Marginal maximum likelihood EM for ordered polytomous items:
\(P(X \ge c \mid \theta) = \mathrm{logit}^{-1}(a(\theta - b_c))\)
with ordered thresholds. The M-step maximizes each item's expected
complete-data log-likelihood with stats::optim on an
order-preserving parameterization.
Arguments
- responses
Integer matrix / data frame of ordered categories (1..C per item; NAs allowed).
- n_quad, max_iter, tol
EM controls as in
morie_irt_2pl.
Value
An object of class morie_irt_grm: list with
discrimination, thresholds (list of ordered
b-vectors), loglik, n_iter, converged,
theta, theta_se, method.
References
Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph, 17.
Examples
set.seed(64)
n <- 1200; k <- 4; a_true <- c(1.2, 1.5, 1.0, 1.8); th <- rnorm(n)
X <- vapply(seq_len(k), function(j) {
bj <- sort(runif(2, -1, 1))
u <- runif(n)
1L + (u < plogis(a_true[j] * (th - bj[1]))) + (u < plogis(a_true[j] * (th - bj[2])))
}, integer(n))
morie_irt_grm(X)
#> $discrimination
#> [1] 1.4498108 1.4839250 0.8085143 2.0172023
#>
#> $thresholds
#> $thresholds[[1]]
#> [1] 0.1325475 0.4228898
#>
#> $thresholds[[2]]
#> [1] -0.09904015 -0.04208353
#>
#> $thresholds[[3]]
#> [1] -0.6443755 0.8031395
#>
#> $thresholds[[4]]
#> [1] -0.309998971 -0.007858394
#>
#>
#> $loglik
#> [1] -4167.469
#>
#> $n_iter
#> [1] 12
#>
#> $converged
#> [1] TRUE
#>
#> $theta
#> [1] -0.34351248 -0.61760379 -0.94629461 1.24047937 0.58815623 -0.02789426
#> [7] 0.02301721 -0.31515422 0.79473923 0.19489690 -0.23755076 -0.59203010
#> [13] -0.59203010 0.36385028 -0.80173205 -1.23357063 -0.02789426 0.57318676
#> [19] 0.14410926 -0.80173205 0.38778200 0.55369450 1.24047937 0.21915462
#> [25] 0.02301721 0.09120698 -0.60643345 0.02301721 -0.72823904 0.57318676
#> [31] 0.38778200 0.55369450 -0.52569610 1.24047937 0.33976858 0.57318676
#> [37] -1.23357063 -0.94629461 0.57318676 -0.23374542 -1.23357063 0.33976858
#> [43] 1.24047937 -0.80173205 0.05210220 1.24047937 0.14410926 -0.39241214
#> [49] 0.19489690 0.21915462 1.24047937 -0.37533976 -0.94629461 -0.60643345
#> [55] 1.24047937 0.21915462 -0.23374542 -0.34351248 -0.23374542 0.21915462
#> [61] 0.23680994 0.79473923 0.79473923 1.24047937 -1.23357063 -0.34351248
#> [67] -0.14660748 0.95261871 1.24047937 1.24047937 -0.04519848 0.95261871
#> [73] -0.59203010 -1.23357063 0.19489690 0.79473923 -0.94629461 0.19489690
#> [79] 0.19489690 -1.23357063 0.59826929 -0.34351248 0.33976858 0.57318676
#> [85] 0.95261871 -0.17340218 0.19489690 0.13805666 0.02301721 -0.39241214
#> [91] 0.57318676 0.95261871 0.95261871 -0.94629461 -0.21349088 -1.23357063
#> [97] 0.95261871 0.14410926 0.59826929 -1.23357063 1.24047937 0.21915462
#> [103] 0.57318676 1.24047937 -0.39241214 0.36385028 1.24047937 -0.44502926
#> [109] 1.24047937 -0.01482987 1.24047937 0.57318676 -1.23357063 0.95261871
#> [115] -1.23357063 -0.80173205 0.19489690 0.30632198 0.36385028 -0.60643345
#> [121] -0.14660748 -1.23357063 -0.72823904 -1.23357063 1.24047937 -0.72823904
#> [127] 0.09120698 0.29764560 0.57318676 1.24047937 -1.23357063 -0.34351248
#> [133] 0.36385028 -0.39064873 -0.94629461 -0.59203010 0.78745005 -0.01482987
#> [139] 1.24047937 -1.23357063 1.24047937 0.21915462 -0.60643345 0.78745005
#> [145] 0.57318676 0.57318676 0.38778200 0.21915462 0.79473923 -0.34351248
#> [151] 0.79473923 -0.80173205 0.57318676 -0.03792181 0.79473923 0.33976858
#> [157] 0.17369036 -0.80173205 -1.23357063 1.24047937 -1.23357063 0.79473923
#> [163] 1.24047937 1.24047937 -0.60643345 1.24047937 -0.94629461 1.24047937
#> [169] 0.09120698 -1.23357063 -0.39241214 0.55369450 -0.23755076 1.24047937
#> [175] 0.38169741 -1.23357063 0.36385028 -0.14660748 -0.52569610 -0.80173205
#> [181] 0.09120698 -0.14660748 -0.94629461 0.79473923 0.57318676 0.33976858
#> [187] 0.38169741 0.44880128 -0.39241214 -0.14660748 -0.80173205 0.19489690
#> [193] -0.39064873 -1.23357063 -0.94629461 -0.72823904 0.95261871 1.24047937
#> [199] 0.24659634 -0.94629461 -0.23374542 -1.23357063 1.24047937 0.14410926
#> [205] -0.94629461 0.79473923 -0.72823904 -0.60643345 -0.21349088 -0.80173205
#> [211] -1.23357063 -1.23357063 -1.23357063 -0.72823904 0.95261871 -1.23357063
#> [217] 1.24047937 1.24047937 -0.80173205 0.21915462 0.38778200 -1.23357063
#> [223] -0.01482987 0.95261871 -0.14660748 0.19489690 0.57318676 1.24047937
#> [229] 0.95261871 0.57318676 -0.60643345 -0.31515422 -1.23357063 -0.94629461
#> [235] -0.80173205 -0.32361221 0.02301721 -0.18984422 -0.94629461 0.79473923
#> [241] -0.59203010 0.21915462 -0.23374542 0.38778200 0.79473923 -1.23357063
#> [247] 0.33976858 0.02301721 0.40854383 0.95261871 -1.23357063 0.24659634
#> [253] -0.80173205 -0.34351248 1.24047937 0.95261871 0.38778200 0.36385028
#> [259] 0.57318676 0.19489690 0.59826929 -0.34351248 -0.18984422 1.24047937
#> [265] -0.44502926 0.19489690 1.24047937 0.79473923 0.79473923 -0.80173205
#> [271] 1.24047937 -0.39241214 -0.80173205 -0.80173205 -0.03792181 0.57318676
#> [277] 0.59826929 0.78745005 -0.76895559 1.24047937 -0.94629461 -0.39241214
#> [283] 0.14410926 -1.23357063 1.24047937 0.57318676 -0.34351248 1.24047937
#> [289] -0.61760379 0.21915462 -0.14660748 -0.39241214 1.24047937 -0.52569610
#> [295] -0.60643345 -0.59203010 -0.21349088 -1.23357063 0.21915462 -0.60643345
#> [301] 0.79473923 -1.23357063 -0.14660748 -0.39241214 0.38778200 1.24047937
#> [307] 0.33976858 -0.59203010 1.24047937 -0.21349088 0.57318676 0.36385028
#> [313] -0.37533976 -0.03792181 0.79473923 -0.59203010 -1.23357063 -0.02789426
#> [319] 0.59826929 -1.23357063 -0.94629461 -1.23357063 0.59826929 -0.59203010
#> [325] -0.59203010 -1.23357063 0.14410926 0.17369036 0.95261871 0.21915462
#> [331] 1.24047937 -0.94629461 0.19489690 -1.23357063 0.36385028 -0.60643345
#> [337] 0.79473923 -0.59203010 0.57318676 1.24047937 -1.23357063 -0.60643345
#> [343] -0.03792181 0.19489690 -0.23374542 -0.14660748 0.13805666 -0.59203010
#> [349] -0.03792181 -0.23374542 -0.32361221 -0.23374542 0.95261871 -1.23357063
#> [355] -0.32361221 0.36385028 -1.23357063 -1.23357063 0.21915462 0.95261871
#> [361] -0.23374542 -0.34351248 -0.21349088 -0.14660748 0.95261871 -0.94629461
#> [367] -1.23357063 -0.04519848 1.24047937 -0.14660748 -1.23357063 -0.80173205
#> [373] -0.14660748 0.38778200 0.95261871 1.24047937 0.07853873 -0.23374542
#> [379] 0.36385028 1.24047937 0.59826929 -0.32361221 0.21915462 0.55369450
#> [385] 0.58815623 -1.23357063 0.13805666 -0.94629461 -0.14660748 0.19489690
#> [391] 1.24047937 0.19489690 -1.23357063 -0.14660748 -0.59203010 -0.60643345
#> [397] 0.09120698 0.78745005 -0.76895559 -0.94629461 1.24047937 -0.39241214
#> [403] -0.23374542 -1.23357063 0.79473923 1.24047937 1.24047937 0.05210220
#> [409] -1.23357063 -1.23357063 -0.59203010 -0.14660748 -1.23357063 -1.23357063
#> [415] -0.59203010 1.24047937 0.33976858 -1.23357063 0.95261871 -0.61760379
#> [421] -0.34351248 -0.94629461 -1.23357063 -0.34351248 -0.34351248 -0.72823904
#> [427] 0.78745005 -1.23357063 -0.21349088 0.36385028 0.19489690 -1.23357063
#> [433] 0.57318676 -1.23357063 0.57318676 -0.03792181 0.59826929 -0.39241214
#> [439] 0.38169741 -0.21349088 1.24047937 -0.06440884 -0.80173205 -0.94629461
#> [445] -0.32361221 1.24047937 -0.17946601 -1.23357063 0.59826929 0.33976858
#> [451] -0.80173205 1.24047937 0.38778200 0.36385028 0.59826929 -0.34351248
#> [457] 0.19489690 0.14410926 1.24047937 -0.94629461 0.09120698 -1.23357063
#> [463] 0.38778200 -0.94629461 -1.23357063 1.24047937 -0.03792181 -0.60643345
#> [469] -0.37533976 -0.94629461 0.78745005 0.55369450 0.21915462 0.79473923
#> [475] -0.03792181 -0.23374542 -0.34351248 0.95261871 -0.34351248 0.44880128
#> [481] -0.34351248 -0.94629461 1.24047937 -0.60643345 0.33976858 0.57318676
#> [487] 0.44880128 -1.23357063 -0.94629461 -0.14660748 -0.23374542 -1.23357063
#> [493] 1.24047937 -0.80173205 -1.23357063 -0.34351248 -0.37533976 0.95261871
#> [499] 0.19489690 -0.80173205 0.02301721 -0.80173205 -0.39241214 0.33976858
#> [505] 0.02301721 0.21915462 0.21915462 0.38778200 0.44880128 0.79473923
#> [511] -0.06440884 -0.34351248 0.74642529 -0.80173205 -1.23357063 0.11039798
#> [517] -0.94629461 0.57318676 0.44880128 -1.23357063 -0.34351248 0.79473923
#> [523] -0.61760379 0.57318676 -1.23357063 -0.07270366 0.33976858 0.19489690
#> [529] 0.95261871 -0.39241214 0.58815623 1.24047937 0.59826929 0.36385028
#> [535] 1.24047937 0.79473923 -1.23357063 0.79473923 -0.44502926 0.24659634
#> [541] -0.59203010 -1.23357063 -1.23357063 1.24047937 -0.21349088 -0.44502926
#> [547] -0.80173205 -0.59203010 0.79473923 -0.72823904 1.24047937 0.55369450
#> [553] 0.78745005 -0.60643345 -0.04519848 0.95261871 -0.80173205 0.95261871
#> [559] -1.23357063 -1.23357063 -0.23374542 0.02301721 -1.23357063 -1.23357063
#> [565] -1.23357063 0.29764560 -0.04519848 1.24047937 1.24047937 0.33976858
#> [571] -0.94629461 -1.23357063 -0.60643345 0.29764560 -1.23357063 -0.80173205
#> [577] -0.80173205 -0.39241214 0.38778200 0.78745005 0.79473923 -0.01482987
#> [583] -0.44502926 0.58815623 0.19489690 0.02301721 -0.80173205 0.36385028
#> [589] 1.24047937 0.02301721 -0.39241214 0.95261871 0.57318676 0.55369450
#> [595] -1.23357063 -0.32361221 0.95261871 0.58815623 0.95261871 0.79473923
#> [601] -0.61760379 0.38778200 -0.60643345 -0.32361221 1.24047937 -0.80173205
#> [607] -0.61760379 -1.23357063 -0.04519848 0.44880128 -0.34351248 -1.23357063
#> [613] -0.61760379 0.19489690 -0.37533976 0.36385028 0.21915462 1.24047937
#> [619] 0.38778200 -0.23374542 -0.94629461 0.19489690 -0.23374542 -0.21349088
#> [625] 0.59826929 1.24047937 -1.23357063 0.38778200 1.24047937 -1.23357063
#> [631] 1.24047937 0.36385028 0.79473923 0.44880128 -0.39241214 0.57318676
#> [637] -0.80173205 -0.94629461 -1.23357063 0.36385028 -0.80173205 -1.23357063
#> [643] 0.59826929 -1.23357063 0.79473923 0.21915462 -0.39241214 0.95261871
#> [649] 0.95261871 -1.23357063 1.24047937 0.19489690 0.95261871 -0.34351248
#> [655] -1.23357063 0.19489690 -0.03792181 -0.44502926 1.24047937 0.19489690
#> [661] 0.79473923 0.19489690 0.33976858 -0.61760379 0.11039798 0.95261871
#> [667] 1.24047937 -1.23357063 0.95261871 0.21915462 -0.94629461 -0.39064873
#> [673] -1.23357063 1.24047937 -0.37533976 -0.80173205 -0.11021079 1.24047937
#> [679] 0.95261871 0.95261871 0.36385028 -0.94629461 -0.60643345 -0.61760379
#> [685] 1.24047937 -1.23357063 0.95261871 -1.23357063 -0.80173205 0.09120698
#> [691] -1.23357063 0.38778200 -0.39064873 0.02301721 0.57318676 -0.23374542
#> [697] -0.60643345 -1.23357063 0.59826929 -0.39241214 1.24047937 -0.60643345
#> [703] 1.24047937 1.24047937 1.24047937 0.02301721 -0.03792181 0.38169741
#> [709] 0.33976858 1.24047937 0.36385028 0.29764560 0.24659634 0.19489690
#> [715] -1.23357063 -0.80173205 0.02301721 -0.18984422 0.19489690 1.24047937
#> [721] 0.38169741 0.19489690 -1.23357063 0.57318676 -0.60643345 -0.60643345
#> [727] -1.23357063 -1.23357063 -1.23357063 1.24047937 -0.80173205 -0.39241214
#> [733] 1.24047937 -1.23357063 0.29764560 1.24047937 1.24047937 0.36385028
#> [739] -1.23357063 -1.23357063 -1.23357063 -1.23357063 -1.23357063 0.19489690
#> [745] 0.79473923 0.79473923 -1.23357063 -1.23357063 0.59826929 0.79473923
#> [751] 0.57318676 1.24047937 1.24047937 0.29764560 0.21915462 -0.80173205
#> [757] -1.23357063 0.57318676 -1.23357063 0.36385028 0.36385028 1.24047937
#> [763] -0.60643345 0.21915462 -1.23357063 0.57318676 0.78745005 0.95261871
#> [769] 0.33976858 -0.23374542 -0.23755076 -0.61760379 0.21915462 0.79473923
#> [775] -0.27361200 0.36385028 0.19489690 0.02301721 1.24047937 -0.37533976
#> [781] -1.23357063 0.36385028 -0.21349088 -0.27361200 -1.23357063 -1.23357063
#> [787] 0.02301721 0.17369036 -0.23374542 -0.23374542 -0.23374542 -0.80173205
#> [793] 0.95261871 0.36385028 0.95261871 0.95261871 -0.80173205 -0.34351248
#> [799] -0.21349088 -1.23357063 1.24047937 -1.23357063 0.38778200 0.21915462
#> [805] 0.79473923 -1.23357063 -1.23357063 0.79473923 -0.60643345 -0.61760379
#> [811] -0.60643345 -0.60643345 -0.80173205 -0.03792181 -0.59203010 -0.02789426
#> [817] -0.39241214 0.54924034 0.57318676 0.21915462 1.24047937 1.24047937
#> [823] -1.23357063 0.59826929 1.24047937 -0.80173205 -0.03792181 -1.23357063
#> [829] 0.57318676 -0.94629461 -0.60643345 -0.56986312 0.57318676 -1.23357063
#> [835] -1.23357063 0.95261871 0.38778200 -0.94629461 1.24047937 0.57318676
#> [841] 0.09120698 -1.23357063 0.57318676 -1.23357063 -0.39241214 -0.34351248
#> [847] 0.57318676 -0.80173205 0.21915462 0.29764560 -0.39241214 1.24047937
#> [853] -0.80173205 -1.23357063 -0.23755076 0.55369450 0.57318676 0.78745005
#> [859] 1.24047937 -0.39064873 0.74642529 -0.03792181 1.24047937 0.79473923
#> [865] -0.39241214 -1.23357063 -0.94629461 0.55369450 -0.34351248 -0.94629461
#> [871] 0.79473923 -1.23357063 -0.80173205 0.03949884 0.21915462 0.79473923
#> [877] -1.23357063 0.59826929 -0.94629461 -1.23357063 0.78745005 -0.21349088
#> [883] -1.23357063 -0.23374542 1.24047937 -0.14660748 -0.32361221 0.59826929
#> [889] 0.58815623 -0.14660748 0.38778200 0.79473923 0.19489690 -0.60643345
#> [895] -0.14660748 -1.23357063 -1.23357063 -0.39241214 -1.23357063 -0.94629461
#> [901] 0.19489690 -1.23357063 -0.94629461 1.24047937 0.02301721 0.29764560
#> [907] -0.60643345 0.21915462 -0.04519848 0.21915462 0.33976858 -0.94629461
#> [913] 0.36385028 0.95261871 1.24047937 -0.59203010 -0.60643345 -1.23357063
#> [919] 1.24047937 0.19489690 0.58815623 0.59826929 0.02301721 -1.23357063
#> [925] -0.60643345 1.24047937 1.24047937 0.59826929 0.57318676 -0.94629461
#> [931] -0.94629461 0.38778200 0.36385028 0.79473923 0.59826929 -0.14660748
#> [937] 0.19489690 -0.39241214 -1.23357063 1.24047937 -0.60643345 0.79473923
#> [943] 0.36385028 -1.23357063 0.57318676 1.24047937 0.19489690 0.78745005
#> [949] 0.11039798 -0.01482987 0.19489690 0.38778200 0.19489690 1.24047937
#> [955] 0.79473923 0.44880128 -0.37533976 -0.60643345 0.79473923 1.24047937
#> [961] 0.59826929 -0.80173205 1.24047937 0.33976858 -1.23357063 -0.31515422
#> [967] 1.24047937 -0.59203010 -1.23357063 0.57318676 0.19489690 -0.80173205
#> [973] -1.23357063 -0.72823904 -0.52569610 -0.04519848 0.95261871 -0.61760379
#> [979] -0.14660748 -0.04519848 1.24047937 -1.23357063 1.24047937 1.24047937
#> [985] 1.24047937 -0.03792181 0.95261871 -0.80173205 -1.23357063 -0.56986312
#> [991] -0.34351248 0.95261871 1.24047937 -0.52569610 -1.23357063 -1.23357063
#> [997] -0.34351248 0.44880128 -1.23357063 -0.60643345 -0.03792181 -0.94629461
#> [1003] -0.94629461 1.24047937 1.24047937 0.38169741 0.36385028 0.29764560
#> [1009] -0.34351248 -0.61760379 -0.07167141 0.19489690 0.95261871 -0.04519848
#> [1015] 0.57318676 0.21915462 1.24047937 0.57318676 -1.23357063 -1.23357063
#> [1021] -0.14660748 -0.37533976 -0.59203010 0.95261871 -0.01482987 -0.23374542
#> [1027] -0.60643345 1.24047937 1.24047937 0.59826929 -0.34351248 0.79473923
#> [1033] -0.14660748 0.57318676 0.57318676 -0.39064873 0.19489690 -1.23357063
#> [1039] -0.32361221 -1.23357063 0.95261871 -1.23357063 -0.72823904 -0.61760379
#> [1045] 1.24047937 0.55369450 -0.32361221 -1.23357063 0.11039798 0.95261871
#> [1051] 0.13805666 -1.23357063 -0.23374542 -0.02789426 -0.61760379 0.79473923
#> [1057] -0.03792181 0.19489690 0.57318676 0.33976858 1.24047937 0.19489690
#> [1063] -0.34351248 -0.14660748 -1.23357063 -0.60643345 -0.59203010 0.57318676
#> [1069] -0.56986312 -1.23357063 -0.60643345 0.36385028 1.24047937 -0.21349088
#> [1075] 0.38778200 0.19489690 0.59826929 -0.34351248 0.33976858 -0.60643345
#> [1081] 1.24047937 -0.39241214 1.24047937 -0.44502926 0.95261871 -0.14660748
#> [1087] -0.61760379 0.79473923 -0.59203010 1.24047937 -0.14660748 0.02301721
#> [1093] 0.57318676 0.79473923 -0.44502926 -0.94629461 0.57318676 0.95261871
#> [1099] 0.58815623 -0.23374542 -0.02789426 1.24047937 -1.23357063 -0.60643345
#> [1105] 0.11039798 0.95261871 0.79473923 -1.23357063 -1.23357063 0.14410926
#> [1111] 0.57318676 -0.80173205 -0.80173205 -0.32361221 1.24047937 -0.37533976
#> [1117] -0.80173205 0.38778200 -0.80173205 1.24047937 0.79473923 0.36385028
#> [1123] 0.79473923 1.24047937 -0.23374542 -0.18984422 1.24047937 0.36385028
#> [1129] 0.79473923 1.24047937 -0.44018478 0.21915462 1.24047937 -0.80173205
#> [1135] 0.95261871 -0.21349088 0.23680994 -0.14660748 -0.34351248 -0.44502926
#> [1141] -0.80173205 -1.23357063 0.57318676 -0.94629461 -0.18984422 -0.94629461
#> [1147] 1.24047937 -0.94629461 -0.03792181 1.24047937 0.38778200 -0.04519848
#> [1153] -0.39241214 0.57318676 1.24047937 0.19489690 0.95261871 -1.23357063
#> [1159] 1.24047937 1.24047937 0.95261871 -0.94629461 0.33976858 0.95261871
#> [1165] 0.79473923 -0.61760379 1.24047937 1.24047937 -1.23357063 0.36385028
#> [1171] -0.44502926 -0.32361221 -1.23357063 -0.80173205 -0.14660748 -0.37533976
#> [1177] 0.57318676 0.36385028 0.14410926 0.38778200 -0.60643345 0.21915462
#> [1183] 0.33976858 -0.23374542 0.55369450 0.29764560 0.29764560 -0.94629461
#> [1189] 1.24047937 -0.23374542 -0.21349088 0.57318676 -0.04519848 1.24047937
#> [1195] 1.24047937 -0.94629461 0.95261871 -0.56986312 -0.34351248 0.59826929
#>
#> $theta_se
#> [1] 0.6041493 0.5483382 0.6332138 0.6929834 0.5595485 0.5129734 0.5944215
#> [8] 0.4977297 0.6438742 0.5976768 0.5557503 0.6188189 0.6188189 0.5889973
#> [15] 0.6370697 0.6846667 0.5129734 0.6207706 0.5885769 0.6370697 0.5898641
#> [22] 0.5613976 0.6929834 0.5995893 0.5944215 0.5253518 0.6137170 0.5944215
#> [29] 0.5905698 0.6207706 0.5898641 0.5613976 0.5594362 0.6929834 0.6150158
#> [36] 0.6207706 0.6846667 0.6332138 0.6207706 0.5983939 0.6846667 0.6150158
#> [43] 0.6929834 0.6370697 0.4917949 0.6929834 0.5885769 0.5860729 0.5976768
#> [50] 0.5995893 0.6929834 0.5903586 0.6332138 0.6137170 0.6929834 0.5995893
#> [57] 0.5983939 0.6041493 0.5983939 0.5995893 0.5512162 0.6438742 0.6438742
#> [64] 0.6929834 0.6846667 0.6041493 0.5802368 0.6411212 0.6929834 0.6929834
#> [71] 0.5105711 0.6411212 0.6188189 0.6846667 0.5976768 0.6438742 0.6332138
#> [78] 0.5976768 0.5976768 0.6846667 0.6203099 0.6041493 0.6150158 0.6207706
#> [85] 0.6411212 0.5244810 0.5976768 0.5373500 0.5944215 0.5860729 0.6207706
#> [92] 0.6411212 0.6411212 0.6332138 0.6024798 0.6846667 0.6411212 0.5885769
#> [99] 0.6203099 0.6846667 0.6929834 0.5995893 0.6207706 0.6929834 0.5860729
#> [106] 0.5889973 0.6929834 0.5228080 0.6929834 0.5502373 0.6929834 0.6207706
#> [113] 0.6846667 0.6411212 0.6846667 0.6370697 0.5976768 0.5029723 0.5889973
#> [120] 0.6137170 0.5802368 0.6846667 0.5905698 0.6846667 0.6929834 0.5905698
#> [127] 0.5253518 0.5539645 0.6207706 0.6929834 0.6846667 0.6041493 0.5889973
#> [134] 0.5648451 0.6332138 0.6188189 0.5915954 0.5502373 0.6929834 0.6846667
#> [141] 0.6929834 0.5995893 0.6137170 0.5915954 0.6207706 0.6207706 0.5898641
#> [148] 0.5995893 0.6438742 0.6041493 0.6438742 0.6370697 0.6207706 0.6003494
#> [155] 0.6438742 0.6150158 0.4863365 0.6370697 0.6846667 0.6929834 0.6846667
#> [162] 0.6438742 0.6929834 0.6929834 0.6137170 0.6929834 0.6332138 0.6929834
#> [169] 0.5253518 0.6846667 0.5860729 0.5613976 0.5557503 0.6929834 0.5327709
#> [176] 0.6846667 0.5889973 0.5802368 0.5594362 0.6370697 0.5253518 0.5802368
#> [183] 0.6332138 0.6438742 0.6207706 0.6150158 0.5327709 0.5634445 0.5860729
#> [190] 0.5802368 0.6370697 0.5976768 0.5648451 0.6846667 0.6332138 0.5905698
#> [197] 0.6411212 0.6929834 0.5350096 0.6332138 0.5983939 0.6846667 0.6929834
#> [204] 0.5885769 0.6332138 0.6438742 0.5905698 0.6137170 0.6024798 0.6370697
#> [211] 0.6846667 0.6846667 0.6846667 0.5905698 0.6411212 0.6846667 0.6929834
#> [218] 0.6929834 0.6370697 0.5995893 0.5898641 0.6846667 0.5502373 0.6411212
#> [225] 0.5802368 0.5976768 0.6207706 0.6929834 0.6411212 0.6207706 0.6137170
#> [232] 0.4977297 0.6846667 0.6332138 0.6370697 0.5277180 0.5944215 0.5216462
#> [239] 0.6332138 0.6438742 0.6188189 0.5995893 0.5983939 0.5898641 0.6438742
#> [246] 0.6846667 0.6150158 0.5944215 0.5621408 0.6411212 0.6846667 0.5350096
#> [253] 0.6370697 0.6041493 0.6929834 0.6411212 0.5898641 0.5889973 0.6207706
#> [260] 0.5976768 0.6203099 0.6041493 0.5216462 0.6929834 0.5228080 0.5976768
#> [267] 0.6929834 0.6438742 0.6438742 0.6370697 0.6929834 0.5860729 0.6370697
#> [274] 0.6370697 0.6003494 0.6207706 0.6203099 0.5915954 0.5828566 0.6929834
#> [281] 0.6332138 0.5860729 0.5885769 0.6846667 0.6929834 0.6207706 0.6041493
#> [288] 0.6929834 0.5483382 0.5995893 0.5802368 0.5860729 0.6929834 0.5594362
#> [295] 0.6137170 0.6188189 0.6024798 0.6846667 0.5995893 0.6137170 0.6438742
#> [302] 0.6846667 0.5802368 0.5860729 0.5898641 0.6929834 0.6150158 0.6188189
#> [309] 0.6929834 0.6024798 0.6207706 0.5889973 0.5903586 0.6003494 0.6438742
#> [316] 0.6188189 0.6846667 0.5129734 0.6203099 0.6846667 0.6332138 0.6846667
#> [323] 0.6203099 0.6188189 0.6188189 0.6846667 0.5885769 0.4863365 0.6411212
#> [330] 0.5995893 0.6929834 0.6332138 0.5976768 0.6846667 0.5889973 0.6137170
#> [337] 0.6438742 0.6188189 0.6207706 0.6929834 0.6846667 0.6137170 0.6003494
#> [344] 0.5976768 0.5983939 0.5802368 0.5373500 0.6188189 0.6003494 0.5983939
#> [351] 0.5277180 0.5983939 0.6411212 0.6846667 0.5277180 0.5889973 0.6846667
#> [358] 0.6846667 0.5995893 0.6411212 0.5983939 0.6041493 0.6024798 0.5802368
#> [365] 0.6411212 0.6332138 0.6846667 0.5105711 0.6929834 0.5802368 0.6846667
#> [372] 0.6370697 0.5802368 0.5898641 0.6411212 0.6929834 0.5550838 0.5983939
#> [379] 0.5889973 0.6929834 0.6203099 0.5277180 0.5995893 0.5613976 0.5595485
#> [386] 0.6846667 0.5373500 0.6332138 0.5802368 0.5976768 0.6929834 0.5976768
#> [393] 0.6846667 0.5802368 0.6188189 0.6137170 0.5253518 0.5915954 0.5828566
#> [400] 0.6332138 0.6929834 0.5860729 0.5983939 0.6846667 0.6438742 0.6929834
#> [407] 0.6929834 0.4917949 0.6846667 0.6846667 0.6188189 0.5802368 0.6846667
#> [414] 0.6846667 0.6188189 0.6929834 0.6150158 0.6846667 0.6411212 0.5483382
#> [421] 0.6041493 0.6332138 0.6846667 0.6041493 0.6041493 0.5905698 0.5915954
#> [428] 0.6846667 0.6024798 0.5889973 0.5976768 0.6846667 0.6207706 0.6846667
#> [435] 0.6207706 0.6003494 0.6203099 0.5860729 0.5327709 0.6024798 0.6929834
#> [442] 0.4912172 0.6370697 0.6332138 0.5277180 0.6929834 0.4834641 0.6846667
#> [449] 0.6203099 0.6150158 0.6370697 0.6929834 0.5898641 0.5889973 0.6203099
#> [456] 0.6041493 0.5976768 0.5885769 0.6929834 0.6332138 0.5253518 0.6846667
#> [463] 0.5898641 0.6332138 0.6846667 0.6929834 0.6003494 0.6137170 0.5903586
#> [470] 0.6332138 0.5915954 0.5613976 0.5995893 0.6438742 0.6003494 0.5983939
#> [477] 0.6041493 0.6411212 0.6041493 0.5634445 0.6041493 0.6332138 0.6929834
#> [484] 0.6137170 0.6150158 0.6207706 0.5634445 0.6846667 0.6332138 0.5802368
#> [491] 0.5983939 0.6846667 0.6929834 0.6370697 0.6846667 0.6041493 0.5903586
#> [498] 0.6411212 0.5976768 0.6370697 0.5944215 0.6370697 0.5860729 0.6150158
#> [505] 0.5944215 0.5995893 0.5995893 0.5898641 0.5634445 0.6438742 0.4912172
#> [512] 0.6041493 0.5909070 0.6370697 0.6846667 0.5275428 0.6332138 0.6207706
#> [519] 0.5634445 0.6846667 0.6041493 0.6438742 0.5483382 0.6207706 0.6846667
#> [526] 0.5406075 0.6150158 0.5976768 0.6411212 0.5860729 0.5595485 0.6929834
#> [533] 0.6203099 0.5889973 0.6929834 0.6438742 0.6846667 0.6438742 0.5228080
#> [540] 0.5350096 0.6188189 0.6846667 0.6846667 0.6929834 0.6024798 0.5228080
#> [547] 0.6370697 0.6188189 0.6438742 0.5905698 0.6929834 0.5613976 0.5915954
#> [554] 0.6137170 0.5105711 0.6411212 0.6370697 0.6411212 0.6846667 0.6846667
#> [561] 0.5983939 0.5944215 0.6846667 0.6846667 0.6846667 0.5539645 0.5105711
#> [568] 0.6929834 0.6929834 0.6150158 0.6332138 0.6846667 0.6137170 0.5539645
#> [575] 0.6846667 0.6370697 0.6370697 0.5860729 0.5898641 0.5915954 0.6438742
#> [582] 0.5502373 0.5228080 0.5595485 0.5976768 0.5944215 0.6370697 0.5889973
#> [589] 0.6929834 0.5944215 0.5860729 0.6411212 0.6207706 0.5613976 0.6846667
#> [596] 0.5277180 0.6411212 0.5595485 0.6411212 0.6438742 0.5483382 0.5898641
#> [603] 0.6137170 0.5277180 0.6929834 0.6370697 0.5483382 0.6846667 0.5105711
#> [610] 0.5634445 0.6041493 0.6846667 0.5483382 0.5976768 0.5903586 0.5889973
#> [617] 0.5995893 0.6929834 0.5898641 0.5983939 0.6332138 0.5976768 0.5983939
#> [624] 0.6024798 0.6203099 0.6929834 0.6846667 0.5898641 0.6929834 0.6846667
#> [631] 0.6929834 0.5889973 0.6438742 0.5634445 0.5860729 0.6207706 0.6370697
#> [638] 0.6332138 0.6846667 0.5889973 0.6370697 0.6846667 0.6203099 0.6846667
#> [645] 0.6438742 0.5995893 0.5860729 0.6411212 0.6411212 0.6846667 0.6929834
#> [652] 0.5976768 0.6411212 0.6041493 0.6846667 0.5976768 0.6003494 0.5228080
#> [659] 0.6929834 0.5976768 0.6438742 0.5976768 0.6150158 0.5483382 0.5275428
#> [666] 0.6411212 0.6929834 0.6846667 0.6411212 0.5995893 0.6332138 0.5648451
#> [673] 0.6846667 0.6929834 0.5903586 0.6370697 0.4872252 0.6929834 0.6411212
#> [680] 0.6411212 0.5889973 0.6332138 0.6137170 0.5483382 0.6929834 0.6846667
#> [687] 0.6411212 0.6846667 0.6370697 0.5253518 0.6846667 0.5898641 0.5648451
#> [694] 0.5944215 0.6207706 0.5983939 0.6137170 0.6846667 0.6203099 0.5860729
#> [701] 0.6929834 0.6137170 0.6929834 0.6929834 0.6929834 0.5944215 0.6003494
#> [708] 0.5327709 0.6150158 0.6929834 0.5889973 0.5539645 0.5350096 0.5976768
#> [715] 0.6846667 0.6370697 0.5944215 0.5216462 0.5976768 0.6929834 0.5327709
#> [722] 0.5976768 0.6846667 0.6207706 0.6137170 0.6137170 0.6846667 0.6846667
#> [729] 0.6846667 0.6929834 0.6370697 0.5860729 0.6929834 0.6846667 0.5539645
#> [736] 0.6929834 0.6929834 0.5889973 0.6846667 0.6846667 0.6846667 0.6846667
#> [743] 0.6846667 0.5976768 0.6438742 0.6438742 0.6846667 0.6846667 0.6203099
#> [750] 0.6438742 0.6207706 0.6929834 0.6929834 0.5539645 0.5995893 0.6370697
#> [757] 0.6846667 0.6207706 0.6846667 0.5889973 0.5889973 0.6929834 0.6137170
#> [764] 0.5995893 0.6846667 0.6207706 0.5915954 0.6411212 0.6150158 0.5983939
#> [771] 0.5557503 0.5483382 0.5995893 0.6438742 0.5529674 0.5889973 0.5976768
#> [778] 0.5944215 0.6929834 0.5903586 0.6846667 0.5889973 0.6024798 0.5529674
#> [785] 0.6846667 0.6846667 0.5944215 0.4863365 0.5983939 0.5983939 0.5983939
#> [792] 0.6370697 0.6411212 0.5889973 0.6411212 0.6411212 0.6370697 0.6041493
#> [799] 0.6024798 0.6846667 0.6929834 0.6846667 0.5898641 0.5995893 0.6438742
#> [806] 0.6846667 0.6846667 0.6438742 0.6137170 0.5483382 0.6137170 0.6137170
#> [813] 0.6370697 0.6003494 0.6188189 0.5129734 0.5860729 0.5586436 0.6207706
#> [820] 0.5995893 0.6929834 0.6929834 0.6846667 0.6203099 0.6929834 0.6370697
#> [827] 0.6003494 0.6846667 0.6207706 0.6332138 0.6137170 0.5527423 0.6207706
#> [834] 0.6846667 0.6846667 0.6411212 0.5898641 0.6332138 0.6929834 0.6207706
#> [841] 0.5253518 0.6846667 0.6207706 0.6846667 0.5860729 0.6041493 0.6207706
#> [848] 0.6370697 0.5995893 0.5539645 0.5860729 0.6929834 0.6370697 0.6846667
#> [855] 0.5557503 0.5613976 0.6207706 0.5915954 0.6929834 0.5648451 0.5909070
#> [862] 0.6003494 0.6929834 0.6438742 0.5860729 0.6846667 0.6332138 0.5613976
#> [869] 0.6041493 0.6332138 0.6438742 0.6846667 0.6370697 0.5528265 0.5995893
#> [876] 0.6438742 0.6846667 0.6203099 0.6332138 0.6846667 0.5915954 0.6024798
#> [883] 0.6846667 0.5983939 0.6929834 0.5802368 0.5277180 0.6203099 0.5595485
#> [890] 0.5802368 0.5898641 0.6438742 0.5976768 0.6137170 0.5802368 0.6846667
#> [897] 0.6846667 0.5860729 0.6846667 0.6332138 0.5976768 0.6846667 0.6332138
#> [904] 0.6929834 0.5944215 0.5539645 0.6137170 0.5995893 0.5105711 0.5995893
#> [911] 0.6150158 0.6332138 0.5889973 0.6411212 0.6929834 0.6188189 0.6137170
#> [918] 0.6846667 0.6929834 0.5976768 0.5595485 0.6203099 0.5944215 0.6846667
#> [925] 0.6137170 0.6929834 0.6929834 0.6203099 0.6207706 0.6332138 0.6332138
#> [932] 0.5898641 0.5889973 0.6438742 0.6203099 0.5802368 0.5976768 0.5860729
#> [939] 0.6846667 0.6929834 0.6137170 0.6438742 0.5889973 0.6846667 0.6207706
#> [946] 0.6929834 0.5976768 0.5915954 0.5275428 0.5502373 0.5976768 0.5898641
#> [953] 0.5976768 0.6929834 0.6438742 0.5634445 0.5903586 0.6137170 0.6438742
#> [960] 0.6929834 0.6203099 0.6370697 0.6929834 0.6150158 0.6846667 0.4977297
#> [967] 0.6929834 0.6188189 0.6846667 0.6207706 0.5976768 0.6370697 0.6846667
#> [974] 0.5905698 0.5594362 0.5105711 0.6411212 0.5483382 0.5802368 0.5105711
#> [981] 0.6929834 0.6846667 0.6929834 0.6929834 0.6929834 0.6003494 0.6411212
#> [988] 0.6370697 0.6846667 0.5527423 0.6041493 0.6411212 0.6929834 0.5594362
#> [995] 0.6846667 0.6846667 0.6041493 0.5634445 0.6846667 0.6137170 0.6003494
#> [1002] 0.6332138 0.6332138 0.6929834 0.6929834 0.5327709 0.5889973 0.5539645
#> [1009] 0.6041493 0.5483382 0.5458554 0.5976768 0.6411212 0.5105711 0.6207706
#> [1016] 0.5995893 0.6929834 0.6207706 0.6846667 0.6846667 0.5802368 0.5903586
#> [1023] 0.6188189 0.6411212 0.5502373 0.5983939 0.6137170 0.6929834 0.6929834
#> [1030] 0.6203099 0.6041493 0.6438742 0.5802368 0.6207706 0.6207706 0.5648451
#> [1037] 0.5976768 0.6846667 0.5277180 0.6846667 0.6411212 0.6846667 0.5905698
#> [1044] 0.5483382 0.6929834 0.5613976 0.5277180 0.6846667 0.5275428 0.6411212
#> [1051] 0.5373500 0.6846667 0.5983939 0.5129734 0.5483382 0.6438742 0.6003494
#> [1058] 0.5976768 0.6207706 0.6150158 0.6929834 0.5976768 0.6041493 0.5802368
#> [1065] 0.6846667 0.6137170 0.6188189 0.6207706 0.5527423 0.6846667 0.6137170
#> [1072] 0.5889973 0.6929834 0.6024798 0.5898641 0.5976768 0.6203099 0.6041493
#> [1079] 0.6150158 0.6137170 0.6929834 0.5860729 0.6929834 0.5228080 0.6411212
#> [1086] 0.5802368 0.5483382 0.6438742 0.6188189 0.6929834 0.5802368 0.5944215
#> [1093] 0.6207706 0.6438742 0.5228080 0.6332138 0.6207706 0.6411212 0.5595485
#> [1100] 0.5983939 0.5129734 0.6929834 0.6846667 0.6137170 0.5275428 0.6411212
#> [1107] 0.6438742 0.6846667 0.6846667 0.5885769 0.6207706 0.6370697 0.6370697
#> [1114] 0.5277180 0.6929834 0.5903586 0.6370697 0.5898641 0.6370697 0.6929834
#> [1121] 0.6438742 0.5889973 0.6438742 0.6929834 0.5983939 0.5216462 0.6929834
#> [1128] 0.5889973 0.6438742 0.6929834 0.5582349 0.5995893 0.6929834 0.6370697
#> [1135] 0.6411212 0.6024798 0.5512162 0.5802368 0.6041493 0.5228080 0.6370697
#> [1142] 0.6846667 0.6207706 0.6332138 0.5216462 0.6332138 0.6929834 0.6332138
#> [1149] 0.6003494 0.6929834 0.5898641 0.5105711 0.5860729 0.6207706 0.6929834
#> [1156] 0.5976768 0.6411212 0.6846667 0.6929834 0.6929834 0.6411212 0.6332138
#> [1163] 0.6150158 0.6411212 0.6438742 0.5483382 0.6929834 0.6929834 0.6846667
#> [1170] 0.5889973 0.5228080 0.5277180 0.6846667 0.6370697 0.5802368 0.5903586
#> [1177] 0.6207706 0.5889973 0.5885769 0.5898641 0.6137170 0.5995893 0.6150158
#> [1184] 0.5983939 0.5613976 0.5539645 0.5539645 0.6332138 0.6929834 0.5983939
#> [1191] 0.6024798 0.6207706 0.5105711 0.6929834 0.6929834 0.6332138 0.6411212
#> [1198] 0.5527423 0.6041493 0.6203099
#>
#> $n_persons
#> [1] 1200
#>
#> $n_items
#> [1] 4
#>
#> $method
#> [1] "GRM Samejima EM (rmorie native)"
#>
#> attr(,"class")
#> [1] "morie_irt_grm" "list"