 -#> 4 1.3 -#> 5 1.2 -#> 6 1.2 -#> 7 1.2 -#> 8 1.1 -#> 9 1.3 -#> 10 1.1 -#> group_3|average -#> 1 1.3 -#> 2 1.4 -#> 3 1.3 -#> 4 1.3 -#> 5 1.2 -#> 6 1.4 -#> 7 1.4 -#> 8 1.4 -#> 9 1.4 -#> 10 1.4 +#> group_1|average group_2|average group_3|average +#> 1 -0.160 1.1 1.3 +#> 2 -0.091 1.2 1.2 +#> 3 -0.189 1.2 1.3 +#> 4 -0.038 1.2 1.4 +#> 5 -0.053 1.3 1.3 +#> 6 -0.151 1.2 1.4 +#> 7 -0.083 1.3 1.3 +#> 8 -0.120 1.2 1.3 +#> 9 -0.131 1.2 1.4 +#> 10 -0.127 1.3 1.3 #> # ... with 3990 more draws #> # ... hidden reserved variables {'.chain', '.iteration', '.draw'} #> #> $change #> # A draws_df: 1000 iterations, 4 chains, and 3 variables -#> group_1|average -#> 1 0.0748 -#> 2 0.1864 -#> 3 -0.0021 -#> 4 0.1967 -#> 5 0.1288 -#> 6 0.1301 -#> 7 0.2612 -#> 8 0.2261 -#> 9 0.2095 -#> 10 0.3126 -#> group_2|average -#> 1 -0.0018 -#> 2 0.2360 -#> 3 -0.1820 -#> 4 0.2526 -#> 5 -0.1151 -#> 6 0.0875 -#> 7 0.3179 -#> 8 0.2231 -#> 9 -0.1209 -#> 10 0.1177 -#> group_3|average -#> 1 -0.0907 -#> 2 -0.0861 -#> 3 0.0031 -#> 4 -0.1024 -#> 5 -0.0029 -#> 6 -0.0714 -#> 7 0.0773 -#> 8 0.0448 -#> 9 -0.1151 -#> 10 0.1042 +#> group_1|average group_2|average group_3|average +#> 1 0.127 0.071 0.148 +#> 2 0.154 0.232 -0.077 +#> 3 -0.132 -0.014 -0.240 +#> 4 -0.037 -0.069 0.038 +#> 5 0.023 0.281 0.260 +#> 6 -0.159 0.016 -0.147 +#> 7 0.014 0.270 0.118 +#> 8 -0.113 0.163 -0.017 +#> 9 0.049 0.271 -0.060 +#> 10 0.103 0.091 0.028 #> # ... with 3990 more draws #> # ... hidden reserved variables {'.chain', '.iteration', '.draw'} #> #> $difference #> # A draws_df: 1000 iterations, 4 chains, and 2 variables -#> group_2|average -#> 1 -0.0766 -#> 2 0.0496 -#> 3 -0.1800 -#> 4 0.0560 -#> 5 -0.2439 -#> 6 -0.0426 -#> 7 0.0567 -#> 8 -0.0031 -#> 9 -0.3304 -#> 10 -0.1949 -#> group_3|average -#> 1 -0.1655 -#> 2 -0.2725 -#> 3 0.0051 -#> 4 -0.2991 -#> 5 -0.1317 -#> 6 -0.2015 -#> 7 -0.1839 -#> 8 -0.1813 -#> 9 -0.3246 -#> 10 -0.2084 +#> group_2|average group_3|average +#> 1 -0.056 0.021 +#> 2 0.078 -0.231 +#> 3 0.118 -0.108 +#> 4 -0.032 0.075 +#> 5 0.258 0.237 +#> 6 0.175 0.012 +#> 7 0.256 0.104 +#> 8 0.277 0.096 +#> 9 0.222 -0.108 +#> 10 -0.012 -0.074 #> # ... with 3990 more draws #> # ... hidden reserved variables {'.chain', '.iteration', '.draw'} #> #> $effect #> # A draws_df: 1000 iterations, 4 chains, and 2 variables -#> group_2|average -#> 1 -0.0727 -#> 2 0.0494 -#> 3 -0.1536 -#> 4 0.0459 -#> 5 -0.2082 -#> 6 -0.0354 -#> 7 0.0491 -#> 8 -0.0019 -#> 9 -0.2772 -#> 10 -0.1623 -#> group_3|average -#> 1 -0.1367 -#> 2 -0.2363 -#> 3 0.0094 -#> 4 -0.2475 -#> 5 -0.1126 -#> 6 -0.1707 -#> 7 -0.1604 -#> 8 -0.1549 -#> 9 -0.2674 -#> 10 -0.1724 +#> group_2|average group_3|average +#> 1 -0.049 0.03107 +#> 2 0.079 -0.19320 +#> 3 0.106 -0.06895 +#> 4 -0.032 0.06376 +#> 5 0.223 0.21688 +#> 6 0.145 -0.00099 +#> 7 0.202 0.09280 +#> 8 0.245 0.08637 +#> 9 0.187 -0.08528 +#> 10 -0.010 -0.05889 #> # ... with 3990 more draws #> # ... hidden reserved variables {'.chain', '.iteration', '.draw'} ``` @@ -899,22 +534,19 @@ summaries <- brm_marginal_summaries(draws, level = 0.95) summaries #> # A tibble: 165 × 6 -#> marginal statistic group -#> -#> 1 change lower group_1 -#> 2 change lower group_1 -#> 3 change lower group_1 -#> 4 change lower group_2 -#> 5 change lower group_2 -#> 6 change lower group_2 -#> 7 change lower group_3 -#> 8 change lower group_3 -#> 9 change lower group_3 -#> 10 change mean group_1 +#> marginal statistic group time value mcse +#> +#> 1 change lower group_1 time_2 1.12 0.00488 +#> 2 change lower group_1 time_3 0.168 0.0102 +#> 3 change lower group_1 time_4 -1.78 0.00876 +#> 4 change lower group_2 time_2 1.15 0.00553 +#> 5 change lower group_2 time_3 0.0160 0.00963 +#> 6 change lower group_2 time_4 -1.84 0.0102 +#> 7 change lower group_3 time_2 1.14 0.00353 +#> 8 change lower group_3 time_3 -0.0223 0.00824 +#> 9 change lower group_3 time_4 -2.06 0.00872 +#> 10 change mean group_1 time_2 1.32 0.00230 #> # ℹ 155 more rows -#> # ℹ 3 more variables: -#> # time , value , -#> # mcse ``` The `brm_marginal_probabilities()` function shows posterior probabilities of the form, @@ -941,22 +573,20 @@ brm_marginal_probabilities( direction = c("greater", "less") ) #> # A tibble: 12 × 5 -#> direction threshold group -#> -#> 1 greater -0.1 group_2 -#> 2 greater -0.1 group_2 -#> 3 greater -0.1 group_2 -#> 4 greater -0.1 group_3 -#> 5 greater -0.1 group_3 -#> 6 greater -0.1 group_3 -#> 7 less 0.1 group_2 -#> 8 less 0.1 group_2 -#> 9 less 0.1 group_2 -#> 10 less 0.1 group_3 -#> 11 less 0.1 group_3 -#> 12 less 0.1 group_3 -#> # ℹ 2 more variables: -#> # time , value +#> direction threshold group time value +#> +#> 1 greater -0.1 group_2 time_2 0.833 +#> 2 greater -0.1 group_2 time_3 0.397 +#> 3 greater -0.1 group_2 time_4 0.549 +#> 4 greater -0.1 group_3 time_2 0.800 +#> 5 greater -0.1 group_3 time_3 0.334 +#> 6 greater -0.1 group_3 time_4 0.244 +#> 7 less 0.1 group_2 time_2 0.660 +#> 8 less 0.1 group_2 time_3 0.860 +#> 9 less 0.1 group_2 time_4 0.768 +#> 10 less 0.1 group_3 time_2 0.705 +#> 11 less 0.1 group_3 time_3 0.890 +#> 12 less 0.1 group_3 time_4 0.938 ``` Finally, the `brm_marignals_data()` computes marginal means and confidence intervals on the response variable in the data, along with other summary statistics. @@ -967,21 +597,19 @@ summaries_data <- brm_marginal_data(data = data, level = 0.95) summaries_data #> # A tibble: 84 × 4 -#> statistic group time -#> -#> 1 lower group_1 time_1 -#> 2 lower group_1 time_2 -#> 3 lower group_1 time_3 -#> 4 lower group_1 time_4 -#> 5 lower group_2 time_1 -#> 6 lower group_2 time_2 -#> 7 lower group_2 time_3 -#> 8 lower group_2 time_4 -#> 9 lower group_3 time_1 -#> 10 lower group_3 time_2 +#> statistic group time value +#> +#> 1 lower group_1 time_1 -0.00263 +#> 2 lower group_1 time_2 1.32 +#> 3 lower group_1 time_3 0.535 +#> 4 lower group_1 time_4 -1.39 +#> 5 lower group_2 time_1 1.33 +#> 6 lower group_2 time_2 2.72 +#> 7 lower group_2 time_3 1.72 +#> 8 lower group_2 time_4 -0.0926 +#> 9 lower group_3 time_1 1.52 +#> 10 lower group_3 time_2 2.90 #> # ℹ 74 more rows -#> # ℹ 1 more variable: -#> # value ``` # Visualization diff --git a/vignettes/usage.Rmd.upstream b/vignettes/usage.Rmd.upstream index ca7d17d0..7230aae8 100644 --- a/vignettes/usage.Rmd.upstream +++ b/vignettes/usage.Rmd.upstream @@ -102,6 +102,39 @@ formula <- brm_formula( formula ``` +# Parameterization + +The formula is not the only factor +that ultimately determines the fixed effect parameterization. +The ordering of the categorical variables in the data, +as well as the `contrast` option in R, affect the +construction of the model matrix. To see the model +matrix that will ultimately be used in `brm_model()`, +run `brms::make_standata()` and examine the `X` element +of the returned list. + +The `contrast` option accepts a named vector of two character vectors which govern `model.matrix()` contrasts for unordered and ordered variables, respectively. + +```{r} +options(contrasts = c(unordered = "contr.SAS", ordered = "contr.poly")) +``` + +The `make_standata()` function lets you see the data that `brms` will generate for Stan. This includes the fixed effects model matrix `X`. Note the differences in the `groupgroup_*` additive terms between the matrix below and the one above. + +```{r} +head(brms::make_standata(formula = formula, data = data)$X) +``` + +If you choose a different contrast method, a different model matrix may result. + +```{r} +options( + contrasts = c(unordered = "contr.treatment", ordered = "contr.poly") +) +# different model matrix than before: +head(brms::make_standata(formula = formula, data = data)$X) +``` + # Priors Some analyses require informative priors, others require non-informative ones. Please use [`brms`](https://paul-buerkner.github.io/brms/) to construct a prior suitable for your analysis. The [`brms`](https://paul-buerkner.github.io/brms/) package has documentation on how its default priors are constructed and how to set your own priors. Once you have an R object that represents the joint prior distribution of your model, you can pass it to the `brm_model()` function described below. 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