Performs the latent trait analysis
latent_trait_analysis.RdThis function performs the latent trait analysis of the datasets/problems after fitting a continuous IRT model. It fits a smoothing spline to the points to compute the latent trait. The autoplot function plots the latent trait and the performance.
latent_trait_analysis(
df,
scale = FALSE,
scale.method = NULL,
max.item = 1,
min.item = 0,
paras,
epsilon = 0.01
)
# S3 method for latenttrait
autoplot(
object,
xlab = "Problem Difficulty",
ylab = "Performance",
plottype = 1,
nrow = 2,
se = TRUE,
ratio = 3,
...
)Arguments
- df
The performance data in a matrix or dataframe with good performances having high values and poor performances having low values.
- scale
If
TRUE, the performance data is scaled to 0-1. The default isFALSE.- scale.method
The method to scale the data. The default is
NULL. If set to"single", it scales the data to 0-1 for the full dataset. If set to"multiple"it scales each column/algorithm separately to 0-1. IfscaleisFALSE, the data is not scaled.- max.item
A vector with the maximum performance value for each algorithm. This can be used to inform the maximum performance value for each algorithm. Only will be used if scale is
FALSE. Default is 1.- min.item
A vector with the minimum performance value for each algorithm. This can be used to inform the minimum performance value for each algorithm. Only will be used if scale is
FALSE. Default is 0.- paras
The parameters from fitting
cirtmodel.- epsilon
A value defining good algorithm performance. If
epsilon = 0, then only the best algorithm is considered. A default- object
For autoplot: the output of the function latent_trait_analysis.
- xlab
For autoplot: the xlabel.
- ylab
For autoplot: the ylabel.
- plottype
For autoplot: plottype = 1 for all algorithm performances in a single plot, plottype = 2 for using facet_wrap to plot individual algorithms, plottype = 3 to plot the smoothing splines and plottype = 4 to plot strengths and weaknesses.
- nrow
For autoplot: If
plottype = 2, the number of rows for facet_wrap.- se
For autoplot: for plotting splines with standard errors.
- ratio
For autoplot: for plotting strengths and weaknesses, ratio between x and y axis.
- ...
Other arguments currently ignored.
Value
A list with the following components:
crmthetaThe problem trait output computed from the R package EstCRM.
strengthsThe strengths of each algorithm and positions on the latent trait that they performs well.
longdfThe dataset in long format of latent trait occupancy.
pltThe ggplot object showing the fitted smoothing splines.
widedfThe dataset in wide format with latent trait.
thetasThe easiness of the problem set instances.
weaknessThe weaknesses of each algorithm and positions on the latent trait that they performs poorly.
Examples
# This is a dummy example.
set.seed(1)
x1 <- runif(200)
x2 <- 2*x1 + rnorm(200, mean=0, sd=0.1)
x3 <- 1 - x1 + rnorm(200, mean=0, sd=0.1)
X <- cbind.data.frame(x1, x2, x3)
max_item <- rep(max(x1, x2, x3),3)
min_item <- rep(min(x1, x2, x3),3)
mod <- cirtmodel(X, max.item=max_item, min.item=min_item)
out <- latent_trait_analysis(X, min.item= min_item, max.item = max_item, paras = mod$model$param)
#> Warning: The `x` argument of `as_tibble.matrix()` must have unique column names if
#> `.name_repair` is omitted as of tibble 2.0.0.
#> ℹ Using compatibility `.name_repair`.
#> ℹ The deprecated feature was likely used in the airt package.
#> Please report the issue to the authors.
#> Joining with `by = join_by(group)`
#> Joining with `by = join_by(group)`
out
#> $crmtheta
#> $thetas
#> ID Theta Est. SE
#> [1,] 1 0.893442463 0.1773573
#> [2,] 2 0.421156502 0.1773573
#> [3,] 3 -0.051170325 0.1773573
#> [4,] 4 -1.423934211 0.1773573
#> [5,] 5 1.170383467 0.1773573
#> [6,] 6 -1.694572222 0.1773573
#> [7,] 7 -1.784671862 0.1773573
#> [8,] 8 -0.500199191 0.1773573
#> [9,] 9 -0.406763813 0.1773573
#> [10,] 10 1.557763507 0.1773573
#> [11,] 11 1.136388138 0.1773573
#> [12,] 12 1.225489686 0.1773573
#> [13,] 13 -0.668895128 0.1773573
#> [14,] 14 0.444731523 0.1773573
#> [15,] 15 -0.781069302 0.1773573
#> [16,] 16 0.113475958 0.1773573
#> [17,] 17 -0.612467032 0.1773573
#> [18,] 18 -1.865433730 0.1773573
#> [19,] 19 0.355044951 0.1773573
#> [20,] 20 -0.790866983 0.1773573
#> [21,] 21 -1.357770576 0.1773573
#> [22,] 22 0.940858588 0.1773573
#> [23,] 23 -0.370803893 0.1773573
#> [24,] 24 1.391865832 0.1773573
#> [25,] 25 0.832253889 0.1773573
#> [26,] 26 0.363772007 0.1773573
#> [27,] 27 2.133308423 0.1773573
#> [28,] 28 0.424511284 0.1773573
#> [29,] 29 -1.147527812 0.1773573
#> [30,] 30 0.597365069 0.1773573
#> [31,] 31 0.091980174 0.1773573
#> [32,] 32 -0.259078309 0.1773573
#> [33,] 33 0.021312188 0.1773573
#> [34,] 34 1.332658000 0.1773573
#> [35,] 35 -1.065805759 0.1773573
#> [36,] 36 -0.321382918 0.1773573
#> [37,] 37 -0.821430087 0.1773573
#> [38,] 38 1.575656818 0.1773573
#> [39,] 39 -0.598774629 0.1773573
#> [40,] 40 0.315798426 0.1773573
#> [41,] 41 -0.764555293 0.1773573
#> [42,] 42 -0.532369752 0.1773573
#> [43,] 43 -0.680838536 0.1773573
#> [44,] 44 -0.084601211 0.1773573
#> [45,] 45 -0.029884570 0.1773573
#> [46,] 46 -0.861728468 0.1773573
#> [47,] 47 1.745021584 0.1773573
#> [48,] 48 0.113634998 0.1773573
#> [49,] 49 -0.533362254 0.1773573
#> [50,] 50 -0.353458691 0.1773573
#> [51,] 51 0.122809016 0.1773573
#> [52,] 52 -1.120352541 0.1773573
#> [53,] 53 0.273770637 0.1773573
#> [54,] 54 0.977545409 0.1773573
#> [55,] 55 2.046180047 0.1773573
#> [56,] 56 1.726309974 0.1773573
#> [57,] 57 0.531714183 0.1773573
#> [58,] 58 0.034838710 0.1773573
#> [59,] 59 -0.408722566 0.1773573
#> [60,] 60 0.197573264 0.1773573
#> [61,] 61 -1.907055997 0.1773573
#> [62,] 62 0.767128789 0.1773573
#> [63,] 63 0.081760323 0.1773573
#> [64,] 64 0.504569733 0.1773573
#> [65,] 65 -0.366323426 0.1773573
#> [66,] 66 0.684427915 0.1773573
#> [67,] 67 0.151915445 0.1773573
#> [68,] 68 -0.636615044 0.1773573
#> [69,] 69 1.643505730 0.1773573
#> [70,] 70 -1.331757460 0.1773573
#> [71,] 71 0.378544702 0.1773573
#> [72,] 72 -1.062680837 0.1773573
#> [73,] 73 0.479565801 0.1773573
#> [74,] 74 0.582503106 0.1773573
#> [75,] 75 0.114672414 0.1773573
#> [76,] 76 -1.288101846 0.1773573
#> [77,] 77 -1.280590309 0.1773573
#> [78,] 78 0.237180930 0.1773573
#> [79,] 79 -0.946020001 0.1773573
#> [80,] 80 -2.214152852 0.1773573
#> [81,] 81 0.361868548 0.1773573
#> [82,] 82 -0.662147690 0.1773573
#> [83,] 83 0.320964644 0.1773573
#> [84,] 84 0.731304880 0.1773573
#> [85,] 85 -0.768656343 0.1773573
#> [86,] 86 1.077666652 0.1773573
#> [87,] 87 -0.833522201 0.1773573
#> [88,] 88 1.540740187 0.1773573
#> [89,] 89 0.886479685 0.1773573
#> [90,] 90 1.421018821 0.1773573
#> [91,] 91 0.962405401 0.1773573
#> [92,] 92 1.742509737 0.1773573
#> [93,] 93 -0.294090922 0.1773573
#> [94,] 94 -1.341668568 0.1773573
#> [95,] 95 -0.721535329 0.1773573
#> [96,] 96 -0.835472487 0.1773573
#> [97,] 97 0.121517989 0.1773573
#> [98,] 98 0.406107741 0.1773573
#> [99,] 99 -1.030070588 0.1773573
#> [100,] 100 -0.214673385 0.1773573
#> [101,] 101 -0.423634001 0.1773573
#> [102,] 102 0.431358669 0.1773573
#> [103,] 103 0.660121625 0.1773573
#> [104,] 104 -1.878240584 0.1773573
#> [105,] 105 -0.196684672 0.1773573
#> [106,] 106 0.801839758 0.1773573
#> [107,] 107 1.311453793 0.1773573
#> [108,] 108 0.069907875 0.1773573
#> [109,] 109 -1.388667471 0.1773573
#> [110,] 110 -0.310394087 0.1773573
#> [111,] 111 -1.792025304 0.1773573
#> [112,] 112 -0.687287789 0.1773573
#> [113,] 113 0.558807159 0.1773573
#> [114,] 114 0.343353110 0.1773573
#> [115,] 115 1.189763801 0.1773573
#> [116,] 116 1.873828421 0.1773573
#> [117,] 117 -0.556458668 0.1773573
#> [118,] 118 1.715419021 0.1773573
#> [119,] 119 0.129560230 0.1773573
#> [120,] 120 -0.324529071 0.1773573
#> [121,] 121 -1.425253662 0.1773573
#> [122,] 122 0.044100128 0.1773573
#> [123,] 123 0.142379331 0.1773573
#> [124,] 124 1.183171246 0.1773573
#> [125,] 125 -0.622838859 0.1773573
#> [126,] 126 0.099567451 0.1773573
#> [127,] 127 -0.007714284 0.1773573
#> [128,] 128 1.194406131 0.1773573
#> [129,] 129 0.926547889 0.1773573
#> [130,] 130 -0.281238837 0.1773573
#> [131,] 131 -0.170849341 0.1773573
#> [132,] 132 2.635251129 0.1773573
#> [133,] 133 2.054770763 0.1773573
#> [134,] 134 -0.431914384 0.1773573
#> [135,] 135 -1.441092685 0.1773573
#> [136,] 136 -0.245851824 0.1773573
#> [137,] 137 -0.152275775 0.1773573
#> [138,] 138 0.057209783 0.1773573
#> [139,] 139 -2.954692320 0.1773573
#> [140,] 140 0.044498115 0.1773573
#> [141,] 141 -0.586425021 0.1773573
#> [142,] 142 -0.290924814 0.1773573
#> [143,] 143 0.899357827 0.1773573
#> [144,] 144 0.944183454 0.1773573
#> [145,] 145 -0.767774559 0.1773573
#> [146,] 146 0.253652733 0.1773573
#> [147,] 147 1.207194419 0.1773573
#> [148,] 148 -0.712478362 0.1773573
#> [149,] 149 1.547039932 0.1773573
#> [150,] 150 -1.524563312 0.1773573
#> [151,] 151 -0.281146306 0.1773573
#> [152,] 152 -0.171140284 0.1773573
#> [153,] 153 0.582172589 0.1773573
#> [154,] 154 0.169286026 0.1773573
#> [155,] 155 -0.043804245 0.1773573
#> [156,] 156 1.049125701 0.1773573
#> [157,] 157 0.149823298 0.1773573
#> [158,] 158 1.561284386 0.1773573
#> [159,] 159 0.719233848 0.1773573
#> [160,] 160 1.075642706 0.1773573
#> [161,] 161 0.661806359 0.1773573
#> [162,] 162 -1.159731225 0.1773573
#> [163,] 163 0.267104209 0.1773573
#> [164,] 164 -0.907852450 0.1773573
#> [165,] 165 -1.591559436 0.1773573
#> [166,] 166 0.306328395 0.1773573
#> [167,] 167 1.814418139 0.1773573
#> [168,] 168 0.682799560 0.1773573
#> [169,] 169 -0.566929662 0.1773573
#> [170,] 170 0.665395657 0.1773573
#> [171,] 171 -0.352673640 0.1773573
#> [172,] 172 -1.212290374 0.1773573
#> [173,] 173 -1.031247493 0.1773573
#> [174,] 174 0.205269990 0.1773573
#> [175,] 175 0.444108666 0.1773573
#> [176,] 176 -1.625261176 0.1773573
#> [177,] 177 -0.204300431 0.1773573
#> [178,] 178 -0.765089635 0.1773573
#> [179,] 179 -0.137173532 0.1773573
#> [180,] 180 -1.534966696 0.1773573
#> [181,] 181 0.676257881 0.1773573
#> [182,] 182 1.125866907 0.1773573
#> [183,] 183 -1.552883692 0.1773573
#> [184,] 184 0.081457790 0.1773573
#> [185,] 185 -1.052421381 0.1773573
#> [186,] 186 1.281062849 0.1773573
#> [187,] 187 -0.703071143 0.1773573
#> [188,] 188 -0.776129820 0.1773573
#> [189,] 189 -1.952868768 0.1773573
#> [190,] 190 -0.155632840 0.1773573
#> [191,] 191 -0.611528187 0.1773573
#> [192,] 192 0.422187587 0.1773573
#> [193,] 193 1.490779068 0.1773573
#> [194,] 194 -1.239508707 0.1773573
#> [195,] 195 0.700976883 0.1773573
#> [196,] 196 -0.269565582 0.1773573
#> [197,] 197 1.407917474 0.1773573
#> [198,] 198 -1.256903609 0.1773573
#> [199,] 199 0.644322309 0.1773573
#> [200,] 200 -0.853229017 0.1773573
#>
#> attr(,"class")
#> [1] "CRMtheta"
#>
#> $strengths
#> $strengths$proportions
#> # A tibble: 2 × 4
#> group Proportion algorithm colour
#> <dbl> <dbl> <chr> <chr>
#> 1 2 0.725 x2 #00BA38
#> 2 3 0.295 x3 #619CFF
#>
#> $strengths$latent
#> # A tibble: 80 × 1
#> x
#> <dbl>
#> 1 -2.95
#> 2 -2.88
#> 3 -2.81
#> 4 -2.74
#> 5 -2.67
#> 6 -2.60
#> 7 -2.53
#> 8 -2.46
#> 9 -2.39
#> 10 -2.32
#> # ℹ 70 more rows
#>
#> $strengths$multilatent
#> latenttrait x1 x2 x3
#> 1 -2.95469232 0 2 0
#> 2 -2.88393354 0 2 0
#> 3 -2.81317476 0 2 0
#> 4 -2.74241599 0 2 0
#> 5 -2.67165721 0 2 0
#> 6 -2.60089843 0 2 0
#> 7 -2.53013965 0 2 0
#> 8 -2.45938087 0 2 0
#> 9 -2.38862210 0 2 0
#> 10 -2.31786332 0 2 0
#> 11 -2.24710454 0 2 0
#> 12 -2.17634576 0 2 0
#> 13 -2.10558699 0 2 0
#> 14 -2.03482821 0 2 0
#> 15 -1.96406943 0 2 0
#> 16 -1.89331065 0 2 0
#> 17 -1.82255187 0 2 0
#> 18 -1.75179310 0 2 0
#> 19 -1.68103432 0 2 0
#> 20 -1.61027554 0 2 0
#> 21 -1.53951676 0 2 0
#> 22 -1.46875799 0 2 0
#> 23 -1.39799921 0 2 0
#> 24 -1.32724043 0 2 0
#> 25 -1.25648165 0 2 0
#> 26 -1.18572287 0 2 0
#> 27 -1.11496410 0 2 0
#> 28 -1.04420532 0 2 0
#> 29 -0.97344654 0 2 0
#> 30 -0.90268776 0 2 0
#> 31 -0.83192898 0 2 0
#> 32 -0.76117021 0 2 0
#> 33 -0.69041143 0 2 0
#> 34 -0.61965265 0 2 0
#> 35 -0.54889387 0 2 0
#> 36 -0.47813510 0 2 0
#> 37 -0.40737632 0 2 0
#> 38 -0.33661754 0 2 0
#> 39 -0.26585876 0 2 0
#> 40 -0.19509998 0 2 0
#> 41 -0.12434121 0 2 0
#> 42 -0.05358243 0 2 0
#> 43 0.01717635 0 2 0
#> 44 0.08793513 0 2 0
#> 45 0.15869390 0 2 0
#> 46 0.22945268 0 2 0
#> 47 0.30021146 0 2 0
#> 48 0.37097024 0 2 0
#> 49 0.44172902 0 2 0
#> 50 0.51248779 0 2 0
#> 51 0.58324657 0 2 3
#> 52 0.65400535 0 0 3
#> 53 0.72476413 0 0 3
#> 54 0.79552291 0 0 3
#> 55 0.86628168 0 0 3
#> 56 0.93704046 0 0 3
#> 57 1.00779924 0 0 3
#> 58 1.07855802 0 0 3
#> 59 1.14931679 0 0 3
#> 60 1.22007557 0 0 3
#> 61 1.29083435 0 0 3
#> 62 1.36159313 0 0 3
#> 63 1.43235191 0 0 3
#> 64 1.50311068 0 0 3
#> 65 1.57386946 0 0 3
#> 66 1.64462824 0 0 3
#> 67 1.71538702 0 0 3
#> 68 1.78614580 0 0 3
#> 69 1.85690457 0 0 3
#> 70 1.92766335 0 0 3
#> 71 1.99842213 0 0 3
#> 72 2.06918091 0 0 3
#> 73 2.13993968 0 0 3
#> 74 2.21069846 0 0 3
#> 75 2.28145724 0 0 3
#> 76 2.35221602 0 0 3
#> 77 2.42297480 0 0 3
#> 78 2.49373357 0 0 3
#> 79 2.56449235 0 0 3
#> 80 2.63525113 0 0 3
#>
#>
#> $longdf
#> # A tibble: 600 × 4
#> Latent_Trait_Order Latent_Trait Algorithm value
#> <int> <dbl> <chr> <dbl>
#> 1 1 -2.95 x1 0.985
#> 2 1 -2.95 x2 2.08
#> 3 1 -2.95 x3 -0.0499
#> 4 2 -2.21 x1 0.961
#> 5 2 -2.21 x2 2.04
#> 6 2 -2.21 x3 0.216
#> 7 3 -1.95 x1 0.944
#> 8 3 -1.95 x2 1.93
#> 9 3 -1.95 x3 -0.141
#> 10 4 -1.91 x1 0.913
#> # ℹ 590 more rows
#>
#> $plt
#>
#> $widedf
#> Latent_Trait x1 x2 x3
#> 139 -2.954692320 0.98509522 2.079868152 -0.049861269
#> 80 -2.214152852 0.96061800 2.042026834 0.215737203
#> 189 -1.952868768 0.94372482 1.930819852 -0.141018312
#> 61 -1.907055997 0.91287592 1.868261886 -0.172108691
#> 104 -1.878240584 0.99268406 1.952277342 -0.031770843
#> 18 -1.865433730 0.99190609 1.955900859 -0.004007106
#> 111 -1.792025304 0.97617069 1.935903807 -0.014987446
#> 7 -1.784671862 0.94467527 1.961021285 0.063621305
#> 6 -1.694572222 0.89838968 1.973508097 0.252831584
#> 176 -1.625261176 0.89544543 1.903911579 -0.027306374
#> 165 -1.591559436 0.88061903 1.933200800 0.119869410
#> 183 -1.552883692 0.88645094 1.905327750 0.061807008
#> 180 -1.534966696 0.90308161 1.898143591 0.094127391
#> 150 -1.524563312 0.86454495 1.831136289 -0.098817261
#> 135 -1.441092685 0.92861520 1.851258072 0.130683272
#> 121 -1.425253662 0.99183862 1.810355399 0.151668337
#> 4 -1.423934211 0.90820779 1.832218457 0.053428999
#> 109 -1.388667471 0.92407447 1.846808987 0.220107571
#> 21 -1.357770576 0.93470523 1.818814716 0.196084921
#> 94 -1.341668568 0.87626921 1.835575742 0.154391273
#> 70 -1.331757460 0.87532133 1.771396494 -0.011650456
#> 76 -1.288101846 0.89219834 1.780924069 0.106970763
#> 77 -1.280590309 0.86433947 1.807442902 0.148546070
#> 198 -1.256903609 0.84050703 1.776527732 0.048803521
#> 194 -1.239508707 0.92730209 1.711978443 0.083808554
#> 172 -1.212290374 0.84061455 1.720667025 -0.002502239
#> 162 -1.159731225 0.89509410 1.751264488 0.321442747
#> 29 -1.147527812 0.86969085 1.671215644 0.043905559
#> 52 -1.120352541 0.86120948 1.720562970 0.206517372
#> 35 -1.065805759 0.82737332 1.685402423 0.139198545
#> 72 -1.062680837 0.83944035 1.689460937 0.188351063
#> 185 -1.052421381 0.87705754 1.696053656 0.357997890
#> 173 -1.031247493 0.85613166 1.627077620 0.132902765
#> 99 -1.030070588 0.81087024 1.662937957 0.117616917
#> 79 -0.946020001 0.77732070 1.657380642 0.206288205
#> 164 -0.907852450 0.77998489 1.645710757 0.279564914
#> 46 -0.861728468 0.78935623 1.503630563 0.069758723
#> 200 -0.853229017 0.78285134 1.535121132 0.129822210
#> 96 -0.835472487 0.79730883 1.489819210 0.110259897
#> 87 -0.833522201 0.71112122 1.568701176 0.075942713
#> 37 -0.821430087 0.79423986 1.558382109 0.300418703
#> 20 -0.790866983 0.77744522 1.537157394 0.271986062
#> 15 -0.781069302 0.76984142 1.518944766 0.226566338
#> 188 -0.776129820 0.72449889 1.543516281 0.171134363
#> 85 -0.768656343 0.75708715 1.566276570 0.358395371
#> 145 -0.767774559 0.72930962 1.574915702 0.291206667
#> 178 -0.765089635 0.74107865 1.556257413 0.282271335
#> 41 -0.764555293 0.82094629 1.450456646 0.253012628
#> 95 -0.721535329 0.77891468 1.437021076 0.210069446
#> 148 -0.712478362 0.74669827 1.467829468 0.210891504
#> 187 -0.703071143 0.75810305 1.449388244 0.225226620
#> 112 -0.687287789 0.73179251 1.505654488 0.333461133
#> 43 -0.680838536 0.78293276 1.399368281 0.241688322
#> 13 -0.668895128 0.68702285 1.517273917 0.267563462
#> 82 -0.662147690 0.71251468 1.523418914 0.398628429
#> 68 -0.636615044 0.76631067 1.390171876 0.290484527
#> 125 -0.622838859 0.75482094 1.393984653 0.302151353
#> 17 -0.612467032 0.71761851 1.403237730 0.233983999
#> 191 -0.611528187 0.71174387 1.384475869 0.179198774
#> 39 -0.598774629 0.72371095 1.382212414 0.241056823
#> 141 -0.586425021 0.68278808 1.436307224 0.273828647
#> 169 -0.566929662 0.72372595 1.414348595 0.424295449
#> 117 -0.556458668 0.71556607 1.400258075 0.386209357
#> 49 -0.533362254 0.73231374 1.335997424 0.348014583
#> 42 -0.532369752 0.64706019 1.411778719 0.246594065
#> 8 -0.500199191 0.66079779 1.412613008 0.395924299
#> 134 -0.431914384 0.64279549 1.342641748 0.354704744
#> 101 -0.423634001 0.65472393 1.350388040 0.452720168
#> 59 -0.408722566 0.66200508 1.185567468 0.146103942
#> 9 -0.406763813 0.62911404 1.296646624 0.268431108
#> 23 -0.370803893 0.65167377 1.281889591 0.429796507
#> 65 -0.366323426 0.65087047 1.239816629 0.332197700
#> 50 -0.353458691 0.69273156 1.221402560 0.496015890
#> 171 -0.352673640 0.63041412 1.234934987 0.288261452
#> 120 -0.324529071 0.64010105 1.275731177 0.530811058
#> 36 -0.321382918 0.66846674 1.183288494 0.404808266
#> 110 -0.310394087 0.59876097 1.248532777 0.331485204
#> 93 -0.294090922 0.64228826 1.211401700 0.466878637
#> 142 -0.290924814 0.60154122 1.306493209 0.575719901
#> 130 -0.281238837 0.59571200 1.217741557 0.336174864
#> 151 -0.281146306 0.61464497 1.242912133 0.481524692
#> 196 -0.269565582 0.59057316 1.194591084 0.298535841
#> 32 -0.259078309 0.59956583 1.140242202 0.243525956
#> 136 -0.245851824 0.59809242 1.186366970 0.382088035
#> 100 -0.214673385 0.60493329 1.171758975 0.481589020
#> 177 -0.204300431 0.64431576 1.059719128 0.392122696
#> 105 -0.196684672 0.63349326 1.038462975 0.324884532
#> 152 -0.171140284 0.55715954 1.155035838 0.382397888
#> 131 -0.170849341 0.57487220 1.051161727 0.221799242
#> 190 -0.155632840 0.54764659 1.195809096 0.503820576
#> 137 -0.152275775 0.56090075 1.177883569 0.528300091
#> 179 -0.137173532 0.60530345 1.078982377 0.514092080
#> 44 -0.084601211 0.55303631 1.059719583 0.418013752
#> 3 -0.051170325 0.57285336 1.054614562 0.624280375
#> 155 -0.043804245 0.50044097 1.070437026 0.354169654
#> 45 -0.029884570 0.52971958 0.947847150 0.243791484
#> 127 -0.007714284 0.51116978 0.989226364 0.325102152
#> 33 0.021312188 0.49354131 1.040232233 0.469713617
#> 58 0.034838710 0.51863426 0.975141857 0.465801483
#> 122 0.044100128 0.49559358 0.991400342 0.433369308
#> 140 0.044498115 0.50764182 1.014749242 0.556994119
#> 138 0.057209783 0.52602772 0.933409584 0.471400769
#> 108 0.069907875 0.47811803 1.010368802 0.492314220
#> 184 0.081457790 0.50333949 0.936555805 0.460448137
#> 63 0.081760323 0.45906573 1.023979757 0.477379974
#> 31 0.091980174 0.48208012 0.970176275 0.485209783
#> 126 0.099567451 0.45389549 1.088105169 0.707339191
#> 16 0.113475958 0.49769924 0.956117691 0.609216904
#> 48 0.113634998 0.47723007 0.956199692 0.503642040
#> 75 0.114672414 0.47635125 0.919302406 0.406882522
#> 97 0.121517989 0.45527445 1.054664678 0.704016922
#> 51 0.122809016 0.47761962 1.000257954 0.669768496
#> 119 0.129560230 0.44628435 0.956792828 0.410716307
#> 123 0.142379331 0.48434952 0.905669015 0.509143718
#> 157 0.149823298 0.52963060 0.818951584 0.521306338
#> 67 0.151915445 0.47854525 0.931587794 0.589288769
#> 154 0.169286026 0.45313145 0.881496457 0.391307395
#> 60 0.197573264 0.40683019 1.000589437 0.573643928
#> 174 0.205269990 0.39135928 1.047635250 0.652729656
#> 78 0.237180930 0.38998954 0.987503588 0.595422894
#> 146 0.253652733 0.45257083 0.705125168 0.246624309
#> 163 0.267104209 0.44623532 0.864037580 0.678339344
#> 53 0.273770637 0.43809711 0.844387377 0.599899161
#> 166 0.306328395 0.41312421 0.853253909 0.614811869
#> 40 0.315798426 0.41127443 0.816859182 0.535756019
#> 83 0.320964644 0.39999437 0.821981218 0.507684936
#> 114 0.343353110 0.43147369 0.725926593 0.491315229
#> 19 0.355044951 0.38003518 0.809489192 0.490550820
#> 81 0.361868548 0.43465948 0.746186627 0.641599166
#> 26 0.363772007 0.38611409 0.843494816 0.659499468
#> 71 0.378544702 0.33907294 0.908943716 0.622054838
#> 98 0.406107741 0.41008408 0.718583418 0.594416978
#> 2 0.421156502 0.37212390 0.748459387 0.523146285
#> 192 0.422187587 0.38890510 0.815447229 0.839560833
#> 28 0.424511284 0.38238796 0.761012497 0.634660990
#> 102 0.431358669 0.35319727 0.875281872 0.836368205
#> 175 0.444108666 0.38049389 0.776588939 0.754605512
#> 14 0.444731523 0.38410372 0.703137801 0.550318097
#> 73 0.479565801 0.34668349 0.739066859 0.571008399
#> 64 0.504569733 0.33239467 0.753431614 0.624607442
#> 57 0.531714183 0.31627171 0.732546295 0.566370599
#> 113 0.558807159 0.35672691 0.673429150 0.755750333
#> 153 0.582172589 0.32877732 0.650589157 0.595934953
#> 74 0.582503106 0.33377493 0.659834568 0.659340976
#> 30 0.597365069 0.34034900 0.648270966 0.727574081
#> 199 0.644322309 0.31796368 0.630870799 0.716801680
#> 103 0.660121625 0.27026015 0.699179135 0.669440124
#> 161 0.661806359 0.28479048 0.664682243 0.669905811
#> 170 0.665395657 0.33761533 0.581247734 0.770727658
#> 181 0.676257881 0.29373016 0.627273326 0.670539959
#> 168 0.682799560 0.33548749 0.552063654 0.727314224
#> 66 0.684427915 0.25801678 0.736643808 0.803205037
#> 195 0.700976883 0.28323250 0.744307929 1.097795168
#> 159 0.719233848 0.27775593 0.592984306 0.621807869
#> 84 0.731304880 0.32535215 0.503979301 0.691082032
#> 62 0.767128789 0.29360337 0.563342035 0.837796844
#> 106 0.801839758 0.21320814 0.676182429 0.749226123
#> 25 0.832253889 0.26722067 0.524422263 0.780982282
#> 89 0.886479685 0.24548851 0.447955853 0.564015941
#> 1 0.893442463 0.26550866 0.468980659 0.823858707
#> 143 0.899357827 0.23886868 0.500085397 0.759305351
#> 129 0.926547889 0.22865814 0.477035629 0.707224164
#> 22 0.940858588 0.21214252 0.558588925 0.937561580
#> 144 0.944183454 0.25816593 0.428461092 0.827115573
#> 91 0.962405401 0.23962942 0.461548434 0.892771017
#> 54 0.977545409 0.24479728 0.396658339 0.735922880
#> 156 1.049125701 0.18086636 0.476355558 0.824766822
#> 160 1.075642706 0.21269952 0.382872266 0.840877653
#> 86 1.077666652 0.20269226 0.389509050 0.791655602
#> 182 1.125866907 0.19126011 0.341767362 0.694058476
#> 11 1.136388138 0.20597457 0.348375504 0.898386671
#> 5 1.170383467 0.20168193 0.337905398 0.963732599
#> 124 1.183171246 0.17344233 0.312787812 0.650610792
#> 115 1.189763801 0.14821156 0.395206948 0.800979818
#> 128 1.194406131 0.20754511 0.254538885 0.714498035
#> 147 1.207194419 0.17512677 0.295774463 0.688262038
#> 12 1.225489686 0.17655675 0.306949032 0.833351096
#> 186 1.281062849 0.18919362 0.278280027 1.055459515
#> 107 1.311453793 0.12937235 0.325451313 0.833964557
#> 34 1.332658000 0.18621760 0.220595795 0.950225891
#> 24 1.391865832 0.12555510 0.233154539 0.687466025
#> 197 1.407917474 0.11036060 0.297281110 0.920396057
#> 90 1.421018821 0.14330438 0.193997809 0.775578605
#> 193 1.490779068 0.10087313 0.226162745 0.810565117
#> 88 1.540740187 0.12169192 0.166775642 0.912792655
#> 149 1.547039932 0.10498764 0.193363177 0.918692726
#> 10 1.557763507 0.06178627 0.291790149 0.970514380
#> 158 1.561284386 0.07527575 0.207825447 0.714935958
#> 38 1.575656818 0.10794363 0.163059261 0.892496245
#> 69 1.643505730 0.08424691 0.154053869 0.858498825
#> 118 1.715419021 0.10318424 0.081039496 0.871699305
#> 56 1.726309974 0.09946616 0.091413091 0.960157251
#> 92 1.742509737 0.05893438 0.158069932 1.002629308
#> 47 1.745021584 0.02333120 0.255379059 1.068270731
#> 167 1.814418139 0.06380848 0.085398560 0.865600907
#> 116 1.873828421 0.01307758 0.178129654 1.039284484
#> 55 2.046180047 0.07067905 -0.007387937 1.087110132
#> 133 2.054770763 0.03554058 0.007032989 0.811279606
#> 27 2.133308423 0.01339033 0.019424226 0.951269638
#> 132 2.635251129 0.07706438 -0.134763307 0.973031976
#>
#> $thetas
#> ID Theta Est. SE
#> [1,] 1 0.893442463 0.1773573
#> [2,] 2 0.421156502 0.1773573
#> [3,] 3 -0.051170325 0.1773573
#> [4,] 4 -1.423934211 0.1773573
#> [5,] 5 1.170383467 0.1773573
#> [6,] 6 -1.694572222 0.1773573
#> [7,] 7 -1.784671862 0.1773573
#> [8,] 8 -0.500199191 0.1773573
#> [9,] 9 -0.406763813 0.1773573
#> [10,] 10 1.557763507 0.1773573
#> [11,] 11 1.136388138 0.1773573
#> [12,] 12 1.225489686 0.1773573
#> [13,] 13 -0.668895128 0.1773573
#> [14,] 14 0.444731523 0.1773573
#> [15,] 15 -0.781069302 0.1773573
#> [16,] 16 0.113475958 0.1773573
#> [17,] 17 -0.612467032 0.1773573
#> [18,] 18 -1.865433730 0.1773573
#> [19,] 19 0.355044951 0.1773573
#> [20,] 20 -0.790866983 0.1773573
#> [21,] 21 -1.357770576 0.1773573
#> [22,] 22 0.940858588 0.1773573
#> [23,] 23 -0.370803893 0.1773573
#> [24,] 24 1.391865832 0.1773573
#> [25,] 25 0.832253889 0.1773573
#> [26,] 26 0.363772007 0.1773573
#> [27,] 27 2.133308423 0.1773573
#> [28,] 28 0.424511284 0.1773573
#> [29,] 29 -1.147527812 0.1773573
#> [30,] 30 0.597365069 0.1773573
#> [31,] 31 0.091980174 0.1773573
#> [32,] 32 -0.259078309 0.1773573
#> [33,] 33 0.021312188 0.1773573
#> [34,] 34 1.332658000 0.1773573
#> [35,] 35 -1.065805759 0.1773573
#> [36,] 36 -0.321382918 0.1773573
#> [37,] 37 -0.821430087 0.1773573
#> [38,] 38 1.575656818 0.1773573
#> [39,] 39 -0.598774629 0.1773573
#> [40,] 40 0.315798426 0.1773573
#> [41,] 41 -0.764555293 0.1773573
#> [42,] 42 -0.532369752 0.1773573
#> [43,] 43 -0.680838536 0.1773573
#> [44,] 44 -0.084601211 0.1773573
#> [45,] 45 -0.029884570 0.1773573
#> [46,] 46 -0.861728468 0.1773573
#> [47,] 47 1.745021584 0.1773573
#> [48,] 48 0.113634998 0.1773573
#> [49,] 49 -0.533362254 0.1773573
#> [50,] 50 -0.353458691 0.1773573
#> [51,] 51 0.122809016 0.1773573
#> [52,] 52 -1.120352541 0.1773573
#> [53,] 53 0.273770637 0.1773573
#> [54,] 54 0.977545409 0.1773573
#> [55,] 55 2.046180047 0.1773573
#> [56,] 56 1.726309974 0.1773573
#> [57,] 57 0.531714183 0.1773573
#> [58,] 58 0.034838710 0.1773573
#> [59,] 59 -0.408722566 0.1773573
#> [60,] 60 0.197573264 0.1773573
#> [61,] 61 -1.907055997 0.1773573
#> [62,] 62 0.767128789 0.1773573
#> [63,] 63 0.081760323 0.1773573
#> [64,] 64 0.504569733 0.1773573
#> [65,] 65 -0.366323426 0.1773573
#> [66,] 66 0.684427915 0.1773573
#> [67,] 67 0.151915445 0.1773573
#> [68,] 68 -0.636615044 0.1773573
#> [69,] 69 1.643505730 0.1773573
#> [70,] 70 -1.331757460 0.1773573
#> [71,] 71 0.378544702 0.1773573
#> [72,] 72 -1.062680837 0.1773573
#> [73,] 73 0.479565801 0.1773573
#> [74,] 74 0.582503106 0.1773573
#> [75,] 75 0.114672414 0.1773573
#> [76,] 76 -1.288101846 0.1773573
#> [77,] 77 -1.280590309 0.1773573
#> [78,] 78 0.237180930 0.1773573
#> [79,] 79 -0.946020001 0.1773573
#> [80,] 80 -2.214152852 0.1773573
#> [81,] 81 0.361868548 0.1773573
#> [82,] 82 -0.662147690 0.1773573
#> [83,] 83 0.320964644 0.1773573
#> [84,] 84 0.731304880 0.1773573
#> [85,] 85 -0.768656343 0.1773573
#> [86,] 86 1.077666652 0.1773573
#> [87,] 87 -0.833522201 0.1773573
#> [88,] 88 1.540740187 0.1773573
#> [89,] 89 0.886479685 0.1773573
#> [90,] 90 1.421018821 0.1773573
#> [91,] 91 0.962405401 0.1773573
#> [92,] 92 1.742509737 0.1773573
#> [93,] 93 -0.294090922 0.1773573
#> [94,] 94 -1.341668568 0.1773573
#> [95,] 95 -0.721535329 0.1773573
#> [96,] 96 -0.835472487 0.1773573
#> [97,] 97 0.121517989 0.1773573
#> [98,] 98 0.406107741 0.1773573
#> [99,] 99 -1.030070588 0.1773573
#> [100,] 100 -0.214673385 0.1773573
#> [101,] 101 -0.423634001 0.1773573
#> [102,] 102 0.431358669 0.1773573
#> [103,] 103 0.660121625 0.1773573
#> [104,] 104 -1.878240584 0.1773573
#> [105,] 105 -0.196684672 0.1773573
#> [106,] 106 0.801839758 0.1773573
#> [107,] 107 1.311453793 0.1773573
#> [108,] 108 0.069907875 0.1773573
#> [109,] 109 -1.388667471 0.1773573
#> [110,] 110 -0.310394087 0.1773573
#> [111,] 111 -1.792025304 0.1773573
#> [112,] 112 -0.687287789 0.1773573
#> [113,] 113 0.558807159 0.1773573
#> [114,] 114 0.343353110 0.1773573
#> [115,] 115 1.189763801 0.1773573
#> [116,] 116 1.873828421 0.1773573
#> [117,] 117 -0.556458668 0.1773573
#> [118,] 118 1.715419021 0.1773573
#> [119,] 119 0.129560230 0.1773573
#> [120,] 120 -0.324529071 0.1773573
#> [121,] 121 -1.425253662 0.1773573
#> [122,] 122 0.044100128 0.1773573
#> [123,] 123 0.142379331 0.1773573
#> [124,] 124 1.183171246 0.1773573
#> [125,] 125 -0.622838859 0.1773573
#> [126,] 126 0.099567451 0.1773573
#> [127,] 127 -0.007714284 0.1773573
#> [128,] 128 1.194406131 0.1773573
#> [129,] 129 0.926547889 0.1773573
#> [130,] 130 -0.281238837 0.1773573
#> [131,] 131 -0.170849341 0.1773573
#> [132,] 132 2.635251129 0.1773573
#> [133,] 133 2.054770763 0.1773573
#> [134,] 134 -0.431914384 0.1773573
#> [135,] 135 -1.441092685 0.1773573
#> [136,] 136 -0.245851824 0.1773573
#> [137,] 137 -0.152275775 0.1773573
#> [138,] 138 0.057209783 0.1773573
#> [139,] 139 -2.954692320 0.1773573
#> [140,] 140 0.044498115 0.1773573
#> [141,] 141 -0.586425021 0.1773573
#> [142,] 142 -0.290924814 0.1773573
#> [143,] 143 0.899357827 0.1773573
#> [144,] 144 0.944183454 0.1773573
#> [145,] 145 -0.767774559 0.1773573
#> [146,] 146 0.253652733 0.1773573
#> [147,] 147 1.207194419 0.1773573
#> [148,] 148 -0.712478362 0.1773573
#> [149,] 149 1.547039932 0.1773573
#> [150,] 150 -1.524563312 0.1773573
#> [151,] 151 -0.281146306 0.1773573
#> [152,] 152 -0.171140284 0.1773573
#> [153,] 153 0.582172589 0.1773573
#> [154,] 154 0.169286026 0.1773573
#> [155,] 155 -0.043804245 0.1773573
#> [156,] 156 1.049125701 0.1773573
#> [157,] 157 0.149823298 0.1773573
#> [158,] 158 1.561284386 0.1773573
#> [159,] 159 0.719233848 0.1773573
#> [160,] 160 1.075642706 0.1773573
#> [161,] 161 0.661806359 0.1773573
#> [162,] 162 -1.159731225 0.1773573
#> [163,] 163 0.267104209 0.1773573
#> [164,] 164 -0.907852450 0.1773573
#> [165,] 165 -1.591559436 0.1773573
#> [166,] 166 0.306328395 0.1773573
#> [167,] 167 1.814418139 0.1773573
#> [168,] 168 0.682799560 0.1773573
#> [169,] 169 -0.566929662 0.1773573
#> [170,] 170 0.665395657 0.1773573
#> [171,] 171 -0.352673640 0.1773573
#> [172,] 172 -1.212290374 0.1773573
#> [173,] 173 -1.031247493 0.1773573
#> [174,] 174 0.205269990 0.1773573
#> [175,] 175 0.444108666 0.1773573
#> [176,] 176 -1.625261176 0.1773573
#> [177,] 177 -0.204300431 0.1773573
#> [178,] 178 -0.765089635 0.1773573
#> [179,] 179 -0.137173532 0.1773573
#> [180,] 180 -1.534966696 0.1773573
#> [181,] 181 0.676257881 0.1773573
#> [182,] 182 1.125866907 0.1773573
#> [183,] 183 -1.552883692 0.1773573
#> [184,] 184 0.081457790 0.1773573
#> [185,] 185 -1.052421381 0.1773573
#> [186,] 186 1.281062849 0.1773573
#> [187,] 187 -0.703071143 0.1773573
#> [188,] 188 -0.776129820 0.1773573
#> [189,] 189 -1.952868768 0.1773573
#> [190,] 190 -0.155632840 0.1773573
#> [191,] 191 -0.611528187 0.1773573
#> [192,] 192 0.422187587 0.1773573
#> [193,] 193 1.490779068 0.1773573
#> [194,] 194 -1.239508707 0.1773573
#> [195,] 195 0.700976883 0.1773573
#> [196,] 196 -0.269565582 0.1773573
#> [197,] 197 1.407917474 0.1773573
#> [198,] 198 -1.256903609 0.1773573
#> [199,] 199 0.644322309 0.1773573
#> [200,] 200 -0.853229017 0.1773573
#>
#> $weakness
#> $weakness$proportions
#> # A tibble: 3 × 4
#> group Proportion algorithm colour
#> <dbl> <dbl> <chr> <chr>
#> 1 3 0.505 x3 #619CFF
#> 2 1 0.475 x1 #F8766D
#> 3 2 0.02 x2 #00BA38
#>
#> $weakness$latent
#> # A tibble: 80 × 1
#> x
#> <dbl>
#> 1 -2.95
#> 2 -2.88
#> 3 -2.81
#> 4 -2.74
#> 5 -2.67
#> 6 -2.60
#> 7 -2.53
#> 8 -2.46
#> 9 -2.39
#> 10 -2.32
#> # ℹ 70 more rows
#>
#> $weakness$multilatent
#> latenttrait x1 x2 x3
#> 1 -2.95469232 0 0 3
#> 2 -2.88393354 0 0 3
#> 3 -2.81317476 0 0 3
#> 4 -2.74241599 0 0 3
#> 5 -2.67165721 0 0 3
#> 6 -2.60089843 0 0 3
#> 7 -2.53013965 0 0 3
#> 8 -2.45938087 0 0 3
#> 9 -2.38862210 0 0 3
#> 10 -2.31786332 0 0 3
#> 11 -2.24710454 0 0 3
#> 12 -2.17634576 0 0 3
#> 13 -2.10558699 0 0 3
#> 14 -2.03482821 0 0 3
#> 15 -1.96406943 0 0 3
#> 16 -1.89331065 0 0 3
#> 17 -1.82255187 0 0 3
#> 18 -1.75179310 0 0 3
#> 19 -1.68103432 0 0 3
#> 20 -1.61027554 0 0 3
#> 21 -1.53951676 0 0 3
#> 22 -1.46875799 0 0 3
#> 23 -1.39799921 0 0 3
#> 24 -1.32724043 0 0 3
#> 25 -1.25648165 0 0 3
#> 26 -1.18572287 0 0 3
#> 27 -1.11496410 0 0 3
#> 28 -1.04420532 0 0 3
#> 29 -0.97344654 0 0 3
#> 30 -0.90268776 0 0 3
#> 31 -0.83192898 0 0 3
#> 32 -0.76117021 0 0 3
#> 33 -0.69041143 0 0 3
#> 34 -0.61965265 0 0 3
#> 35 -0.54889387 0 0 3
#> 36 -0.47813510 0 0 3
#> 37 -0.40737632 0 0 3
#> 38 -0.33661754 0 0 3
#> 39 -0.26585876 0 0 3
#> 40 -0.19509998 0 0 3
#> 41 -0.12434121 0 0 3
#> 42 -0.05358243 0 0 3
#> 43 0.01717635 0 0 3
#> 44 0.08793513 1 0 0
#> 45 0.15869390 1 0 0
#> 46 0.22945268 1 0 0
#> 47 0.30021146 1 0 0
#> 48 0.37097024 1 0 0
#> 49 0.44172902 1 0 0
#> 50 0.51248779 1 0 0
#> 51 0.58324657 1 0 0
#> 52 0.65400535 1 0 0
#> 53 0.72476413 1 0 0
#> 54 0.79552291 1 0 0
#> 55 0.86628168 1 0 0
#> 56 0.93704046 1 0 0
#> 57 1.00779924 1 0 0
#> 58 1.07855802 1 0 0
#> 59 1.14931679 1 0 0
#> 60 1.22007557 1 0 0
#> 61 1.29083435 1 0 0
#> 62 1.36159313 1 0 0
#> 63 1.43235191 1 0 0
#> 64 1.50311068 1 0 0
#> 65 1.57386946 1 0 0
#> 66 1.64462824 1 0 0
#> 67 1.71538702 1 0 0
#> 68 1.78614580 1 0 0
#> 69 1.85690457 1 0 0
#> 70 1.92766335 1 2 0
#> 71 1.99842213 1 2 0
#> 72 2.06918091 0 2 0
#> 73 2.13993968 0 2 0
#> 74 2.21069846 0 2 0
#> 75 2.28145724 0 2 0
#> 76 2.35221602 0 2 0
#> 77 2.42297480 0 2 0
#> 78 2.49373357 0 2 0
#> 79 2.56449235 0 2 0
#> 80 2.63525113 0 2 0
#>
#>
#> $call
#> latent_trait_analysis(df = X, max.item = max_item, min.item = min_item,
#> paras = mod$model$param)
#>
#> attr(,"class")
#> [1] "latenttrait"
# To plot performance against the problem difficulty
autoplot(out)
# To plot individual panels
autoplot(out, plottype = 2)
# To plot smoothing splines
autoplot(out, plottype = 3)
# To plot strengths and weaknesses
autoplot(out, plottype = 4)
