🎃 - Introduction to ExtendedRtIrtModeling.jl through JuliaConnectoR

I’ve just updated my Julia package, ExtendedRtIrtModeling.jl, to version 0.2.0. There are a few new features in there that I’ll run through in the next few sections.

But that’s not all! If you’re an R user, I’ll introduce you to an R package called JuliaConnectoR that lets you run Julia programs in R. It’ll bridge the two languages seamlessly.

Using in Julia

See the Github page.

Using in R

All you have to do is to install and library the JuliaConnectoR as usual, and then you can use the juliaImport function to import any Julia package. It seems like the package’s version you get depends on which copy version you’ve had on your computer (confirmed). ~~The great thing is, it’ll always download the newest version from Github, but not the stable one.~~

Code

library(tidyverse)

── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr     1.1.4     ✔ readr     2.1.5
✔ forcats   1.0.0     ✔ stringr   1.5.1
✔ ggplot2   3.5.1     ✔ tibble    3.2.1
✔ lubridate 1.9.3     ✔ tidyr     1.3.1
✔ purrr     1.0.2     
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

Code

library(JuliaConnectoR)

Warning: package 'JuliaConnectoR' was built under R version 4.4.1

I’ve got a toy data set to test, but I’ll run through the demo anyway. As you can see from the data below, the data set includes 25 columns: one for ID, 10 for item responses, 10 for (log-)response time, and four for explanatory variables.

Code

demo <- read.csv('https://raw.githubusercontent.com/jiewenTsai/ExtendedRtIrtModeling.jl/refs/heads/main/data/demo.csv')
head(demo)

    id y1 y2 y3 y4 y5 y6 y7 y8 y9 y10    t1    t2    t3    t4    t5    t6    t7
1 s001  0  0  0  0  1  0  0  0  0   0 2.961 4.225 3.322 2.164 2.273 2.631 2.505
2 s002  0  0  0  0  1  1  1  0  0   0 3.848 3.996 4.434 3.246 2.663 3.819 2.158
3 s003  0  0  0  0  0  1  1  1  0   0 3.122 3.273 4.489 3.891 3.410 3.879 2.951
4 s004  0  1  0  0  0  0  1  0  0   0 3.515 3.162 4.151 3.371 2.885 3.026 1.439
5 s005  0  0  0  0  0  0  1  0  1   0 3.060 3.962 4.058 3.696 2.732 2.560 2.517
6 s006  0  0  0  0  1  0  0  0  0   0 3.546 3.360 3.382 3.262 1.931 1.629 1.463
     t8    t9   t10 x1     x2     x3    x4
1 3.924 2.198 2.878  0 -3.362 -0.200 1.063
2 2.848 2.492 4.038  1 -0.081  2.347 1.063
3 3.891 3.877 3.553  0 -0.829 -1.068 1.063
4 3.243 2.694 3.603  1 -0.829 -0.676 1.063
5 3.339 3.421 3.314  0 -0.829  0.097 1.063
6 2.475 2.373 2.909  1 -1.251 -3.096 1.063

Code

glimpse(demo)

Rows: 300
Columns: 25
$ id  <chr> "s001", "s002", "s003", "s004", "s005", "s006", "s007", "s008", "s…
$ y1  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, …
$ y2  <int> 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ y3  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ y4  <int> 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ y5  <int> 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, …
$ y6  <int> 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, …
$ y7  <int> 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, …
$ y8  <int> 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, …
$ y9  <int> 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, …
$ y10 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$ t1  <dbl> 2.961, 3.848, 3.122, 3.515, 3.060, 3.546, 2.579, 3.854, 4.516, 2.9…
$ t2  <dbl> 4.225, 3.996, 3.273, 3.162, 3.962, 3.360, 3.448, 3.451, 4.943, 4.1…
$ t3  <dbl> 3.322, 4.434, 4.489, 4.151, 4.058, 3.382, 3.753, 2.875, 2.945, 5.0…
$ t4  <dbl> 2.164, 3.246, 3.891, 3.371, 3.696, 3.262, 3.575, 3.634, 4.444, 4.0…
$ t5  <dbl> 2.273, 2.663, 3.410, 2.885, 2.732, 1.931, 2.846, 2.560, 2.718, 2.8…
$ t6  <dbl> 2.631, 3.819, 3.879, 3.026, 2.560, 1.629, 3.153, 2.499, 1.442, 3.3…
$ t7  <dbl> 2.505, 2.158, 2.951, 1.439, 2.517, 1.463, 3.370, 2.581, 1.666, 3.2…
$ t8  <dbl> 3.924, 2.848, 3.891, 3.243, 3.339, 2.475, 2.424, 2.124, 3.301, 3.3…
$ t9  <dbl> 2.198, 2.492, 3.877, 2.694, 3.421, 2.373, 2.039, 2.749, 1.962, 2.7…
$ t10 <dbl> 2.878, 4.038, 3.553, 3.603, 3.314, 2.909, 2.923, 2.366, 4.804, 3.6…
$ x1  <int> 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, …
$ x2  <dbl> -3.362, -0.081, -0.829, -0.829, -0.829, -1.251, 1.174, -0.829, -1.…
$ x3  <dbl> -0.200, 2.347, -1.068, -0.676, 0.097, -3.096, -1.944, -1.258, -1.4…
$ x4  <dbl> 1.063, 1.063, 1.063, 1.063, 1.063, 1.063, 0.104, -0.587, -2.002, -…

Next, let’s take a look at how accuracy and speed related to each other, barely using the raw data (mean of y and mean of t) to get a rough idea.

Code

tibble(
  accuracy = rowMeans(demo[2:11]),
  speed = -rowMeans(demo[12:21])
) |>
  ggplot(aes(x=accuracy, y=speed)) +
  geom_point() +
  geom_jitter() +
  geom_smooth(method = "loess")

`geom_smooth()` using formula = 'y ~ x'

The modeling part.

Let’s follow the example from the Github readme post to show how a basic RT-IRT model works. This package is version 0.2.0.

Code

## You have to give a name to the Julia Environment.
ex <- juliaImport("ExtendedRtIrtModeling")

Starting Julia ...

Code

juliaEval('Pkg.status("ExtendedRtIrtModeling")')

Status `~/.julia/environments/v1.10/Project.toml`
  [1fd685a6] ExtendedRtIrtModeling v0.2.0 `https://github.com/jiewenTsai/ExtendedRtIrtModeling.jl#main`

In the original Github post, the user doesn’t have to fill in all five arguments of InputData because the values for \(\kappa\) and logT are automatically calculated by Y and T. However, to get it working with R, I’ve come up with another struct called InputData4R, which is specifically for R users.

Code

## import your data set
Cond = ex$setCond(
  nChain=3, 
  nIter=3000,
  nSubj=300,
  nItem=10,
  nFeat=4
  )
Data = ex$InputData4R(
    Y = as.matrix(demo[2:11]),
    # you must write this line!
    κ = as.matrix(demo[2:11]-0.5),
    T = as.matrix(exp(demo[12:21])),
    logT = as.matrix(demo[12:21]),
    X = as.matrix(demo[22:25])
)

## build a model and sample it!
MCMC = ex$GibbsRtIrt(Cond, Data=Data)
## Notice the `` style for sample!
ex$`sample!`(MCMC)

<Julia object of type ExtendedRtIrtModeling.GibbsRtIrt>
ExtendedRtIrtModeling.GibbsRtIrt(ExtendedRtIrtModeling.SimConditions(300, 10, 4, 3000, 3, 1500, 1, 10, 0.5, 0.5), ExtendedRtIrtModeling.InputData4R([0 0 … 0 0; 0 0 … 0 0; … ; 0 0 … 1 0; 0 1 … 1 0], [-0.5 -0.5 … -0.5 -0.5; -0.5 -0.5 … -0.5 -0.5; … ; -0.5 -0.5 … 0.5 -0.5; -0.5 0.5 … 0.5 -0.5], [19.31727937946127 68.3745035485581 … 9.006981510434914 17.778680238058843; 46.89917102861648 54.38019363641357 … 12.085422811327593 56.71280369681312; … ; 27.194098966393437 42.182270397465956 … 25.584840292351714 119.46219960089533; 35.05786562994266 82.26946350420168 … 43.991656898689 24.754319523777408], [2.961 4.225 … 2.198 2.878; 3.848 3.996 … 2.492 4.038; … ; 3.303 3.742 … 3.242 4.783; 3.557 4.41 … 3.784 3.209], [0.0 -3.362 -0.2 1.063; 1.0 -0.081 2.347 1.063; … ; 1.0 -0.064 0.445 -0.318; 0.0 -0.449 -0.676 1.063]), Float64[], ExtendedRtIrtModeling.InputPara([0.03803954836290282 0.15232909667566663 … 0.05161322853812894 0.13813548640620224; 0.6820446079265877 0.34147419401485857 … 0.08950104948637522 0.14098614046303293; … ; 0.10597207519925943 0.1647379067865525 … 0.39929612168578055 0.07881275553602582; 0.029065140357117505 0.11420999068850912 … 0.067385411002555 0.08432507233276894], [-3.2940883047383913; -0.8556087208746063; … ; 0.2957471460780982; -0.5130925360110484;;], [1.1729970641986105; 1.5458803495092144; … ; 1.6853029639293666; 1.530409031452339;;], [-0.517568491848459; -0.982877174566527; … ; -0.7583810973883602; -0.09740730421271002;;], [0.5187822333228932; 0.17945796808241804; … ; -0.4089531330263851; -0.28036133076001346;;], [3.3393118348012587; 3.87644094752713; … ; 2.8577060562598415; 3.7101671096169406;;], [0.36835845733426814; 0.32471225592571945; … ; 0.2879305608202483; 0.2535185154875389;;], Float64[], [0.0 0.0; -0.13955836192391025 0.19017204916811675; … ; 0.19452561633168883 -0.02569275995793209; 0.008873056157746655 -0.020109568214501022], Float64[], [1.0320100623914066 -0.07785061758422016; -0.07785061758422016 0.16895129102317735]), ExtendedRtIrtModeling.OutputPost([-2.5316054308599174 -1.0201149676069194 … -0.5075576803546703 -0.08864269630953704; -2.385233298441571 -1.4283258309850775 … -1.4219131141778978 0.2129493136184259; … ; -1.9741175809894413 -1.0250130746899613 … -0.5718654341855209 -0.1284281480151264; -2.844235988213971 -1.316783874105525 … -0.6786711872540668 -0.05857460754134373;;; -4.6483512794741735 0.3493888705714854 … -2.4506544874705565 0.6788249924528524; -3.7301650282003234 -0.35206014753877 … -1.060147038895324 -0.022847830081273553; … ; -2.3228954038123826 -0.7633078075173486 … -0.5218305601114234 -0.006863193064532861; -2.947459210211141 -1.1136049934548102 … -0.7818335114896942 -0.07936515200090292;;; -2.8110340000021417 -0.03212862955989345 … -2.025504239319318 0.45657793306823946; -4.1596980425369825 -0.14333259949396085 … -1.1332579574632875 0.3222192608749193; … ; -2.9995248309035096 -0.5025283160730506 … -0.7183550769803037 0.0676513203886467; -3.2940883047383913 -0.8556087208746063 … -0.7583810973883602 -0.09740730421271002], [1.4408516602399948 0.3119398314847293 … 1.436388830030692 1.7594573686009332; 0.6485769988459371 0.09799817794512869 … 0.31841190001990965 0.24727987392394055; … ; 0.6627543140062743 0.062379143944078154 … 0.2865093185798355 0.24389872189259454; 0.44614964292947934 -0.0009854797366953515 … 0.28884633266179777 0.21660633195557716;;; 0.20771950271501474 0.07470008557255679 … 0.4103878498912844 0.3363959900787248; 0.4426062385974111 0.5151675445567098 … 0.29291788454958345 0.2503375597447657; … ; 0.7070645022178579 0.20368876114203885 … 0.28272533057375293 0.24136415837075093; 0.45753666379890207 -0.18874208624041255 … 0.2834510081524539 0.2551776999849949;;; 0.30915139077679943 0.11755077510470256 … 0.33693480204725546 0.2526349715282094; 0.5271674464554031 -0.03412047093349183 … 0.31415501362293397 0.23995328803270566; … ; 0.4020971899295065 0.0677768958301857 … 0.3122296334816429 0.27227850933927056; 0.5187822333228932 0.17945796808241804 … 0.2879305608202483 0.2535185154875389], [0.0 -0.0887285183553337 … -0.01884626579878293 1.1285784837010724; 0.0 -0.08011816664565659 … -0.04343663237172715 0.18452860531678966; … ; 0.0 0.008086425833789466 … -0.025520812462631465 0.1612415796308012; 0.0 -0.12264846253365731 … -0.07384019130048343 0.17262190728489224;;; 0.0 -0.03664858006607563 … 0.0067944616781861365 0.338624461155973; 0.0 -0.1073789503209682 … -0.029642765491720922 0.19165667155122298; … ; 0.0 0.043887021217047927 … -0.03532031809739464 0.17413726452088615; 0.0 -0.1643751390334616 … -0.010822072367220475 0.18541630144658308;;; 0.0 -0.08211729186350054 … -0.08333707459658027 0.17415795145027568; 0.0 -0.13250855065322767 … -0.08673313781096505 0.187742906364859; … ; 0.0 -0.10128227451428869 … -0.03748007560750125 0.19121942907428163; 0.0 -0.13955836192391025 … -0.07785061758422016 0.16895129102317735], [-6445.598553588707; -4656.228890248507; … ; -4456.902783934122; -4505.806270733834;;; -4920.580097790624; -4651.149283501899; … ; -4485.579809921432; -4486.097395433786;;; -4738.516081862697; -4563.873634836814; … ; -4488.181661060116; -4498.276381449872], ExtendedRtIrtModeling.InputPara(Float64[], [-2.3178527540742926, -0.8727691300728337, -1.1270941644815011, -1.314220325940113, -1.312310125131537, -2.1240213345575376, -1.536219741784194, -0.8795771064111, -1.4058283159119116, -1.0523714562500226  …  -0.5537072915566369, -0.546197426858273, -0.29753429086726474, -0.7788845545983953, -0.4288798781746426, -0.6379621032854847, -0.8723359959589986, -0.7208395955141799, -0.361997792920653, -0.8277817235912058], [1.3646887304206927, 1.6249134397666332, 1.8934917297683258, 2.3652619116146667, 1.18944805219959, 1.6927963067386411, 1.9296843928969347, 0.8667577372850178, 1.3957341191353294, 1.6386217111971437], [-0.44883650701461625, -0.9009311334699093, 0.006551607624680888, -0.031151287825124063, -0.17518461393355453, -0.6986473086575202, -1.6871943987780424, -1.1352908353580398, -0.669812431184789, 0.04696243181135186], [0.509589166741046, 0.1857693357346427, -0.07550905171544396, 0.40371837798105975, 0.2002234493228274, 0.8028492233370474, 0.48629288082779365, 0.6280950508585535, 0.22958288133607635, -0.023509851785120262  …  -0.6163152317061098, -0.29266789451650377, -0.14583684556223742, -0.4492481178106896, -0.03887259744200821, -0.5674806365619091, -0.012016840151132151, 0.2897716967247682, -0.18971397270938126, -0.2222280311361607], [3.3110772418218453, 3.886891015780442, 4.585028345763602, 3.826681898387007, 3.035741278162338, 3.2494618858904034, 2.989106232465927, 3.7133118321634933, 2.871836307215324, 3.744248102212496], [0.37849522314915657, 0.3038684647893873, 0.2969197289574867, 0.3476434750321475, 0.3346892263551741, 0.48005082463379584, 0.26467319279133117, 0.294736952213553, 0.2975538551713775, 0.25231757824913936], Float64[], [0.0, -0.06626064690505433, 0.5352570881253667, 0.20818335593211268, -0.007044876853338413, 0.0, 0.19162663035539299, 0.0034722578078704674, -0.0358442425489261, -0.02106863957469503], Float64[], [1.0021210968899932, -0.04248597908967541, -0.04248597908967541, 0.17550175200038612])))

Code

ex$coef(MCMC)

>> Results for ExtendedRtIrtModeling.GibbsRtIrt.
1) Item Parameters.
┌───────┬─────────┬─────────┬─────────┬─────────┐
│  Item │       a │       b │       λ │     σ²t │
│ Int64 │ Float64 │ Float64 │ Float64 │ Float64 │
├───────┼─────────┼─────────┼─────────┼─────────┤
│     1 │   1.365 │  -0.449 │   3.311 │   0.378 │
│     2 │   1.625 │  -0.901 │   3.887 │   0.304 │
│     3 │   1.893 │   0.007 │   4.585 │   0.297 │
│     4 │   2.365 │  -0.031 │   3.827 │   0.348 │
│     5 │   1.189 │  -0.175 │   3.036 │   0.335 │
│     6 │   1.693 │  -0.699 │   3.249 │   0.480 │
│     7 │   1.930 │  -1.687 │   2.989 │   0.265 │
│     8 │   0.867 │  -1.135 │   3.713 │   0.295 │
│     9 │   1.396 │  -0.670 │   2.872 │   0.298 │
│    10 │   1.639 │   0.047 │   3.744 │   0.252 │
└───────┴─────────┴─────────┴─────────┴─────────┘
2) Covariance of Person Parameters.
┌──────┬────────┬────────┐
│ Coef │      θ │      ζ │
├──────┼────────┼────────┤
│    θ │  1.002 │ -0.042 │
│    ζ │ -0.042 │  0.176 │
└──────┴────────┴────────┘
3) Regression Coefficients.
┌──────┬────────┬────────┐
│ Coef │      θ │      ζ │
├──────┼────────┼────────┤
│   β0 │  0.000 │  0.000 │
│   β1 │ -0.066 │  0.192 │
│   β2 │  0.535 │  0.003 │
│   β3 │  0.208 │ -0.036 │
│   β4 │ -0.007 │ -0.021 │
└──────┴────────┴────────┘
4) Criterion.
┌──────────┬──────────┐
│ Deviance │      DIC │
├──────────┼──────────┤
│ 8960.496 │ 9606.992 │
└──────────┴──────────┘

Code

ex$precis(MCMC)

>> Results for ExtendedRtIrtModeling.GibbsRtIrt.
1) Item Response Model.
┌────────────┬─────────┬─────────┬──────────┬─────────┬─────────┬─────────┬────────┐
│ parameters │    mean │     std │      ess │    rhat │     q05 │     q95 │    Sig │
│     Symbol │ Float64 │ Float64 │  Float64 │ Float64 │ Float64 │ Float64 │ String │
├────────────┼─────────┼─────────┼──────────┼─────────┼─────────┼─────────┼────────┤
│         a1 │   1.365 │   0.206 │ 2342.603 │   1.002 │   1.035 │   1.722 │      * │
│         a2 │   1.625 │   0.280 │ 1002.293 │   0.999 │   1.217 │   2.111 │      * │
│         a3 │   1.893 │   0.285 │ 1781.794 │   1.000 │   1.445 │   2.378 │      * │
│         a4 │   2.365 │   0.409 │  667.978 │   1.004 │   1.789 │   3.120 │      * │
│         a5 │   1.189 │   0.188 │ 2477.290 │   1.000 │   0.891 │   1.499 │      * │
│         a6 │   1.693 │   0.288 │ 1083.316 │   1.003 │   1.274 │   2.226 │      * │
│         a7 │   1.930 │   0.415 │  437.238 │   1.000 │   1.318 │   2.666 │      * │
│         a8 │   0.867 │   0.166 │ 2222.551 │   0.999 │   0.606 │   1.158 │      * │
│         a9 │   1.396 │   0.231 │ 1552.240 │   1.000 │   1.053 │   1.803 │      * │
│        a10 │   1.639 │   0.246 │ 1767.400 │   1.003 │   1.253 │   2.063 │      * │
│         b1 │  -0.449 │   0.126 │ 2041.894 │   1.000 │  -0.656 │  -0.249 │      * │
│         b2 │  -0.901 │   0.133 │ 1252.257 │   1.000 │  -1.129 │  -0.694 │      * │
│         b3 │   0.007 │   0.105 │ 1805.927 │   0.999 │  -0.165 │   0.184 │        │
│         b4 │  -0.031 │   0.098 │ 1509.874 │   1.000 │  -0.192 │   0.131 │        │
│         b5 │  -0.175 │   0.131 │ 2126.633 │   1.000 │  -0.394 │   0.035 │        │
│         b6 │  -0.699 │   0.120 │ 1534.142 │   1.000 │  -0.901 │  -0.510 │      * │
│         b7 │  -1.687 │   0.204 │  572.695 │   1.000 │  -2.031 │  -1.393 │      * │
│         b8 │  -1.135 │   0.234 │ 2535.208 │   0.999 │  -1.546 │  -0.808 │      * │
│         b9 │  -0.670 │   0.131 │ 1621.498 │   1.002 │  -0.892 │  -0.458 │      * │
│        b10 │   0.047 │   0.113 │ 1964.482 │   1.001 │  -0.135 │   0.232 │        │
└────────────┴─────────┴─────────┴──────────┴─────────┴─────────┴─────────┴────────┘
2) Response Time Model.
┌────────────┬─────────┬─────────┬──────────┬─────────┬─────────┬─────────┬────────┐
│ parameters │    mean │     std │      ess │    rhat │     q05 │     q95 │    Sig │
│     Symbol │ Float64 │ Float64 │  Float64 │ Float64 │ Float64 │ Float64 │ String │
├────────────┼─────────┼─────────┼──────────┼─────────┼─────────┼─────────┼────────┤
│         λ1 │   3.311 │   0.043 │ 2245.581 │   1.000 │   3.241 │   3.383 │      * │
│         λ2 │   3.887 │   0.039 │ 2229.885 │   1.001 │   3.821 │   3.950 │      * │
│         λ3 │   4.585 │   0.040 │ 2065.252 │   1.001 │   4.518 │   4.649 │      * │
│         λ4 │   3.827 │   0.042 │ 2276.559 │   1.001 │   3.757 │   3.895 │      * │
│         λ5 │   3.036 │   0.042 │ 2077.418 │   1.002 │   2.966 │   3.106 │      * │
│         λ6 │   3.249 │   0.047 │ 2262.640 │   1.000 │   3.173 │   3.327 │      * │
│         λ7 │   2.989 │   0.038 │ 2005.202 │   1.001 │   2.926 │   3.051 │      * │
│         λ8 │   3.713 │   0.039 │ 2132.332 │   1.000 │   3.648 │   3.777 │      * │
│         λ9 │   2.872 │   0.040 │ 2067.979 │   1.000 │   2.806 │   2.936 │      * │
│        λ10 │   3.744 │   0.037 │ 1937.055 │   1.001 │   3.685 │   3.806 │      * │
│       σ²t1 │   0.378 │   0.033 │ 4312.348 │   1.000 │   0.326 │   0.437 │      * │
│       σ²t2 │   0.304 │   0.027 │ 4453.444 │   1.000 │   0.261 │   0.352 │      * │
│       σ²t3 │   0.297 │   0.027 │ 4489.086 │   1.000 │   0.255 │   0.345 │      * │
│       σ²t4 │   0.348 │   0.031 │ 4547.821 │   1.000 │   0.299 │   0.403 │      * │
│       σ²t5 │   0.335 │   0.030 │ 4006.528 │   1.000 │   0.288 │   0.386 │      * │
│       σ²t6 │   0.480 │   0.042 │ 4358.406 │   1.001 │   0.416 │   0.552 │      * │
│       σ²t7 │   0.265 │   0.024 │ 4278.401 │   1.000 │   0.227 │   0.306 │      * │
│       σ²t8 │   0.295 │   0.027 │ 4373.160 │   1.000 │   0.253 │   0.342 │      * │
│       σ²t9 │   0.298 │   0.026 │ 4630.517 │   1.000 │   0.257 │   0.344 │      * │
│      σ²t10 │   0.252 │   0.023 │ 4613.353 │   1.000 │   0.216 │   0.292 │      * │
└────────────┴─────────┴─────────┴──────────┴─────────┴─────────┴─────────┴────────┘
3) Structural Model.
┌────────────┬─────────┬─────────┬──────────┬─────────┬─────────┬─────────┬────────┐
│ parameters │    mean │     std │      ess │    rhat │     q05 │     q95 │    Sig │
│     Symbol │ Float64 │ Float64 │  Float64 │ Float64 │ Float64 │ Float64 │ String │
├────────────┼─────────┼─────────┼──────────┼─────────┼─────────┼─────────┼────────┤
│     β[0,1] │   0.000 │   0.000 │      NaN │     NaN │   0.000 │   0.000 │      * │
│     β[1,1] │  -0.066 │   0.066 │ 3169.522 │   1.000 │  -0.176 │   0.039 │        │
│     β[2,1] │   0.535 │   0.041 │ 1605.987 │   1.000 │   0.470 │   0.604 │      * │
│     β[3,1] │   0.208 │   0.035 │ 2846.589 │   1.000 │   0.153 │   0.267 │      * │
│     β[4,1] │  -0.007 │   0.031 │ 3443.779 │   1.001 │  -0.058 │   0.043 │        │
│     β[0,2] │   0.000 │   0.000 │      NaN │     NaN │   0.000 │   0.000 │      * │
│     β[1,2] │   0.192 │   0.020 │ 4490.908 │   1.000 │   0.159 │   0.224 │      * │
│     β[2,2] │   0.003 │   0.010 │ 3946.057 │   1.000 │  -0.013 │   0.019 │        │
│     β[3,2] │  -0.036 │   0.010 │ 4445.270 │   1.000 │  -0.052 │  -0.020 │      * │
│     β[4,2] │  -0.021 │   0.010 │ 4444.982 │   0.999 │  -0.037 │  -0.005 │      * │
│     Σ[1,1] │   1.002 │   0.115 │ 2450.285 │   1.000 │   0.827 │   1.206 │      * │
│     Σ[1,2] │  -0.042 │   0.029 │ 4313.151 │   1.000 │  -0.089 │   0.005 │        │
│     Σ[2,1] │  -0.042 │   0.029 │ 4313.151 │   1.000 │  -0.089 │   0.005 │        │
│     Σ[2,2] │   0.176 │   0.017 │ 4028.813 │   1.000 │   0.150 │   0.204 │      * │
└────────────┴─────────┴─────────┴──────────┴─────────┴─────────┴─────────┴────────┘

If you want to use the MCMC class data in R, you can use the juliaGet function to convert Julia’s objects to R’s. But it’ll take a loooooot of time.

Code

time <- Sys.time()
MCMC4R <- juliaGet(MCMC)
Sys.time() - time

Time difference of 2.703941 mins

Code

ls(MCMC4R)

[1] "Cond"     "Data"     "Para"     "Post"     "truePara"

Code

ls(MCMC4R$Post$mean)

 [1] "a"   "b"   "β"   "ζ"   "θ"   "λ"   "ν"   "ρ"   "σ²t" "Σp"  "ω"

Code

MCMC4R$Post$ra[,311,] |> 
  as.data.frame() |>
  pivot_longer(cols = everything(), names_to = "variable", values_to = "value") %>%
  ggplot(aes(x = 1:nrow(.), y = value, color = variable, group = variable)) +
  geom_line() +
  labs(x = "Index", y = "Value", title = "b1 MCMC chains")

Lastly, let’s check out this package.

Code

## See the objects in ex.
ls(ex)

 [1] "coef"                          "drawItemDifficulty"           
 [3] "drawItemDiscrimination"        "drawItemIntensity"            
 [5] "drawItemIntensityCross"        "drawItemIntensityCrossQr"     
 [7] "drawItemTimeResidual"          "drawItemTimeResidualCross"    
 [9] "drawItemTimeResidualCrossQr"   "drawQrWeightsCrossQr"         
[11] "drawQrWeightsLatentQr"         "drawRaPgRandomVariable"       
[13] "drawSubjAbility"               "drawSubjAbilityNull"          
[15] "drawSubjCoefficients"          "drawSubjCorrCross"            
[17] "drawSubjCorrCrossQr"           "drawSubjCovariance"           
[19] "drawSubjCovariance2One"        "drawSubjCovarianceLatent"     
[21] "drawSubjCovarianceLatentQr"    "drawSubjCovarianceNull"       
[23] "drawSubjCovarianceNull2One"    "drawSubjSpeed"                
[25] "drawSubjSpeedCross"            "drawSubjSpeedCrossQr"         
[27] "drawSubjSpeedLatent"           "drawSubjSpeedLatentQr"        
[29] "drawSubjSpeedNull"             "eval"                         
[31] "evaluate"                      "getBias"                      
[33] "getDic"                        "getLogLikelihoodMlIrt"        
[35] "getLogLikelihoodRtIrt"         "getLogLikelihoodRtIrtCross"   
[37] "getLogLikelihoodRtIrtCrossQr"  "getLogLikelihoodRtIrtLatent"  
[39] "getLogLikelihoodRtIrtLatentQr" "getLogLikelihoodRtIrtNull"    
[41] "getPrecisTable"                "getRmse"                      
[43] "getSubjCoefficients"           "getSubjCoefficientsLatent"    
[45] "getSubjCoefficientsLatentQr"   "getSubjCoefficientsMlIrt"     
[47] "GibbsMlIrt"                    "GibbsRtIrt"                   
[49] "GibbsRtIrt2"                   "GibbsRtIrtCross"              
[51] "GibbsRtIrtCross2"              "GibbsRtIrtCrossQr"            
[53] "GibbsRtIrtLatent"              "GibbsRtIrtLatent2"            
[55] "GibbsRtIrtLatentQr"            "GibbsRtIrtNull"               
[57] "include"                       "InputData"                    
[59] "InputData4R"                   "InputPara"                    
[61] "OutputDic"                     "OutputPost"                   
[63] "OutputPostCross"               "OutputPostCrossQr"            
[65] "OutputPostMlIrt"               "OutputPostRtIrtLatent"        
[67] "OutputPostRtIrtLatentQr"       "precis"                       
[69] "sample!"                       "setCond"                      
[71] "setTrueParaRtIrt"              "SimConditions"                
[73] "SimEvaluation"

Citation

BibTeX citation:

@online{tsai2024,
  author = {Tsai, JW},
  title = {Introduction to {`ExtendedRtIrtModeling.jl`} Through
    {`JuliaConnectoR`}},
  date = {2024-11-19},
  langid = {en}
}

For attribution, please cite this work as:

Tsai, J. (2024, November 19). Introduction to `ExtendedRtIrtModeling.jl` through `JuliaConnectoR`.