I am trying to model accuracies and reaction times in psychophysical data using the Wiener diffusion model in brms. see the excellent tutorial by Henrik Singmann. The Wiener family has four distributional parameters: the drift rate, boundary separation, bias and non-decision time.
I am having trouble sampling from the model (both for sampling convergence and even chain initialization). The problem seems to arise from the non-decision time parameter: the NDT parameter creates a hard lower bound for the lpdf output such that the random variable output by the other model parameters must be larger than the NDT. If this is not the case the family function throws an error. NDT must also be positive.
This last part is handled by using a log link function for that parameter in the family by default. The problem is that very large NDTs can be sampled in chain initialization and exploration, leading to many rejected samples and problems initializing.
Since I don’t have any theoretical interest in the NDT, I would like to fix or strongly bound the parameter to facilitate sampling in the rest of the model, but I’m unsure how to achieve this.
A simplified version of the model with problems is shown below:
model_formula <- brmsformula(rt | dec(response_yes) ~ factor_a +
(factor_a | p | subj) +
(1 | im_filename),
bs ~ factor_b +
(factor_b | p | subj),
ndt ~ 1,
bias ~ factor_b +
(factor_b | p | subj),
family = wiener(link_bs = "log",
link_ndt = "log",
link_bias = "logit")
)
I would like to be able to do something like:
ndt = 0.5
(i.e. fixing the ndt to a single value)
or
ndt ~ inv_logit(factor_b)*2.0
(i.e. bounding the NDT parameter in the model to be within 0–2 by using an inverse logit link).
Neither of these attempts works. Can anyone more familiar with brms or this distributional model suggest how I could achieve these bounds or fixed parameter?
Thanks!
sessionInfo()
[I’m running this in a docker container]:
R version 3.5.2 (2018-12-20)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Debian GNU/Linux 9 (stretch)
Matrix products: default
BLAS: /usr/lib/openblas-base/libblas.so.3
LAPACK: /usr/lib/libopenblasp-r0.2.19.so
locale:
[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C LC_TIME=en_US.UTF-8
[4] LC_COLLATE=en_US.UTF-8 LC_MONETARY=en_US.UTF-8 LC_MESSAGES=C
[7] LC_PAPER=en_US.UTF-8 LC_NAME=C LC_ADDRESS=C
[10] LC_TELEPHONE=C LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] bindrcpp_0.2.2 foreach_1.4.4 here_0.1 forcats_0.3.0 stringr_1.3.1 dplyr_0.7.8
[7] purrr_0.2.5 readr_1.3.0 tidyr_0.8.2 tibble_1.4.2 tidyverse_1.2.1 brms_2.7.0
[13] ggplot2_3.1.0 Rcpp_1.0.0
loaded via a namespace (and not attached):
[1] nlme_3.1-137 matrixStats_0.54.0 xts_0.11-2 lubridate_1.7.4
[5] threejs_0.3.1 httr_1.4.0 rprojroot_1.3-2 rstan_2.18.2
[9] tools_3.5.2 backports_1.1.3 R6_2.3.0 DT_0.5
[13] lazyeval_0.2.1 colorspace_1.3-2 withr_2.1.2 tidyselect_0.2.5
[17] gridExtra_2.3 prettyunits_1.0.2 processx_3.2.1 Brobdingnag_1.2-6
[21] compiler_3.5.2 rvest_0.3.2 cli_1.0.1 xml2_1.2.0
[25] shinyjs_1.0 colourpicker_1.0 scales_1.0.0 dygraphs_1.1.1.6
[29] mvtnorm_1.0-8 ggridges_0.5.1 callr_3.1.0 digest_0.6.18
[33] StanHeaders_2.18.0-1 base64enc_0.1-3 pkgconfig_2.0.2 htmltools_0.3.6
[37] readxl_1.2.0 htmlwidgets_1.3 rlang_0.3.0.1 rstudioapi_0.8
[41] shiny_1.2.0 bindr_0.1.1 generics_0.0.2 zoo_1.8-4
[45] jsonlite_1.6 crosstalk_1.0.0 gtools_3.8.1 inline_0.3.15
[49] magrittr_1.5 loo_2.0.0 bayesplot_1.6.0 Matrix_1.2-15
[53] munsell_0.5.0 abind_1.4-5 stringi_1.2.4 yaml_2.2.0
[57] pkgbuild_1.0.2 plyr_1.8.4 grid_3.5.2 parallel_3.5.2
[61] promises_1.0.1 crayon_1.3.4 miniUI_0.1.1.1 lattice_0.20-38
[65] haven_2.0.0 hms_0.4.2 ps_1.2.1 pillar_1.3.1
[69] igraph_1.2.2 markdown_0.9 shinystan_2.5.0 codetools_0.2-15
[73] reshape2_1.4.3 stats4_3.5.2 rstantools_1.5.1 glue_1.3.0
[77] modelr_0.1.2 httpuv_1.4.5.1 cellranger_1.1.0 gtable_0.2.0
[81] assertthat_0.2.0 mime_0.6 xtable_1.8-3 broom_0.5.1
[85] coda_0.19-2 later_0.7.5 rsconnect_0.8.12 iterators_1.0.10
[89] shinythemes_1.1.2 bridgesampling_0.6-0