This 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 is FALSE.

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. If scale is FALSE, 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:

crmtheta

The problem trait output computed from the R package EstCRM.

strengths

The strengths of each algorithm and positions on the latent trait that they performs well.

longdf

The dataset in long format of latent trait occupancy.

plt

The ggplot object showing the fitted smoothing splines.

widedf

The dataset in wide format with latent trait.

thetas

The easiness of the problem set instances.

weakness

The 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.
#>  Using compatibility `.name_repair`.
#>  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)