implement predict, fitted, residual methods for "hts_inla"

[njtierney]

Can we add arguments to predict to also return standard error estimates and friends?

[njtierney]

Issue with trying to get the predictions out:

library(yahtsee)
#> Loading required package: tsibble
#> 
#> Attaching package: 'tsibble'
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, union

The helpfile for the “summary.linear.predictor” in inla says:

A matrix containing the mean and sd (plus, possibly quantiles and cdf) of the linear predictors η in the model

The formula used to fit the model is:

# hts_example_model <- fit_hts(
#   #inputs are  the levels of hierarchy, in order of decreasing size
#   formula = pr ~ avg_lower_age + hts(who_subregion, country),
#   .data = malaria_africa_ts,
#   family = "gaussian",
#   special_index = month_num
# )

The number of rows of the predictors aren’t the same as the number of rows in the data?

dim(hts_example_model$summary.linear.predictor)
#> [1] 3116    7
dim(malaria_africa_ts)
#> [1] 1046   15

exploring further

head(hts_example_model$summary.linear.predictor)
#>                      mean         sd 0.025quant  0.5quant 0.975quant      mode
#> APredictor.0001 0.3252638 0.09400785 0.14029390 0.3253923  0.5094822 0.3256548
#> APredictor.0002 0.2416014 0.05435747 0.13518114 0.2415354  0.3484451 0.2414064
#> APredictor.0003 0.3139412 0.06155918 0.19373684 0.3137367  0.4353352 0.3133427
#> APredictor.0004 0.1825636 0.05737481 0.06998894 0.1825701  0.2950798 0.1825834
#> APredictor.0005 0.1831001 0.05826603 0.06873181 0.1831166  0.2973431 0.1831501
#> APredictor.0006 0.2959515 0.06926421 0.16066124 0.2957178  0.4325799 0.2952749
#>                          kld
#> APredictor.0001 6.594523e-06
#> APredictor.0002 7.115063e-07
#> APredictor.0003 6.288670e-07
#> APredictor.0004 3.922522e-07
#> APredictor.0005 5.845695e-07
#> APredictor.0006 1.300368e-06
tail(hts_example_model$summary.linear.predictor)
#>                       mean         sd 0.025quant    0.5quant 0.975quant
#> Predictor.2065 -0.03899639 0.11579578 -0.2697727 -0.03788110  0.1855605
#> Predictor.2066 -0.03925871 0.11709601 -0.2726995 -0.03810259  0.1877585
#> Predictor.2067 -0.03849500 0.11819788 -0.2741148 -0.03734011  0.1906912
#> Predictor.2068 -0.03781523 0.11924636 -0.2755223 -0.03665615  0.1934664
#> Predictor.2069 -0.03735069 0.12027057 -0.2771224 -0.03617712  0.1959417
#> Predictor.2070  0.25135076 0.05013947  0.1441325  0.25334592  0.3464479
#>                       mode          kld
#> Predictor.2065 -0.03556253 1.833651e-05
#> Predictor.2066 -0.03570182 1.844227e-05
#> Predictor.2067 -0.03494526 1.824962e-05
#> Predictor.2068 -0.03425564 1.807765e-05
#> Predictor.2069 -0.03374920 1.792919e-05
#> Predictor.2070  0.25622487 2.820810e-05
head(rownames(hts_example_model$summary.linear.predictor))
#> [1] "APredictor.0001" "APredictor.0002" "APredictor.0003" "APredictor.0004"
#> [5] "APredictor.0005" "APredictor.0006"
tail(rownames(hts_example_model$summary.linear.predictor))
#> [1] "Predictor.2065" "Predictor.2066" "Predictor.2067" "Predictor.2068"
#> [5] "Predictor.2069" "Predictor.2070"

again, the “summary.fitted.values” are not the same dimensions as the data. Here is the description from the helpfile

A matrix containing the mean and sd (plus, possibly quantiles and cdf) of the fitted values g^{-1}(η) obtained by transforming the linear predictors by the inverse of the link function. This quantity is only computed if marginals.fitted.values is computed. Note that if an observation is NA then the identity link is used. You can manually transform a marginal using inla.marginal.transform() or set the argument link in the control.predictor-list; see ?control.predictor

dim(hts_example_model$summary.fitted.values)
#> [1] 3116    6
dim(malaria_africa_ts)
#> [1] 1046   15

head(hts_example_model$summary.fitted.values)
#>                             mean         sd 0.025quant  0.5quant 0.975quant
#> fitted.APredictor.0001 0.3252638 0.09400786 0.14029390 0.3253923  0.5094822
#> fitted.APredictor.0002 0.2416014 0.05435746 0.13518114 0.2415354  0.3484451
#> fitted.APredictor.0003 0.3139412 0.06155918 0.19373684 0.3137367  0.4353352
#> fitted.APredictor.0004 0.1825636 0.05737480 0.06998894 0.1825701  0.2950798
#> fitted.APredictor.0005 0.1831001 0.05826603 0.06873181 0.1831166  0.2973431
#> fitted.APredictor.0006 0.2959515 0.06926421 0.16066124 0.2957178  0.4325799
#>                             mode
#> fitted.APredictor.0001 0.3256548
#> fitted.APredictor.0002 0.2414064
#> fitted.APredictor.0003 0.3133426
#> fitted.APredictor.0004 0.1825834
#> fitted.APredictor.0005 0.1831501
#> fitted.APredictor.0006 0.2952749
tail(hts_example_model$summary.fitted.values)
#>                              mean         sd 0.025quant    0.5quant 0.975quant
#> fitted.Predictor.2065 -0.03899639 0.11579578 -0.2697727 -0.03788110  0.1855605
#> fitted.Predictor.2066 -0.03925871 0.11709600 -0.2726995 -0.03810259  0.1877585
#> fitted.Predictor.2067 -0.03849500 0.11819789 -0.2741148 -0.03734011  0.1906912
#> fitted.Predictor.2068 -0.03781523 0.11924636 -0.2755223 -0.03665615  0.1934664
#> fitted.Predictor.2069 -0.03735069 0.12027057 -0.2771224 -0.03617712  0.1959417
#> fitted.Predictor.2070  0.25135075 0.05013947  0.1441325  0.25334592  0.3464479
#>                              mode
#> fitted.Predictor.2065 -0.03556253
#> fitted.Predictor.2066 -0.03570181
#> fitted.Predictor.2067 -0.03494526
#> fitted.Predictor.2068 -0.03425564
#> fitted.Predictor.2069 -0.03374920
#> fitted.Predictor.2070  0.25622488
head(rownames(hts_example_model$summary.fitted.values))
#> [1] "fitted.APredictor.0001" "fitted.APredictor.0002" "fitted.APredictor.0003"
#> [4] "fitted.APredictor.0004" "fitted.APredictor.0005" "fitted.APredictor.0006"
tail(rownames(hts_example_model$summary.fitted.values))
#> [1] "fitted.Predictor.2065" "fitted.Predictor.2066" "fitted.Predictor.2067"
#> [4] "fitted.Predictor.2068" "fitted.Predictor.2069" "fitted.Predictor.2070"

^{Created on 2021-06-30 by the reprex package (v2.0.0)}

Session info

``` r sessioninfo::session_info() #> ─ Session info ─────────────────────────────────────────────────────────────── #> setting value #> version R version 4.1.0 (2021-05-18) #> os macOS Big Sur 10.16 #> system x86_64, darwin17.0 #> ui X11 #> language (EN) #> collate en_AU.UTF-8 #> ctype en_AU.UTF-8 #> tz Australia/Perth #> date 2021-06-30 #> #> ─ Packages ─────────────────────────────────────────────────────────────────── #> package * version date lib source #> anytime 0.3.9 2020-08-27 [1] CRAN (R 4.1.0) #> assertthat 0.2.1 2019-03-21 [1] CRAN (R 4.1.0) #> backports 1.2.1 2020-12-09 [1] CRAN (R 4.1.0) #> cli 2.5.0.9000 2021-06-14 [1] Github (r-lib/cli@571fea6) #> crayon 1.4.1 2021-02-08 [1] CRAN (R 4.1.0) #> DBI 1.1.1 2021-01-15 [1] CRAN (R 4.1.0) #> digest 0.6.27 2020-10-24 [1] CRAN (R 4.1.0) #> dplyr 1.0.6 2021-05-05 [1] CRAN (R 4.1.0) #> ellipsis 0.3.2 2021-04-29 [1] CRAN (R 4.1.0) #> evaluate 0.14 2019-05-28 [1] CRAN (R 4.1.0) #> fansi 0.5.0 2021-05-25 [1] CRAN (R 4.1.0) #> fs 1.5.0 2020-07-31 [1] CRAN (R 4.1.0) #> generics 0.1.0 2020-10-31 [1] CRAN (R 4.1.0) #> glue 1.4.2 2020-08-27 [1] CRAN (R 4.1.0) #> highr 0.9 2021-04-16 [1] CRAN (R 4.1.0) #> htmltools 0.5.1.1 2021-01-22 [1] CRAN (R 4.1.0) #> knitr 1.33 2021-04-24 [1] CRAN (R 4.1.0) #> lifecycle 1.0.0 2021-02-15 [1] CRAN (R 4.1.0) #> lubridate 1.7.10 2021-02-26 [1] CRAN (R 4.1.0) #> magrittr 2.0.1 2020-11-17 [1] CRAN (R 4.1.0) #> pillar 1.6.1 2021-05-16 [1] CRAN (R 4.1.0) #> pkgconfig 2.0.3 2019-09-22 [1] CRAN (R 4.1.0) #> purrr 0.3.4 2020-04-17 [1] CRAN (R 4.1.0) #> R6 2.5.0 2020-10-28 [1] CRAN (R 4.1.0) #> Rcpp 1.0.6 2021-01-15 [1] CRAN (R 4.1.0) #> reprex 2.0.0 2021-04-02 [1] CRAN (R 4.1.0) #> rlang 0.4.11 2021-04-30 [1] CRAN (R 4.1.0) #> rmarkdown 2.8 2021-05-07 [1] CRAN (R 4.1.0) #> sessioninfo 1.1.1 2018-11-05 [1] CRAN (R 4.1.0) #> stringi 1.6.2 2021-05-17 [1] CRAN (R 4.1.0) #> stringr 1.4.0 2019-02-10 [1] CRAN (R 4.1.0) #> styler 1.4.1 2021-03-30 [1] CRAN (R 4.1.0) #> tibble 3.1.2 2021-05-16 [1] CRAN (R 4.1.0) #> tidyselect 1.1.1 2021-04-30 [1] CRAN (R 4.1.0) #> tsibble * 1.0.1 2021-04-12 [1] CRAN (R 4.1.0) #> utf8 1.2.1 2021-03-12 [1] CRAN (R 4.1.0) #> vctrs 0.3.8 2021-04-29 [1] CRAN (R 4.1.0) #> withr 2.4.2 2021-04-18 [1] CRAN (R 4.1.0) #> xfun 0.23 2021-05-15 [1] CRAN (R 4.1.0) #> yahtsee * 0.0.0.9000 2021-06-30 [1] local #> yaml 2.2.1 2020-02-01 [1] CRAN (R 4.1.0) #> #> [1] /Library/Frameworks/R.framework/Versions/4.1/Resources/library ```

[njtierney]

See : https://inbo.github.io/tutorials/tutorials/r_inla/inlabru.pdf for details on prediction

[njtierney]

My descent into madness regarding getting predictions out - it appears the missing link is the "formula" argument of "predict".

However, the predictions are terrible!

library(yahtsee)
#> Loading required package: tsibble
#> 
#> Attaching package: 'tsibble'
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, union
library(tidyverse)

malaria_africa_ts_subset <- malaria_africa_ts %>% 
  filter(who_subregion %in% c("AFRO-W", "AFRO-C")) %>% 
  group_by(who_subregion) %>% 
  filter(country %in% c("Angola",
                        "Benin",
                        "Cameroon",
                        "Cape Verde",
                        "Central African Republic",
                        "Gabon",
                        "Gambia",
                        "Guinea-Bissau",
                        "Nigeria",
                        "Togo"))

malaria_africa_ts_subset
#> # A tsibble: 186 x 15 [1D]
#> # Key:       country [46]
#> # Groups:    who_subregion [2]
#>    who_region who_subregion country date       month_num positive examined
#>    <fct>      <fct>         <fct>   <date>         <dbl>    <dbl>    <int>
#>  1 AFRO       AFRO-W        Angola  1989-06-01       120     15.8       50
#>  2 AFRO       AFRO-W        Angola  2005-11-01       372     82        111
#>  3 AFRO       AFRO-W        Angola  2006-04-01       300    102        197
#>  4 AFRO       AFRO-W        Angola  2006-11-01       384     41        347
#>  5 AFRO       AFRO-W        Angola  2006-12-01       396    173        734
#>  6 AFRO       AFRO-W        Angola  2007-01-01       276    216        828
#>  7 AFRO       AFRO-W        Angola  2007-02-01       288     42         71
#>  8 AFRO       AFRO-W        Angola  2007-03-01       300    119        448
#>  9 AFRO       AFRO-W        Angola  2011-01-01       324      1        239
#> 10 AFRO       AFRO-W        Angola  2011-02-01       336    148       1132
#> # … with 176 more rows, and 8 more variables: pr <dbl>, avg_lower_age <dbl>,
#> #   continent_id <fct>, country_id <fct>, year <int>, month <int>,
#> #   avg_upper_age <dbl>, species <fct>

model_yah <- fit_hts(
  #inputs are  the levels of hierarchy, in order of decreasing size
  formula = pr ~ avg_lower_age + hts(who_subregion, country),
  .data = malaria_africa_ts_subset,
  family = "gaussian",
  special_index = month_num
)
#> ℹ Fitting model with inlabru
#> ✓ Fitting model with inlabru ... done
#> 

model_yah
#> <hts_inla> model (fit in 12.15s)
#> Formula:
#> • ~
#> • pr
#> • avg_lower_age + hts(who_subregion, country)
#> 

model_predictions <- predict(object = model_yah)

tibble(model_predictions$Predictor)
#> # A tibble: 506 × 9
#>           mean      sd  q0.025     median q0.975    smin   smax      cv      var
#>          <dbl>   <dbl>   <dbl>      <dbl>  <dbl>   <dbl>  <dbl>   <dbl>    <dbl>
#>  1  0.00270    0.00641 -0.0105  0.00263   0.0153 -0.0144 0.0218    2.37  4.11e-5
#>  2  0.00151    0.0118  -0.0149  0.000890  0.0271 -0.0386 0.0695    7.81  1.39e-4
#>  3 -0.00151    0.0136  -0.0245 -0.00124   0.0224 -0.0693 0.0315   -8.98  1.84e-4
#>  4  0.000653   0.0102  -0.0169  0.0000251 0.0228 -0.0304 0.0297   15.6   1.03e-4
#>  5 -0.000666   0.0122  -0.0254 -0.000188  0.0211 -0.0587 0.0410  -18.4   1.50e-4
#>  6  0.00116    0.0102  -0.0200  0.00129   0.0219 -0.0321 0.0328    8.81  1.04e-4
#>  7  0.00000436 0.0125  -0.0187 -0.000740  0.0305 -0.0376 0.0514 2876.    1.57e-4
#>  8 -0.000355   0.0135  -0.0233  0.000233  0.0216 -0.0816 0.0499  -38.2   1.84e-4
#>  9  0.000158   0.0124  -0.0252  0.000206  0.0229 -0.0566 0.0430   78.7   1.54e-4
#> 10  0.00183    0.00975 -0.0153  0.000566  0.0240 -0.0214 0.0305    5.33  9.51e-5
#> # … with 496 more rows

malaria_africa_ts_subset$pr
#>   [1] 0.31500000 0.73873874 0.51776650 0.11815562 0.23569482 0.26086957
#>   [7] 0.59154930 0.26562500 0.00418410 0.13074205 0.10107198 0.04938272
#>  [13] 0.18803419 0.04152824 0.14010989 0.19752066 0.22789539 0.15978129
#>  [19] 0.22033898 0.19549550 0.27333333 0.85156250 0.05177112 0.14133333
#>  [25] 0.21775899 0.21913580 0.31430446 0.27266963 0.42792793 0.28571429
#>  [31] 0.12759644 0.18623025 0.19940476 0.17826087 0.38565629 0.12719298
#>  [37] 0.06338028 0.33514493 0.40935673 0.54516129 0.81521739 0.92553191
#>  [43] 0.76826722 0.54285714 0.14071511 0.43750000 0.83333333 0.65517241
#>  [49] 0.28000000 0.18439716 0.11728395 0.23529412 0.40000000 0.30188679
#>  [55] 0.63461538 0.61488673 0.55026455 0.05181347 0.26236559 0.52083333
#>  [61] 0.51908397 0.57458564 0.67965368 0.31967213 0.53614458 0.47989950
#>  [67] 0.32532751 0.44531250 0.60680529 0.42635659 0.64885496 0.20000000
#>  [73] 0.16666667 1.00000000 0.02222222 0.08438819 0.21402660 0.21590909
#>  [79] 0.29256360 0.33841132 0.19723866 0.36000000 0.65116279 0.00000000
#>  [85] 0.00000000 0.19590643 0.42976939 0.75862069 0.52525253 0.28279570
#>  [91] 0.28382353 0.14583333 0.32647059 0.10086455 0.37974684 0.55263158
#>  [97] 0.36111111 0.41401274 0.63861386 0.19018405 0.65088757 0.67213115
#> [103] 0.37704918 0.28688525 0.25405405 0.26966292 0.26146789 0.14117647
#> [109] 0.25431034 0.21379310 0.51937984 0.08510638 0.51242236 0.33091787
#> [115] 0.23275862 0.52700000 0.24900000 0.29411765 0.37786260 0.02072539
#> [121] 0.04676259 0.19583333 0.18000000 0.24120603 0.42180095 0.36005314
#> [127] 0.67256637 0.37073171 0.35958904 0.62039660 0.11658456 0.23916811
#> [133] 0.19354839 0.17035775 0.36641221 0.14917127 0.14609053 0.12430939
#> [139] 0.32136752 0.33333333 0.27813505 0.23491379 0.46428571 0.59154930
#> [145] 0.03846154 0.02718447 0.03956835 0.21003717 0.69090909 0.03301887
#> [151] 0.48669426 0.03105590 0.70178282 0.55833333 0.04000000 0.52229299
#> [157] 0.00000000 0.04599212 0.50000000 0.51977401 0.36054422 0.82524272
#> [163] 0.51851852 0.29118774 0.70879121 0.80000000 0.71366594 0.12793177
#> [169] 0.41497976 0.33303167 0.33509700 0.38405797 0.27071823 0.23970944
#> [175] 0.33097595 0.80710660 0.60957179 0.05431310 0.34669556 0.48020833
#> [181] 0.48000000 0.41047297 0.23809524 0.08552632 0.29964695 0.15384615
# it says that there are 506 values - why are there 506 values from predictions
# if there are only 

new_preds <- malaria_africa_ts_subset %>% 
  predict(object = model_yah, formula = ~ avg_lower_age + who_subregion + country)

new_preds
#> # A tsibble: 186 x 24 [1D]
#> # Key:       country [46]
#> # Groups:    who_subregion [2]
#>    who_region who_subregion country date       month_num positive examined
#>    <fct>      <fct>         <fct>   <date>         <dbl>    <dbl>    <int>
#>  1 AFRO       AFRO-W        Angola  1989-06-01       120     15.8       50
#>  2 AFRO       AFRO-W        Angola  2005-11-01       372     82        111
#>  3 AFRO       AFRO-W        Angola  2006-04-01       300    102        197
#>  4 AFRO       AFRO-W        Angola  2006-11-01       384     41        347
#>  5 AFRO       AFRO-W        Angola  2006-12-01       396    173        734
#>  6 AFRO       AFRO-W        Angola  2007-01-01       276    216        828
#>  7 AFRO       AFRO-W        Angola  2007-02-01       288     42         71
#>  8 AFRO       AFRO-W        Angola  2007-03-01       300    119        448
#>  9 AFRO       AFRO-W        Angola  2011-01-01       324      1        239
#> 10 AFRO       AFRO-W        Angola  2011-02-01       336    148       1132
#> # … with 176 more rows, and 17 more variables: pr <dbl>, avg_lower_age <dbl>,
#> #   continent_id <fct>, country_id <fct>, year <int>, month <int>,
#> #   avg_upper_age <dbl>, species <fct>, mean <dbl>, sd <dbl>, q0.025 <dbl>,
#> #   median <dbl>, q0.975 <dbl>, smin <dbl>, smax <dbl>, cv <dbl>, var <dbl>

ggplot(new_preds,
       aes(x = date,
           y = mean,
           group = country)) + 
  geom_line() + 
  geom_point(aes(y = pr)) + 
  facet_wrap(~country)

^{Created on 2022-01-27 by the reprex package (v2.0.1)}

Session info

``` r sessioninfo::session_info() #> ─ Session info ─────────────────────────────────────────────────────────────── #> setting value #> version R version 4.1.2 (2021-11-01) #> os macOS Big Sur 10.16 #> system x86_64, darwin17.0 #> ui X11 #> language (EN) #> collate en_AU.UTF-8 #> ctype en_AU.UTF-8 #> tz Australia/Brisbane #> date 2022-01-27 #> pandoc 2.14.0.3 @ /Applications/RStudio.app/Contents/MacOS/pandoc/ (via rmarkdown) #> #> ─ Packages ─────────────────────────────────────────────────────────────────── #> package * version date (UTC) lib source #> anytime 0.3.9 2020-08-27 [1] CRAN (R 4.1.0) #> assertthat 0.2.1 2019-03-21 [1] CRAN (R 4.1.0) #> backports 1.4.1 2021-12-13 [1] CRAN (R 4.1.0) #> broom 0.7.10 2021-10-31 [1] CRAN (R 4.1.0) #> cellranger 1.1.0 2016-07-27 [1] CRAN (R 4.1.0) #> cli 3.1.0 2021-10-27 [1] CRAN (R 4.1.1) #> colorspace 2.0-2 2021-06-24 [1] CRAN (R 4.1.0) #> crayon 1.4.2 2021-10-29 [1] CRAN (R 4.1.0) #> curl 4.3.2 2021-06-23 [1] CRAN (R 4.1.0) #> DBI 1.1.1 2021-01-15 [1] CRAN (R 4.1.0) #> dbplyr 2.1.1 2021-04-06 [1] CRAN (R 4.1.0) #> digest 0.6.29 2021-12-01 [1] CRAN (R 4.1.0) #> dplyr * 1.0.7 2021-06-18 [1] CRAN (R 4.1.0) #> ellipsis 0.3.2 2021-04-29 [1] CRAN (R 4.1.0) #> evaluate 0.14 2019-05-28 [1] CRAN (R 4.1.0) #> fansi 1.0.2 2022-01-14 [1] CRAN (R 4.1.2) #> farver 2.1.0 2021-02-28 [1] CRAN (R 4.1.0) #> fastmap 1.1.0 2021-01-25 [1] CRAN (R 4.1.0) #> forcats * 0.5.1 2021-01-27 [1] CRAN (R 4.1.0) #> fs 1.5.2 2021-12-08 [1] CRAN (R 4.1.0) #> generics 0.1.1 2021-10-25 [1] CRAN (R 4.1.0) #> ggplot2 * 3.3.5 2021-06-25 [1] CRAN (R 4.1.0) #> glue 1.6.0 2021-12-17 [1] CRAN (R 4.1.0) #> gtable 0.3.0 2019-03-25 [1] CRAN (R 4.1.0) #> haven 2.4.3 2021-08-04 [1] CRAN (R 4.1.0) #> highr 0.9 2021-04-16 [1] CRAN (R 4.1.0) #> hms 1.1.1 2021-09-26 [1] CRAN (R 4.1.0) #> htmltools 0.5.2 2021-08-25 [1] CRAN (R 4.1.0) #> httr 1.4.2 2020-07-20 [1] CRAN (R 4.1.0) #> INLA 21.05.02 2021-05-03 [1] local #> inlabru 2.3.1 2021-03-22 [1] CRAN (R 4.1.0) #> jsonlite 1.7.2 2020-12-09 [1] CRAN (R 4.1.0) #> knitr 1.37 2021-12-16 [1] CRAN (R 4.1.0) #> labeling 0.4.2 2020-10-20 [1] CRAN (R 4.1.0) #> lattice 0.20-45 2021-09-22 [1] CRAN (R 4.1.2) #> lifecycle 1.0.1 2021-09-24 [1] CRAN (R 4.1.0) #> lubridate 1.8.0 2021-10-07 [1] CRAN (R 4.1.0) #> magrittr 2.0.1 2020-11-17 [1] CRAN (R 4.1.0) #> Matrix 1.3-4 2021-06-01 [1] CRAN (R 4.1.2) #> MatrixModels 0.5-0 2021-03-02 [1] CRAN (R 4.1.0) #> mime 0.12 2021-09-28 [1] CRAN (R 4.1.0) #> mnormt 2.0.2 2020-09-01 [1] CRAN (R 4.1.0) #> modelr 0.1.8 2020-05-19 [1] CRAN (R 4.1.0) #> munsell 0.5.0 2018-06-12 [1] CRAN (R 4.1.0) #> numDeriv 2016.8-1.1 2019-06-06 [1] CRAN (R 4.1.0) #> pillar 1.6.4 2021-10-18 [1] CRAN (R 4.1.0) #> pkgconfig 2.0.3 2019-09-22 [1] CRAN (R 4.1.0) #> purrr * 0.3.4 2020-04-17 [1] CRAN (R 4.1.0) #> R.cache 0.15.0 2021-04-30 [1] CRAN (R 4.1.0) #> R.methodsS3 1.8.1 2020-08-26 [1] CRAN (R 4.1.0) #> R.oo 1.24.0 2020-08-26 [1] CRAN (R 4.1.0) #> R.utils 2.11.0 2021-09-26 [1] CRAN (R 4.1.0) #> R6 2.5.1 2021-08-19 [1] CRAN (R 4.1.0) #> Rcpp 1.0.8 2022-01-13 [1] CRAN (R 4.1.2) #> readr * 2.1.1 2021-11-30 [1] CRAN (R 4.1.0) #> readxl 1.3.1 2019-03-13 [1] CRAN (R 4.1.0) #> reprex 2.0.1 2021-08-05 [1] CRAN (R 4.1.0) #> rlang 0.4.12 2021-10-18 [1] CRAN (R 4.1.0) #> rmarkdown 2.11 2021-09-14 [1] CRAN (R 4.1.0) #> rstudioapi 0.13 2020-11-12 [1] CRAN (R 4.1.0) #> rvest 1.0.2 2021-10-16 [1] CRAN (R 4.1.0) #> scales 1.1.1 2020-05-11 [1] CRAN (R 4.1.0) #> sessioninfo 1.2.2 2021-12-06 [1] CRAN (R 4.1.1) #> sn 2.0.1 2021-11-26 [1] CRAN (R 4.1.0) #> sp 1.4-6 2021-11-14 [1] CRAN (R 4.1.0) #> stringi 1.7.6 2021-11-29 [1] CRAN (R 4.1.0) #> stringr * 1.4.0 2019-02-10 [1] CRAN (R 4.1.0) #> styler 1.6.2 2021-09-23 [1] CRAN (R 4.1.0) #> tibble * 3.1.6 2021-11-07 [1] CRAN (R 4.1.0) #> tidyr * 1.1.4 2021-09-27 [1] CRAN (R 4.1.0) #> tidyselect 1.1.1 2021-04-30 [1] CRAN (R 4.1.0) #> tidyverse * 1.3.1 2021-04-15 [1] CRAN (R 4.1.0) #> tmvnsim 1.0-2 2016-12-15 [1] CRAN (R 4.1.0) #> tsibble * 1.1.1 2021-12-03 [1] CRAN (R 4.1.0) #> tzdb 0.2.0 2021-10-27 [1] CRAN (R 4.1.0) #> utf8 1.2.2 2021-07-24 [1] CRAN (R 4.1.0) #> vctrs 0.3.8 2021-04-29 [1] CRAN (R 4.1.0) #> withr 2.4.3 2021-11-30 [1] CRAN (R 4.1.0) #> xfun 0.29 2021-12-14 [1] CRAN (R 4.1.0) #> xml2 1.3.3 2021-11-30 [1] CRAN (R 4.1.0) #> yahtsee * 0.0.0.9000 2022-01-11 [1] local #> yaml 2.2.1 2020-02-01 [1] CRAN (R 4.1.0) #> #> [1] /Library/Frameworks/R.framework/Versions/4.1/Resources/library #> #> ────────────────────────────────────────────────────────────────────────────── ```