The goal of irtplay is to examine the IRT model-data fit on item-level in different ways as well as provide useful functions related to unidimensional item response theory (IRT). In terms of assessing the IRT model-data fit, one of distinguished features of this package is that it gives not only item fit statistics (e.g., chi-square fit statistic (X2; e.g., Bock, 1960; Yen, 1981), likelihood ratio chi-square fit statistic (G2; McKinley & Mills, 1985), infit and outfit statistics (Ames et al., 2015), and S-X2 (Orlando & Thissen, 2000, 2003)) but also graphical displays to look at residuals between between the observed data and model-based predictions (Hambleton, Swaminathan, & Rogers, 1991). More evaluation methods will be included in the future updated version. In addition to the evaluation of IRT model-data fit, there are several useful functions such as estimating proficiency parameters, calibrating item parameters given the fixed effects (aka. ability values), computing asymptotic variance-covariance matrices of item parameter estimates, importing item and/or ability parameters from popular IRT software, generating simulated data, computing the conditional distribution of observed scores using the Lord-Wingersky recursion formula, computing item and test information functions, computing item and test characteristic curve functions, and plotting item and test characteristic curves and item and test information functions.
You can install the released version of irtplay from CRAN with:
One way to assess goodness of IRT model-data fit is through an item fit analysis by examining the traditional item fit statistics and looking at the discrepancy between the observed data and model-based predictions. Using irtplay package, the traditional approach of evaluating the IRT model-data fit on item-level can be implemented with three main steps:
irtfit function.irtfit) obtained in step 2, draw the IRT residual plots (i.e., raw residual and standardized residual plots) using plot method.Before conducting the IRT model fit analysis, it is necessary to prepare a data set. To run the irtfit function, it requires three data sets:
shape_df function or by creating a data.frame of the item meta data by yourself. If you have output files of item parameter estimates obtained from one of the IRT software such as BILOG-MG 3, PARSCALE 4, flexMIRT, and mirt (R package), the item meta data can be easily obtained using the functions of bring.bilog, bring.parscale, bring.flexmirt, bring.mirt. See the functions of irtfit, test.info, or simdat for more details about the item meta data format.The irtfit function computes the traditional IRT item fit statistics such as X2, G2, infit, and outfit statistics. To calculate the X2 and G2 statistics, two methods are available to divide the ability scale into several groups. The two methods are “equal.width” for dividing the scale by an equal length of the interval and “equal.freq” for dividing the scale by an equal frequency of examinees. Also, you need to specify the location of ability point at each group (or interval) where the expected probabilities of score categories are calculated from the IRT models. Available locations are “average” for computing the expected probability at the average point of examinees’ ability estimates in each group and “middle” for computing the expected probability at the midpoint of each group.
To use the irtfit function, you need to insert the item meta data in the argument x, the ability estimates in the argument score, and the response data in the argument data. If you want to divide the ability scale into other than ten groups, you need to specify the number of groups in the argument n.width. In addition, if the response data include missing values, you must indicate the missing value in argument missing.
Once the irtfit function has been implemented, you’ll get the fit statistic results and the contingency tables for every item used to calculate the X2 and G2 fit statistics.
Using the saved object of class irtfit, you can use the plot method to evaluate the IRT raw residual and standardized residual plots.
Because the plot method can draw the residual plots for an item at a time, you have to indicate which item will be examined. For this, you can specify an integer value, which is the location of the studied item, in the argument item.loc.
In terms of the raw residual plot, the argument ci.method is used to select a method to estimate the confidence intervals among four methods. Those methods are “wald” for the Wald interval, which is based on the normal approximation (Laplace, 1812), “cp” for Clopper-Pearson interval (Clopper & Pearson, 1934), “wilson” for Wilson score interval (Wilson, 1927), and “wilson.cr” for Wilson score interval with continuity correction (Newcombe, 1998).
The example code below shows how to prepare the data sets and how to conduct the IRT model-data fit analysis:
library(irtplay)
##----------------------------------------------------------------------------
## Step 1: prepare a data set for IRT
## In this example, we use the simulated mixed-item format CAT Data
## But, only items that have item responses more than 1,000 are assessed.
# find the location of items that have more than 1,000 item responses
over1000 <- which(colSums(simCAT_MX$res.dat, na.rm=TRUE) > 1000)
# (1) item meta data
x <- simCAT_MX$item.prm[over1000, ]
dim(x)
#> [1] 113 7
print(x[1:10, ])
#> id cats model par.1 par.2 par.3 par.4
#> 2 V2 2 2PLM 0.9152754 1.3843593 NA NA
#> 3 V3 2 2PLM 1.3454796 -1.2554919 NA NA
#> 5 V5 2 2PLM 1.0862914 1.7114409 NA NA
#> 6 V6 2 2PLM 1.1311496 -0.6029080 NA NA
#> 7 V7 2 2PLM 1.2012407 -0.4721664 NA NA
#> 8 V8 2 2PLM 1.3244155 -0.6353713 NA NA
#> 10 V10 2 2PLM 1.2487125 0.1381082 NA NA
#> 11 V11 2 2PLM 1.4413208 1.2276303 NA NA
#> 12 V12 2 2PLM 1.2077273 -0.8017795 NA NA
#> 13 V13 2 2PLM 1.1715456 -1.0803926 NA NA
# (2) examinee's ability estimates
score <- simCAT_MX$score
length(score)
#> [1] 30000
print(score[1:100])
#> [1] -0.30311440 -0.67224807 -0.73474583 1.76935738 -0.91017203
#> [6] -0.28448278 0.81656431 -1.66434615 0.59312008 -0.35182937
#> [11] 0.23129679 -0.93107524 -0.29971993 -0.32700449 -0.22271651
#> [16] 1.48912121 -0.92927809 0.43453041 -0.01795450 -0.28365286
#> [21] 0.01115173 -0.76101441 0.12144273 0.83096135 1.96600585
#> [26] -0.83510402 -0.40268865 -0.05605526 0.72398446 -0.16026059
#> [31] -1.09011778 1.22126764 -0.13340360 -1.28230720 -1.05581980
#> [36] 0.83484173 -0.52136360 -0.66913590 -1.08580804 1.73214834
#> [41] 0.56950387 0.48016332 -0.03472720 -2.17577824 0.44127032
#> [46] 0.98913071 1.43861714 -1.08133809 -0.69016072 0.19325797
#> [51] 0.89998383 1.25383167 -1.09600809 0.50519143 -0.51707395
#> [56] -0.39474484 -0.45031102 1.85675021 1.50768131 1.06011811
#> [61] -0.41064797 1.10960278 -0.68853387 -0.59397660 -0.65326436
#> [66] 0.29147751 -1.86787473 1.04838050 -1.14582092 1.07395234
#> [71] -0.03828693 0.08445559 0.34582524 0.72300905 0.84448992
#> [76] -1.86488055 0.77121937 1.66573208 0.10311673 -0.50768866
#> [81] -1.60992457 -0.23074682 0.16162326 0.26091160 0.60682182
#> [86] 0.65415304 -0.69923141 1.07545766 0.24060267 -0.93542383
#> [91] 1.24988766 -0.01826940 1.27403936 0.10985621 -1.19092047
#> [96] 0.79614598 0.62302338 -0.89455596 -0.03472720 0.20250837
# (3) response data
data <- simCAT_MX$res.dat[, over1000]
dim(data)
#> [1] 30000 113
print(data[1:20, 1:6])
#> Item.dc.2 Item.dc.3 Item.dc.5 Item.dc.6 Item.dc.7 Item.dc.8
#> [1,] NA NA NA NA 0 1
#> [2,] NA NA NA NA 0 1
#> [3,] NA NA NA NA 1 1
#> [4,] NA NA 0 NA NA NA
#> [5,] NA 1 NA 0 1 1
#> [6,] NA 0 NA 0 1 0
#> [7,] NA NA NA NA NA NA
#> [8,] NA 1 NA 1 1 0
#> [9,] NA NA 0 NA NA NA
#> [10,] NA 0 NA 1 1 0
#> [11,] NA NA 0 NA NA NA
#> [12,] NA 1 NA 0 1 1
#> [13,] NA 0 NA 1 1 0
#> [14,] NA NA NA NA 1 NA
#> [15,] NA NA NA 1 1 1
#> [16,] 1 NA 0 NA NA NA
#> [17,] NA 0 NA 0 1 0
#> [18,] NA NA NA NA NA NA
#> [19,] NA 0 NA 0 1 1
#> [20,] NA NA NA NA NA NA
##----------------------------------------------------------------------------
## Step 2: Compute the IRT mode-data fit statistics
# (1) the use of "equal.width"
fit1 <- irtfit(x=x, score=score, data=data, group.method="equal.width",
n.width=11, loc.theta="average", range.score=c(-4, 4), D=1, alpha=0.05,
missing=NA, overSR = 2.5)
# what kinds of internal objects does the results have?
names(fit1)
#> [1] "fit_stat" "contingency.fitstat" "contingency.plot"
#> [4] "item_df" "individual.info" "ancillary"
#> [7] "call"
# show the results of the fit statistics
fit1$fit_stat[1:10, ]
#> id X2 G2 df.X2 df.G2 crit.value.X2 crit.value.G2 p.value.X2
#> 1 V2 75.070 75.209 8 10 15.51 18.31 0
#> 2 V3 186.880 168.082 8 10 15.51 18.31 0
#> 3 V5 151.329 139.213 8 10 15.51 18.31 0
#> 4 V6 178.409 157.911 8 10 15.51 18.31 0
#> 5 V7 185.438 170.360 9 11 16.92 19.68 0
#> 6 V8 209.653 193.001 8 10 15.51 18.31 0
#> 7 V10 267.444 239.563 9 11 16.92 19.68 0
#> 8 V11 148.896 133.209 7 9 14.07 16.92 0
#> 9 V12 139.295 125.647 9 11 16.92 19.68 0
#> 10 V13 128.422 117.439 9 11 16.92 19.68 0
#> p.value.G2 outfit infit N overSR.prop
#> 1 0 1.018 1.016 2018 0.364
#> 2 0 1.124 1.090 11041 0.636
#> 3 0 1.133 1.111 5181 0.727
#> 4 0 1.056 1.045 13599 0.545
#> 5 0 1.078 1.059 18293 0.455
#> 6 0 1.098 1.075 16163 0.636
#> 7 0 1.097 1.073 19702 0.727
#> 8 0 1.129 1.083 13885 0.455
#> 9 0 1.065 1.051 12118 0.636
#> 10 0 1.075 1.059 10719 0.545
# show the contingency tables for the first item (dichotomous)
fit1$contingency.fitstat[[1]]
#> N freq.0 freq.1 obs.prop.0 obs.prop.1 exp.prob.0 exp.prob.1
#> 1 8 5 3 0.6250000 0.3750000 0.7627914 0.2372086
#> 2 14 8 6 0.5714286 0.4285714 0.7121079 0.2878921
#> 3 60 34 26 0.5666667 0.4333333 0.6708959 0.3291041
#> 4 185 99 86 0.5351351 0.4648649 0.6230537 0.3769463
#> 5 240 115 125 0.4791667 0.5208333 0.5765337 0.4234663
#> 6 349 145 204 0.4154728 0.5845272 0.5301760 0.4698240
#> 7 325 114 211 0.3507692 0.6492308 0.4784096 0.5215904
#> 8 246 82 164 0.3333333 0.6666667 0.4419993 0.5580007
#> 9 377 139 238 0.3687003 0.6312997 0.4086532 0.5913468
#> 10 214 78 136 0.3644860 0.6355140 0.3394647 0.6605353
#> raw_resid.0 raw_resid.1
#> 1 -0.13779141 0.13779141
#> 2 -0.14067932 0.14067932
#> 3 -0.10422928 0.10422928
#> 4 -0.08791853 0.08791853
#> 5 -0.09736699 0.09736699
#> 6 -0.11470327 0.11470327
#> 7 -0.12764036 0.12764036
#> 8 -0.10866594 0.10866594
#> 9 -0.03995295 0.03995295
#> 10 0.02502128 -0.02502128
# (2) the use of "equal.freq"
fit2 <- irtfit(x=x, score=score, data=data, group.method="equal.freq",
n.width=11, loc.theta="average", range.score=c(-4, 4), D=1, alpha=0.05,
missing=NA)
# show the results of the fit statistics
fit2$fit_stat[1:10, ]
#> id X2 G2 df.X2 df.G2 crit.value.X2 crit.value.G2 p.value.X2
#> 1 V2 77.967 78.144 9 11 16.92 19.68 0
#> 2 V3 202.035 181.832 9 11 16.92 19.68 0
#> 3 V5 146.383 135.908 9 11 16.92 19.68 0
#> 4 V6 140.038 133.287 9 11 16.92 19.68 0
#> 5 V7 188.814 177.526 9 11 16.92 19.68 0
#> 6 V8 211.279 196.328 9 11 16.92 19.68 0
#> 7 V10 259.669 239.292 9 11 16.92 19.68 0
#> 8 V11 166.427 150.419 9 11 16.92 19.68 0
#> 9 V12 145.789 134.690 9 11 16.92 19.68 0
#> 10 V13 141.283 132.270 9 11 16.92 19.68 0
#> p.value.G2 outfit infit N overSR.prop
#> 1 0 1.018 1.016 2018 0.727
#> 2 0 1.124 1.090 11041 0.636
#> 3 0 1.133 1.111 5181 0.727
#> 4 0 1.056 1.045 13599 0.545
#> 5 0 1.078 1.059 18293 0.455
#> 6 0 1.098 1.075 16163 0.545
#> 7 0 1.097 1.073 19702 0.636
#> 8 0 1.129 1.083 13885 0.636
#> 9 0 1.065 1.051 12118 0.364
#> 10 0 1.075 1.059 10719 0.636
# show the contingency table for the fourth item (polytomous)
fit2$contingency.fitstat[[4]]
#> N freq.0 freq.1 obs.prop.0 obs.prop.1 exp.prob.0 exp.prob.1
#> 1 1241 967 274 0.7792103 0.2207897 0.8038510 0.1961490
#> 2 1243 879 364 0.7071601 0.2928399 0.7161793 0.2838207
#> 3 1243 784 459 0.6307321 0.3692679 0.6575849 0.3424151
#> 4 1219 747 472 0.6127974 0.3872026 0.6049393 0.3950607
#> 5 1236 705 531 0.5703883 0.4296117 0.5613454 0.4386546
#> 6 1243 677 566 0.5446500 0.4553500 0.5279560 0.4720440
#> 7 1270 662 608 0.5212598 0.4787402 0.4925592 0.5074408
#> 8 1230 616 614 0.5008130 0.4991870 0.4491759 0.5508241
#> 9 1207 553 654 0.4581607 0.5418393 0.4027790 0.5972210
#> 10 1233 494 739 0.4006488 0.5993512 0.3509261 0.6490739
#> 11 1234 465 769 0.3768233 0.6231767 0.2630181 0.7369819
#> raw_resid.0 raw_resid.1
#> 1 -0.024640641 0.024640641
#> 2 -0.009019180 0.009019180
#> 3 -0.026852795 0.026852795
#> 4 0.007858099 -0.007858099
#> 5 0.009042942 -0.009042942
#> 6 0.016694048 -0.016694048
#> 7 0.028700633 -0.028700633
#> 8 0.051637085 -0.051637085
#> 9 0.055381721 -0.055381721
#> 10 0.049722759 -0.049722759
#> 11 0.113805214 -0.113805214
##----------------------------------------------------------------------------
## Step 3: Draw the IRT residual plots
# 1. the dichotomous item
# (1) both raw and standardized residual plots using the object "fit1"
plot(x=fit1, item.loc=1, type = "both", ci.method = "wald", ylim.sr.adjust=TRUE)
#> theta N freq.0 freq.1 obs.prop.0
#> [-0.1218815,0.08512996] -0.02529272 3 3 0 1.0000000
#> (0.08512996,0.2921415] 0.18431014 5 2 3 0.4000000
#> (0.2921415,0.499153] 0.39488272 14 8 6 0.5714286
#> (0.499153,0.7061645] 0.60618911 60 34 26 0.5666667
#> (0.7061645,0.913176] 0.83531169 185 99 86 0.5351351
#> (0.913176,1.120187] 1.04723712 240 115 125 0.4791667
#> (1.120187,1.327199] 1.25232143 349 145 204 0.4154728
#> (1.327199,1.53421] 1.47877397 325 114 211 0.3507692
#> (1.53421,1.741222] 1.63898436 246 82 164 0.3333333
#> (1.741222,1.948233] 1.78810197 377 139 238 0.3687003
#> (1.948233,2.155245] 2.11166019 214 78 136 0.3644860
#> obs.prop.1 exp.prob.0 exp.prob.1 raw_resid.0
#> [-0.1218815,0.08512996] 0.0000000 0.7841844 0.2158156 0.21581559
#> (0.08512996,0.2921415] 0.6000000 0.7499556 0.2500444 -0.34995561
#> (0.2921415,0.499153] 0.4285714 0.7121079 0.2878921 -0.14067932
#> (0.499153,0.7061645] 0.4333333 0.6708959 0.3291041 -0.10422928
#> (0.7061645,0.913176] 0.4648649 0.6230537 0.3769463 -0.08791853
#> (0.913176,1.120187] 0.5208333 0.5765337 0.4234663 -0.09736699
#> (1.120187,1.327199] 0.5845272 0.5301760 0.4698240 -0.11470327
#> (1.327199,1.53421] 0.6492308 0.4784096 0.5215904 -0.12764036
#> (1.53421,1.741222] 0.6666667 0.4419993 0.5580007 -0.10866594
#> (1.741222,1.948233] 0.6312997 0.4086532 0.5913468 -0.03995295
#> (1.948233,2.155245] 0.6355140 0.3394647 0.6605353 0.02502128
#> raw_resid.1 se.0 se.1 std_resid.0
#> [-0.1218815,0.08512996] -0.21581559 0.23751437 0.23751437 0.9086423
#> (0.08512996,0.2921415] 0.34995561 0.19366063 0.19366063 -1.8070560
#> (0.2921415,0.499153] 0.14067932 0.12101070 0.12101070 -1.1625362
#> (0.499153,0.7061645] 0.10422928 0.06066226 0.06066226 -1.7181899
#> (0.7061645,0.913176] 0.08791853 0.03563007 0.03563007 -2.4675377
#> (0.913176,1.120187] 0.09736699 0.03189453 0.03189453 -3.0527806
#> (1.120187,1.327199] 0.11470327 0.02671560 0.02671560 -4.2934941
#> (1.327199,1.53421] 0.12764036 0.02770914 0.02770914 -4.6064351
#> (1.53421,1.741222] 0.10866594 0.03166362 0.03166362 -3.4318859
#> (1.741222,1.948233] 0.03995295 0.02531791 0.02531791 -1.5780508
#> (1.948233,2.155245] -0.02502128 0.03236968 0.03236968 0.7729850
#> std_resid.1 raw.resid.0 raw.resid.1 se.0.1
#> [-0.1218815,0.08512996] -0.9086423 0.21581559 -0.21581559 0.23751437
#> (0.08512996,0.2921415] 1.8070560 -0.34995561 0.34995561 0.19366063
#> (0.2921415,0.499153] 1.1625362 -0.14067932 0.14067932 0.12101070
#> (0.499153,0.7061645] 1.7181899 -0.10422928 0.10422928 0.06066226
#> (0.7061645,0.913176] 2.4675377 -0.08791853 0.08791853 0.03563007
#> (0.913176,1.120187] 3.0527806 -0.09736699 0.09736699 0.03189453
#> (1.120187,1.327199] 4.2934941 -0.11470327 0.11470327 0.02671560
#> (1.327199,1.53421] 4.6064351 -0.12764036 0.12764036 0.02770914
#> (1.53421,1.741222] 3.4318859 -0.10866594 0.10866594 0.03166362
#> (1.741222,1.948233] 1.5780508 -0.03995295 0.03995295 0.02531791
#> (1.948233,2.155245] -0.7729850 0.02502128 -0.02502128 0.03236968
#> se.1.1 std.resid.0 std.resid.1
#> [-0.1218815,0.08512996] 0.23751437 0.9086423 -0.9086423
#> (0.08512996,0.2921415] 0.19366063 -1.8070560 1.8070560
#> (0.2921415,0.499153] 0.12101070 -1.1625362 1.1625362
#> (0.499153,0.7061645] 0.06066226 -1.7181899 1.7181899
#> (0.7061645,0.913176] 0.03563007 -2.4675377 2.4675377
#> (0.913176,1.120187] 0.03189453 -3.0527806 3.0527806
#> (1.120187,1.327199] 0.02671560 -4.2934941 4.2934941
#> (1.327199,1.53421] 0.02770914 -4.6064351 4.6064351
#> (1.53421,1.741222] 0.03166362 -3.4318859 3.4318859
#> (1.741222,1.948233] 0.02531791 -1.5780508 1.5780508
#> (1.948233,2.155245] 0.03236968 0.7729850 -0.7729850
# (2) the raw residual plots using the object "fit1"
plot(x=fit1, item.loc=1, type = "icc", ci.method = "wald", ylim.sr.adjust=TRUE)
#> theta N freq.0 freq.1 obs.prop.0
#> [-0.1218815,0.08512996] -0.02529272 3 3 0 1.0000000
#> (0.08512996,0.2921415] 0.18431014 5 2 3 0.4000000
#> (0.2921415,0.499153] 0.39488272 14 8 6 0.5714286
#> (0.499153,0.7061645] 0.60618911 60 34 26 0.5666667
#> (0.7061645,0.913176] 0.83531169 185 99 86 0.5351351
#> (0.913176,1.120187] 1.04723712 240 115 125 0.4791667
#> (1.120187,1.327199] 1.25232143 349 145 204 0.4154728
#> (1.327199,1.53421] 1.47877397 325 114 211 0.3507692
#> (1.53421,1.741222] 1.63898436 246 82 164 0.3333333
#> (1.741222,1.948233] 1.78810197 377 139 238 0.3687003
#> (1.948233,2.155245] 2.11166019 214 78 136 0.3644860
#> obs.prop.1 exp.prob.0 exp.prob.1 raw_resid.0
#> [-0.1218815,0.08512996] 0.0000000 0.7841844 0.2158156 0.21581559
#> (0.08512996,0.2921415] 0.6000000 0.7499556 0.2500444 -0.34995561
#> (0.2921415,0.499153] 0.4285714 0.7121079 0.2878921 -0.14067932
#> (0.499153,0.7061645] 0.4333333 0.6708959 0.3291041 -0.10422928
#> (0.7061645,0.913176] 0.4648649 0.6230537 0.3769463 -0.08791853
#> (0.913176,1.120187] 0.5208333 0.5765337 0.4234663 -0.09736699
#> (1.120187,1.327199] 0.5845272 0.5301760 0.4698240 -0.11470327
#> (1.327199,1.53421] 0.6492308 0.4784096 0.5215904 -0.12764036
#> (1.53421,1.741222] 0.6666667 0.4419993 0.5580007 -0.10866594
#> (1.741222,1.948233] 0.6312997 0.4086532 0.5913468 -0.03995295
#> (1.948233,2.155245] 0.6355140 0.3394647 0.6605353 0.02502128
#> raw_resid.1 se.0 se.1 std_resid.0
#> [-0.1218815,0.08512996] -0.21581559 0.23751437 0.23751437 0.9086423
#> (0.08512996,0.2921415] 0.34995561 0.19366063 0.19366063 -1.8070560
#> (0.2921415,0.499153] 0.14067932 0.12101070 0.12101070 -1.1625362
#> (0.499153,0.7061645] 0.10422928 0.06066226 0.06066226 -1.7181899
#> (0.7061645,0.913176] 0.08791853 0.03563007 0.03563007 -2.4675377
#> (0.913176,1.120187] 0.09736699 0.03189453 0.03189453 -3.0527806
#> (1.120187,1.327199] 0.11470327 0.02671560 0.02671560 -4.2934941
#> (1.327199,1.53421] 0.12764036 0.02770914 0.02770914 -4.6064351
#> (1.53421,1.741222] 0.10866594 0.03166362 0.03166362 -3.4318859
#> (1.741222,1.948233] 0.03995295 0.02531791 0.02531791 -1.5780508
#> (1.948233,2.155245] -0.02502128 0.03236968 0.03236968 0.7729850
#> std_resid.1 raw.resid.0 raw.resid.1 se.0.1
#> [-0.1218815,0.08512996] -0.9086423 0.21581559 -0.21581559 0.23751437
#> (0.08512996,0.2921415] 1.8070560 -0.34995561 0.34995561 0.19366063
#> (0.2921415,0.499153] 1.1625362 -0.14067932 0.14067932 0.12101070
#> (0.499153,0.7061645] 1.7181899 -0.10422928 0.10422928 0.06066226
#> (0.7061645,0.913176] 2.4675377 -0.08791853 0.08791853 0.03563007
#> (0.913176,1.120187] 3.0527806 -0.09736699 0.09736699 0.03189453
#> (1.120187,1.327199] 4.2934941 -0.11470327 0.11470327 0.02671560
#> (1.327199,1.53421] 4.6064351 -0.12764036 0.12764036 0.02770914
#> (1.53421,1.741222] 3.4318859 -0.10866594 0.10866594 0.03166362
#> (1.741222,1.948233] 1.5780508 -0.03995295 0.03995295 0.02531791
#> (1.948233,2.155245] -0.7729850 0.02502128 -0.02502128 0.03236968
#> se.1.1 std.resid.0 std.resid.1
#> [-0.1218815,0.08512996] 0.23751437 0.9086423 -0.9086423
#> (0.08512996,0.2921415] 0.19366063 -1.8070560 1.8070560
#> (0.2921415,0.499153] 0.12101070 -1.1625362 1.1625362
#> (0.499153,0.7061645] 0.06066226 -1.7181899 1.7181899
#> (0.7061645,0.913176] 0.03563007 -2.4675377 2.4675377
#> (0.913176,1.120187] 0.03189453 -3.0527806 3.0527806
#> (1.120187,1.327199] 0.02671560 -4.2934941 4.2934941
#> (1.327199,1.53421] 0.02770914 -4.6064351 4.6064351
#> (1.53421,1.741222] 0.03166362 -3.4318859 3.4318859
#> (1.741222,1.948233] 0.02531791 -1.5780508 1.5780508
#> (1.948233,2.155245] 0.03236968 0.7729850 -0.7729850
# (3) the standardized residual plots using the object "fit1"
plot(x=fit1, item.loc=113, type = "sr", ci.method = "wald", ylim.sr.adjust=TRUE)
#> theta N freq.0 freq.1 freq.2 freq.3 obs.prop.0
#> [0.3564295,0.5199582] 0.3564295 1 1 0 0 0 1.00000000
#> (0.5199582,0.6834869] 0.6081321 5 3 2 0 0 0.60000000
#> (0.6834869,0.8470155] 0.7400138 15 5 10 0 0 0.33333333
#> (0.8470155,1.010544] 0.8866202 55 5 15 34 1 0.09090909
#> (1.010544,1.174073] 1.0821064 133 6 40 53 34 0.04511278
#> (1.174073,1.337602] 1.2832293 260 8 37 153 62 0.03076923
#> (1.337602,1.50113] 1.4747336 98 0 23 57 18 0.00000000
#> (1.50113,1.664659] 1.5311735 306 0 7 85 214 0.00000000
#> (1.664659,1.828188] 1.7632607 418 0 0 145 273 0.00000000
#> (1.828188,1.991716] 1.8577191 69 0 0 0 69 0.00000000
#> (1.991716,2.155245] 2.1021956 263 0 0 0 263 0.00000000
#> obs.prop.1 obs.prop.2 obs.prop.3 exp.prob.0
#> [0.3564295,0.5199582] 0.00000000 0.0000000 0.00000000 0.196511833
#> (0.5199582,0.6834869] 0.40000000 0.0000000 0.00000000 0.130431315
#> (0.6834869,0.8470155] 0.66666667 0.0000000 0.00000000 0.102631449
#> (0.8470155,1.010544] 0.27272727 0.6181818 0.01818182 0.077129446
#> (1.010544,1.174073] 0.30075188 0.3984962 0.25563910 0.051169395
#> (1.174073,1.337602] 0.14230769 0.5884615 0.23846154 0.032494074
#> (1.337602,1.50113] 0.23469388 0.5816327 0.18367347 0.020534959
#> (1.50113,1.664659] 0.02287582 0.2777778 0.69934641 0.017857642
#> (1.664659,1.828188] 0.00000000 0.3468900 0.65311005 0.009866868
#> (1.828188,1.991716] 0.00000000 0.0000000 1.00000000 0.007690015
#> (1.991716,2.155245] 0.00000000 0.0000000 1.00000000 0.003962699
#> exp.prob.1 exp.prob.2 exp.prob.3 raw_resid.0
#> [0.3564295,0.5199582] 0.31299790 0.3472692 0.1432210 0.803488167
#> (0.5199582,0.6834869] 0.27025065 0.3900531 0.2092649 0.469568685
#> (0.6834869,0.8470155] 0.24407213 0.4043226 0.2489738 0.230701885
#> (0.8470155,1.010544] 0.21379299 0.4127992 0.2962784 0.013779645
#> (1.010544,1.174073] 0.17398130 0.4120662 0.3627831 -0.006056613
#> (1.174073,1.337602] 0.13632441 0.3983962 0.4327853 -0.001724843
#> (1.337602,1.50113] 0.10523862 0.3756891 0.4985373 -0.020534959
#> (1.50113,1.664659] 0.09707782 0.3676106 0.5174539 -0.017857642
#> (1.664659,1.828188] 0.06836048 0.3299158 0.5918569 -0.009866868
#> (1.828188,1.991716] 0.05880602 0.3132481 0.6202558 -0.007690015
#> (1.991716,2.155245] 0.03912356 0.2690653 0.6878484 -0.003962699
#> raw_resid.1 raw_resid.2 raw_resid.3 se.0
#> [0.3564295,0.5199582] -0.312997903 -0.34726922 -0.14322104 0.397359953
#> (0.5199582,0.6834869] 0.129749354 -0.39005312 -0.20926492 0.150611412
#> (0.6834869,0.8470155] 0.422594537 -0.40432265 -0.24897378 0.078357401
#> (0.8470155,1.010544] 0.058934282 0.20538261 -0.27809653 0.035974863
#> (1.010544,1.174073] 0.126770584 -0.01356995 -0.10714402 0.019106171
#> (1.174073,1.337602] 0.005983284 0.19006531 -0.19432375 0.010996190
#> (1.337602,1.50113] 0.129455259 0.20594357 -0.31486387 0.014326112
#> (1.50113,1.664659] -0.074201998 -0.08983281 0.18189246 0.007570744
#> (1.664659,1.828188] -0.068360484 0.01697418 0.06125317 0.004834464
#> (1.828188,1.991716] -0.058806016 -0.31324812 0.37974416 0.010516294
#> (1.991716,2.155245] -0.039123555 -0.26906531 0.31215156 0.003873963
#> se.1 se.2 se.3 std_resid.0
#> [0.3564295,0.5199582] 0.46371351 0.47610220 0.35029812 2.0220663
#> (0.5199582,0.6834869] 0.19860274 0.21813376 0.18191928 3.1177497
#> (0.6834869,0.8470155] 0.11090564 0.12671381 0.11165000 2.9442258
#> (0.8470155,1.010544] 0.05528201 0.06638675 0.06156999 0.3830354
#> (1.010544,1.174073] 0.03287157 0.04267975 0.04169091 -0.3169978
#> (1.174073,1.337602] 0.02128019 0.03036171 0.03072722 -0.1568583
#> (1.337602,1.50113] 0.03099761 0.04892172 0.05050741 -1.4333937
#> (1.50113,1.664659] 0.01692484 0.02756294 0.02856568 -2.3587698
#> (1.664659,1.828188] 0.01234350 0.02299737 0.02403956 -2.0409436
#> (1.828188,1.991716] 0.02832213 0.05583668 0.05842604 -0.7312476
#> (1.991716,2.155245] 0.01195570 0.02734578 0.02857270 -1.0229057
#> std_resid.1 std_resid.2 std_resid.3 raw.resid.0
#> [0.3564295,0.5199582] -0.6749812 -0.7294006 -0.4088547 0.803488167
#> (0.5199582,0.6834869] 0.6533110 -1.7881373 -1.1503175 0.469568685
#> (0.6834869,0.8470155] 3.8103971 -3.1908333 -2.2299488 0.230701885
#> (0.8470155,1.010544] 1.0660662 3.0937290 -4.5167547 0.013779645
#> (1.010544,1.174073] 3.8565422 -0.3179482 -2.5699613 -0.006056613
#> (1.174073,1.337602] 0.2811669 6.2600333 -6.3241558 -0.001724843
#> (1.337602,1.50113] 4.1762987 4.2096551 -6.2340132 -0.020534959
#> (1.50113,1.664659] -4.3842081 -3.2591881 6.3675177 -0.017857642
#> (1.664659,1.828188] -5.5381760 0.7380923 2.5480159 -0.009866868
#> (1.828188,1.991716] -2.0763275 -5.6100775 6.4995706 -0.007690015
#> (1.991716,2.155245] -3.2723764 -9.8393733 10.9248190 -0.003962699
#> raw.resid.1 raw.resid.2 raw.resid.3 se.0.1
#> [0.3564295,0.5199582] -0.312997903 -0.34726922 -0.14322104 0.397359953
#> (0.5199582,0.6834869] 0.129749354 -0.39005312 -0.20926492 0.150611412
#> (0.6834869,0.8470155] 0.422594537 -0.40432265 -0.24897378 0.078357401
#> (0.8470155,1.010544] 0.058934282 0.20538261 -0.27809653 0.035974863
#> (1.010544,1.174073] 0.126770584 -0.01356995 -0.10714402 0.019106171
#> (1.174073,1.337602] 0.005983284 0.19006531 -0.19432375 0.010996190
#> (1.337602,1.50113] 0.129455259 0.20594357 -0.31486387 0.014326112
#> (1.50113,1.664659] -0.074201998 -0.08983281 0.18189246 0.007570744
#> (1.664659,1.828188] -0.068360484 0.01697418 0.06125317 0.004834464
#> (1.828188,1.991716] -0.058806016 -0.31324812 0.37974416 0.010516294
#> (1.991716,2.155245] -0.039123555 -0.26906531 0.31215156 0.003873963
#> se.1.1 se.2.1 se.3.1 std.resid.0
#> [0.3564295,0.5199582] 0.46371351 0.47610220 0.35029812 2.0220663
#> (0.5199582,0.6834869] 0.19860274 0.21813376 0.18191928 3.1177497
#> (0.6834869,0.8470155] 0.11090564 0.12671381 0.11165000 2.9442258
#> (0.8470155,1.010544] 0.05528201 0.06638675 0.06156999 0.3830354
#> (1.010544,1.174073] 0.03287157 0.04267975 0.04169091 -0.3169978
#> (1.174073,1.337602] 0.02128019 0.03036171 0.03072722 -0.1568583
#> (1.337602,1.50113] 0.03099761 0.04892172 0.05050741 -1.4333937
#> (1.50113,1.664659] 0.01692484 0.02756294 0.02856568 -2.3587698
#> (1.664659,1.828188] 0.01234350 0.02299737 0.02403956 -2.0409436
#> (1.828188,1.991716] 0.02832213 0.05583668 0.05842604 -0.7312476
#> (1.991716,2.155245] 0.01195570 0.02734578 0.02857270 -1.0229057
#> std.resid.1 std.resid.2 std.resid.3
#> [0.3564295,0.5199582] -0.6749812 -0.7294006 -0.4088547
#> (0.5199582,0.6834869] 0.6533110 -1.7881373 -1.1503175
#> (0.6834869,0.8470155] 3.8103971 -3.1908333 -2.2299488
#> (0.8470155,1.010544] 1.0660662 3.0937290 -4.5167547
#> (1.010544,1.174073] 3.8565422 -0.3179482 -2.5699613
#> (1.174073,1.337602] 0.2811669 6.2600333 -6.3241558
#> (1.337602,1.50113] 4.1762987 4.2096551 -6.2340132
#> (1.50113,1.664659] -4.3842081 -3.2591881 6.3675177
#> (1.664659,1.828188] -5.5381760 0.7380923 2.5480159
#> (1.828188,1.991716] -2.0763275 -5.6100775 6.4995706
#> (1.991716,2.155245] -3.2723764 -9.8393733 10.9248190
# 2. the polytomous item
# (1) both raw and standardized residual plots using the object "fit1"
plot(x=fit1, item.loc=113, type = "both", ci.method = "wald", ylim.sr.adjust=TRUE)
#> theta N freq.0 freq.1 freq.2 freq.3 obs.prop.0
#> [0.3564295,0.5199582] 0.3564295 1 1 0 0 0 1.00000000
#> (0.5199582,0.6834869] 0.6081321 5 3 2 0 0 0.60000000
#> (0.6834869,0.8470155] 0.7400138 15 5 10 0 0 0.33333333
#> (0.8470155,1.010544] 0.8866202 55 5 15 34 1 0.09090909
#> (1.010544,1.174073] 1.0821064 133 6 40 53 34 0.04511278
#> (1.174073,1.337602] 1.2832293 260 8 37 153 62 0.03076923
#> (1.337602,1.50113] 1.4747336 98 0 23 57 18 0.00000000
#> (1.50113,1.664659] 1.5311735 306 0 7 85 214 0.00000000
#> (1.664659,1.828188] 1.7632607 418 0 0 145 273 0.00000000
#> (1.828188,1.991716] 1.8577191 69 0 0 0 69 0.00000000
#> (1.991716,2.155245] 2.1021956 263 0 0 0 263 0.00000000
#> obs.prop.1 obs.prop.2 obs.prop.3 exp.prob.0
#> [0.3564295,0.5199582] 0.00000000 0.0000000 0.00000000 0.196511833
#> (0.5199582,0.6834869] 0.40000000 0.0000000 0.00000000 0.130431315
#> (0.6834869,0.8470155] 0.66666667 0.0000000 0.00000000 0.102631449
#> (0.8470155,1.010544] 0.27272727 0.6181818 0.01818182 0.077129446
#> (1.010544,1.174073] 0.30075188 0.3984962 0.25563910 0.051169395
#> (1.174073,1.337602] 0.14230769 0.5884615 0.23846154 0.032494074
#> (1.337602,1.50113] 0.23469388 0.5816327 0.18367347 0.020534959
#> (1.50113,1.664659] 0.02287582 0.2777778 0.69934641 0.017857642
#> (1.664659,1.828188] 0.00000000 0.3468900 0.65311005 0.009866868
#> (1.828188,1.991716] 0.00000000 0.0000000 1.00000000 0.007690015
#> (1.991716,2.155245] 0.00000000 0.0000000 1.00000000 0.003962699
#> exp.prob.1 exp.prob.2 exp.prob.3 raw_resid.0
#> [0.3564295,0.5199582] 0.31299790 0.3472692 0.1432210 0.803488167
#> (0.5199582,0.6834869] 0.27025065 0.3900531 0.2092649 0.469568685
#> (0.6834869,0.8470155] 0.24407213 0.4043226 0.2489738 0.230701885
#> (0.8470155,1.010544] 0.21379299 0.4127992 0.2962784 0.013779645
#> (1.010544,1.174073] 0.17398130 0.4120662 0.3627831 -0.006056613
#> (1.174073,1.337602] 0.13632441 0.3983962 0.4327853 -0.001724843
#> (1.337602,1.50113] 0.10523862 0.3756891 0.4985373 -0.020534959
#> (1.50113,1.664659] 0.09707782 0.3676106 0.5174539 -0.017857642
#> (1.664659,1.828188] 0.06836048 0.3299158 0.5918569 -0.009866868
#> (1.828188,1.991716] 0.05880602 0.3132481 0.6202558 -0.007690015
#> (1.991716,2.155245] 0.03912356 0.2690653 0.6878484 -0.003962699
#> raw_resid.1 raw_resid.2 raw_resid.3 se.0
#> [0.3564295,0.5199582] -0.312997903 -0.34726922 -0.14322104 0.397359953
#> (0.5199582,0.6834869] 0.129749354 -0.39005312 -0.20926492 0.150611412
#> (0.6834869,0.8470155] 0.422594537 -0.40432265 -0.24897378 0.078357401
#> (0.8470155,1.010544] 0.058934282 0.20538261 -0.27809653 0.035974863
#> (1.010544,1.174073] 0.126770584 -0.01356995 -0.10714402 0.019106171
#> (1.174073,1.337602] 0.005983284 0.19006531 -0.19432375 0.010996190
#> (1.337602,1.50113] 0.129455259 0.20594357 -0.31486387 0.014326112
#> (1.50113,1.664659] -0.074201998 -0.08983281 0.18189246 0.007570744
#> (1.664659,1.828188] -0.068360484 0.01697418 0.06125317 0.004834464
#> (1.828188,1.991716] -0.058806016 -0.31324812 0.37974416 0.010516294
#> (1.991716,2.155245] -0.039123555 -0.26906531 0.31215156 0.003873963
#> se.1 se.2 se.3 std_resid.0
#> [0.3564295,0.5199582] 0.46371351 0.47610220 0.35029812 2.0220663
#> (0.5199582,0.6834869] 0.19860274 0.21813376 0.18191928 3.1177497
#> (0.6834869,0.8470155] 0.11090564 0.12671381 0.11165000 2.9442258
#> (0.8470155,1.010544] 0.05528201 0.06638675 0.06156999 0.3830354
#> (1.010544,1.174073] 0.03287157 0.04267975 0.04169091 -0.3169978
#> (1.174073,1.337602] 0.02128019 0.03036171 0.03072722 -0.1568583
#> (1.337602,1.50113] 0.03099761 0.04892172 0.05050741 -1.4333937
#> (1.50113,1.664659] 0.01692484 0.02756294 0.02856568 -2.3587698
#> (1.664659,1.828188] 0.01234350 0.02299737 0.02403956 -2.0409436
#> (1.828188,1.991716] 0.02832213 0.05583668 0.05842604 -0.7312476
#> (1.991716,2.155245] 0.01195570 0.02734578 0.02857270 -1.0229057
#> std_resid.1 std_resid.2 std_resid.3 raw.resid.0
#> [0.3564295,0.5199582] -0.6749812 -0.7294006 -0.4088547 0.803488167
#> (0.5199582,0.6834869] 0.6533110 -1.7881373 -1.1503175 0.469568685
#> (0.6834869,0.8470155] 3.8103971 -3.1908333 -2.2299488 0.230701885
#> (0.8470155,1.010544] 1.0660662 3.0937290 -4.5167547 0.013779645
#> (1.010544,1.174073] 3.8565422 -0.3179482 -2.5699613 -0.006056613
#> (1.174073,1.337602] 0.2811669 6.2600333 -6.3241558 -0.001724843
#> (1.337602,1.50113] 4.1762987 4.2096551 -6.2340132 -0.020534959
#> (1.50113,1.664659] -4.3842081 -3.2591881 6.3675177 -0.017857642
#> (1.664659,1.828188] -5.5381760 0.7380923 2.5480159 -0.009866868
#> (1.828188,1.991716] -2.0763275 -5.6100775 6.4995706 -0.007690015
#> (1.991716,2.155245] -3.2723764 -9.8393733 10.9248190 -0.003962699
#> raw.resid.1 raw.resid.2 raw.resid.3 se.0.1
#> [0.3564295,0.5199582] -0.312997903 -0.34726922 -0.14322104 0.397359953
#> (0.5199582,0.6834869] 0.129749354 -0.39005312 -0.20926492 0.150611412
#> (0.6834869,0.8470155] 0.422594537 -0.40432265 -0.24897378 0.078357401
#> (0.8470155,1.010544] 0.058934282 0.20538261 -0.27809653 0.035974863
#> (1.010544,1.174073] 0.126770584 -0.01356995 -0.10714402 0.019106171
#> (1.174073,1.337602] 0.005983284 0.19006531 -0.19432375 0.010996190
#> (1.337602,1.50113] 0.129455259 0.20594357 -0.31486387 0.014326112
#> (1.50113,1.664659] -0.074201998 -0.08983281 0.18189246 0.007570744
#> (1.664659,1.828188] -0.068360484 0.01697418 0.06125317 0.004834464
#> (1.828188,1.991716] -0.058806016 -0.31324812 0.37974416 0.010516294
#> (1.991716,2.155245] -0.039123555 -0.26906531 0.31215156 0.003873963
#> se.1.1 se.2.1 se.3.1 std.resid.0
#> [0.3564295,0.5199582] 0.46371351 0.47610220 0.35029812 2.0220663
#> (0.5199582,0.6834869] 0.19860274 0.21813376 0.18191928 3.1177497
#> (0.6834869,0.8470155] 0.11090564 0.12671381 0.11165000 2.9442258
#> (0.8470155,1.010544] 0.05528201 0.06638675 0.06156999 0.3830354
#> (1.010544,1.174073] 0.03287157 0.04267975 0.04169091 -0.3169978
#> (1.174073,1.337602] 0.02128019 0.03036171 0.03072722 -0.1568583
#> (1.337602,1.50113] 0.03099761 0.04892172 0.05050741 -1.4333937
#> (1.50113,1.664659] 0.01692484 0.02756294 0.02856568 -2.3587698
#> (1.664659,1.828188] 0.01234350 0.02299737 0.02403956 -2.0409436
#> (1.828188,1.991716] 0.02832213 0.05583668 0.05842604 -0.7312476
#> (1.991716,2.155245] 0.01195570 0.02734578 0.02857270 -1.0229057
#> std.resid.1 std.resid.2 std.resid.3
#> [0.3564295,0.5199582] -0.6749812 -0.7294006 -0.4088547
#> (0.5199582,0.6834869] 0.6533110 -1.7881373 -1.1503175
#> (0.6834869,0.8470155] 3.8103971 -3.1908333 -2.2299488
#> (0.8470155,1.010544] 1.0660662 3.0937290 -4.5167547
#> (1.010544,1.174073] 3.8565422 -0.3179482 -2.5699613
#> (1.174073,1.337602] 0.2811669 6.2600333 -6.3241558
#> (1.337602,1.50113] 4.1762987 4.2096551 -6.2340132
#> (1.50113,1.664659] -4.3842081 -3.2591881 6.3675177
#> (1.664659,1.828188] -5.5381760 0.7380923 2.5480159
#> (1.828188,1.991716] -2.0763275 -5.6100775 6.4995706
#> (1.991716,2.155245] -3.2723764 -9.8393733 10.9248190
# (2) the raw residual plots using the object "fit1"
plot(x=fit1, item.loc=113, type = "icc", ci.method = "wald", layout.col=2, ylim.sr.adjust=TRUE)
#> theta N freq.0 freq.1 freq.2 freq.3 obs.prop.0
#> [0.3564295,0.5199582] 0.3564295 1 1 0 0 0 1.00000000
#> (0.5199582,0.6834869] 0.6081321 5 3 2 0 0 0.60000000
#> (0.6834869,0.8470155] 0.7400138 15 5 10 0 0 0.33333333
#> (0.8470155,1.010544] 0.8866202 55 5 15 34 1 0.09090909
#> (1.010544,1.174073] 1.0821064 133 6 40 53 34 0.04511278
#> (1.174073,1.337602] 1.2832293 260 8 37 153 62 0.03076923
#> (1.337602,1.50113] 1.4747336 98 0 23 57 18 0.00000000
#> (1.50113,1.664659] 1.5311735 306 0 7 85 214 0.00000000
#> (1.664659,1.828188] 1.7632607 418 0 0 145 273 0.00000000
#> (1.828188,1.991716] 1.8577191 69 0 0 0 69 0.00000000
#> (1.991716,2.155245] 2.1021956 263 0 0 0 263 0.00000000
#> obs.prop.1 obs.prop.2 obs.prop.3 exp.prob.0
#> [0.3564295,0.5199582] 0.00000000 0.0000000 0.00000000 0.196511833
#> (0.5199582,0.6834869] 0.40000000 0.0000000 0.00000000 0.130431315
#> (0.6834869,0.8470155] 0.66666667 0.0000000 0.00000000 0.102631449
#> (0.8470155,1.010544] 0.27272727 0.6181818 0.01818182 0.077129446
#> (1.010544,1.174073] 0.30075188 0.3984962 0.25563910 0.051169395
#> (1.174073,1.337602] 0.14230769 0.5884615 0.23846154 0.032494074
#> (1.337602,1.50113] 0.23469388 0.5816327 0.18367347 0.020534959
#> (1.50113,1.664659] 0.02287582 0.2777778 0.69934641 0.017857642
#> (1.664659,1.828188] 0.00000000 0.3468900 0.65311005 0.009866868
#> (1.828188,1.991716] 0.00000000 0.0000000 1.00000000 0.007690015
#> (1.991716,2.155245] 0.00000000 0.0000000 1.00000000 0.003962699
#> exp.prob.1 exp.prob.2 exp.prob.3 raw_resid.0
#> [0.3564295,0.5199582] 0.31299790 0.3472692 0.1432210 0.803488167
#> (0.5199582,0.6834869] 0.27025065 0.3900531 0.2092649 0.469568685
#> (0.6834869,0.8470155] 0.24407213 0.4043226 0.2489738 0.230701885
#> (0.8470155,1.010544] 0.21379299 0.4127992 0.2962784 0.013779645
#> (1.010544,1.174073] 0.17398130 0.4120662 0.3627831 -0.006056613
#> (1.174073,1.337602] 0.13632441 0.3983962 0.4327853 -0.001724843
#> (1.337602,1.50113] 0.10523862 0.3756891 0.4985373 -0.020534959
#> (1.50113,1.664659] 0.09707782 0.3676106 0.5174539 -0.017857642
#> (1.664659,1.828188] 0.06836048 0.3299158 0.5918569 -0.009866868
#> (1.828188,1.991716] 0.05880602 0.3132481 0.6202558 -0.007690015
#> (1.991716,2.155245] 0.03912356 0.2690653 0.6878484 -0.003962699
#> raw_resid.1 raw_resid.2 raw_resid.3 se.0
#> [0.3564295,0.5199582] -0.312997903 -0.34726922 -0.14322104 0.397359953
#> (0.5199582,0.6834869] 0.129749354 -0.39005312 -0.20926492 0.150611412
#> (0.6834869,0.8470155] 0.422594537 -0.40432265 -0.24897378 0.078357401
#> (0.8470155,1.010544] 0.058934282 0.20538261 -0.27809653 0.035974863
#> (1.010544,1.174073] 0.126770584 -0.01356995 -0.10714402 0.019106171
#> (1.174073,1.337602] 0.005983284 0.19006531 -0.19432375 0.010996190
#> (1.337602,1.50113] 0.129455259 0.20594357 -0.31486387 0.014326112
#> (1.50113,1.664659] -0.074201998 -0.08983281 0.18189246 0.007570744
#> (1.664659,1.828188] -0.068360484 0.01697418 0.06125317 0.004834464
#> (1.828188,1.991716] -0.058806016 -0.31324812 0.37974416 0.010516294
#> (1.991716,2.155245] -0.039123555 -0.26906531 0.31215156 0.003873963
#> se.1 se.2 se.3 std_resid.0
#> [0.3564295,0.5199582] 0.46371351 0.47610220 0.35029812 2.0220663
#> (0.5199582,0.6834869] 0.19860274 0.21813376 0.18191928 3.1177497
#> (0.6834869,0.8470155] 0.11090564 0.12671381 0.11165000 2.9442258
#> (0.8470155,1.010544] 0.05528201 0.06638675 0.06156999 0.3830354
#> (1.010544,1.174073] 0.03287157 0.04267975 0.04169091 -0.3169978
#> (1.174073,1.337602] 0.02128019 0.03036171 0.03072722 -0.1568583
#> (1.337602,1.50113] 0.03099761 0.04892172 0.05050741 -1.4333937
#> (1.50113,1.664659] 0.01692484 0.02756294 0.02856568 -2.3587698
#> (1.664659,1.828188] 0.01234350 0.02299737 0.02403956 -2.0409436
#> (1.828188,1.991716] 0.02832213 0.05583668 0.05842604 -0.7312476
#> (1.991716,2.155245] 0.01195570 0.02734578 0.02857270 -1.0229057
#> std_resid.1 std_resid.2 std_resid.3 raw.resid.0
#> [0.3564295,0.5199582] -0.6749812 -0.7294006 -0.4088547 0.803488167
#> (0.5199582,0.6834869] 0.6533110 -1.7881373 -1.1503175 0.469568685
#> (0.6834869,0.8470155] 3.8103971 -3.1908333 -2.2299488 0.230701885
#> (0.8470155,1.010544] 1.0660662 3.0937290 -4.5167547 0.013779645
#> (1.010544,1.174073] 3.8565422 -0.3179482 -2.5699613 -0.006056613
#> (1.174073,1.337602] 0.2811669 6.2600333 -6.3241558 -0.001724843
#> (1.337602,1.50113] 4.1762987 4.2096551 -6.2340132 -0.020534959
#> (1.50113,1.664659] -4.3842081 -3.2591881 6.3675177 -0.017857642
#> (1.664659,1.828188] -5.5381760 0.7380923 2.5480159 -0.009866868
#> (1.828188,1.991716] -2.0763275 -5.6100775 6.4995706 -0.007690015
#> (1.991716,2.155245] -3.2723764 -9.8393733 10.9248190 -0.003962699
#> raw.resid.1 raw.resid.2 raw.resid.3 se.0.1
#> [0.3564295,0.5199582] -0.312997903 -0.34726922 -0.14322104 0.397359953
#> (0.5199582,0.6834869] 0.129749354 -0.39005312 -0.20926492 0.150611412
#> (0.6834869,0.8470155] 0.422594537 -0.40432265 -0.24897378 0.078357401
#> (0.8470155,1.010544] 0.058934282 0.20538261 -0.27809653 0.035974863
#> (1.010544,1.174073] 0.126770584 -0.01356995 -0.10714402 0.019106171
#> (1.174073,1.337602] 0.005983284 0.19006531 -0.19432375 0.010996190
#> (1.337602,1.50113] 0.129455259 0.20594357 -0.31486387 0.014326112
#> (1.50113,1.664659] -0.074201998 -0.08983281 0.18189246 0.007570744
#> (1.664659,1.828188] -0.068360484 0.01697418 0.06125317 0.004834464
#> (1.828188,1.991716] -0.058806016 -0.31324812 0.37974416 0.010516294
#> (1.991716,2.155245] -0.039123555 -0.26906531 0.31215156 0.003873963
#> se.1.1 se.2.1 se.3.1 std.resid.0
#> [0.3564295,0.5199582] 0.46371351 0.47610220 0.35029812 2.0220663
#> (0.5199582,0.6834869] 0.19860274 0.21813376 0.18191928 3.1177497
#> (0.6834869,0.8470155] 0.11090564 0.12671381 0.11165000 2.9442258
#> (0.8470155,1.010544] 0.05528201 0.06638675 0.06156999 0.3830354
#> (1.010544,1.174073] 0.03287157 0.04267975 0.04169091 -0.3169978
#> (1.174073,1.337602] 0.02128019 0.03036171 0.03072722 -0.1568583
#> (1.337602,1.50113] 0.03099761 0.04892172 0.05050741 -1.4333937
#> (1.50113,1.664659] 0.01692484 0.02756294 0.02856568 -2.3587698
#> (1.664659,1.828188] 0.01234350 0.02299737 0.02403956 -2.0409436
#> (1.828188,1.991716] 0.02832213 0.05583668 0.05842604 -0.7312476
#> (1.991716,2.155245] 0.01195570 0.02734578 0.02857270 -1.0229057
#> std.resid.1 std.resid.2 std.resid.3
#> [0.3564295,0.5199582] -0.6749812 -0.7294006 -0.4088547
#> (0.5199582,0.6834869] 0.6533110 -1.7881373 -1.1503175
#> (0.6834869,0.8470155] 3.8103971 -3.1908333 -2.2299488
#> (0.8470155,1.010544] 1.0660662 3.0937290 -4.5167547
#> (1.010544,1.174073] 3.8565422 -0.3179482 -2.5699613
#> (1.174073,1.337602] 0.2811669 6.2600333 -6.3241558
#> (1.337602,1.50113] 4.1762987 4.2096551 -6.2340132
#> (1.50113,1.664659] -4.3842081 -3.2591881 6.3675177
#> (1.664659,1.828188] -5.5381760 0.7380923 2.5480159
#> (1.828188,1.991716] -2.0763275 -5.6100775 6.4995706
#> (1.991716,2.155245] -3.2723764 -9.8393733 10.9248190
# (3) the standardized residual plots using the object "fit1"
plot(x=fit1, item.loc=113, type = "sr", ci.method = "wald", layout.col=4, ylim.sr.adjust=TRUE)
#> theta N freq.0 freq.1 freq.2 freq.3 obs.prop.0
#> [0.3564295,0.5199582] 0.3564295 1 1 0 0 0 1.00000000
#> (0.5199582,0.6834869] 0.6081321 5 3 2 0 0 0.60000000
#> (0.6834869,0.8470155] 0.7400138 15 5 10 0 0 0.33333333
#> (0.8470155,1.010544] 0.8866202 55 5 15 34 1 0.09090909
#> (1.010544,1.174073] 1.0821064 133 6 40 53 34 0.04511278
#> (1.174073,1.337602] 1.2832293 260 8 37 153 62 0.03076923
#> (1.337602,1.50113] 1.4747336 98 0 23 57 18 0.00000000
#> (1.50113,1.664659] 1.5311735 306 0 7 85 214 0.00000000
#> (1.664659,1.828188] 1.7632607 418 0 0 145 273 0.00000000
#> (1.828188,1.991716] 1.8577191 69 0 0 0 69 0.00000000
#> (1.991716,2.155245] 2.1021956 263 0 0 0 263 0.00000000
#> obs.prop.1 obs.prop.2 obs.prop.3 exp.prob.0
#> [0.3564295,0.5199582] 0.00000000 0.0000000 0.00000000 0.196511833
#> (0.5199582,0.6834869] 0.40000000 0.0000000 0.00000000 0.130431315
#> (0.6834869,0.8470155] 0.66666667 0.0000000 0.00000000 0.102631449
#> (0.8470155,1.010544] 0.27272727 0.6181818 0.01818182 0.077129446
#> (1.010544,1.174073] 0.30075188 0.3984962 0.25563910 0.051169395
#> (1.174073,1.337602] 0.14230769 0.5884615 0.23846154 0.032494074
#> (1.337602,1.50113] 0.23469388 0.5816327 0.18367347 0.020534959
#> (1.50113,1.664659] 0.02287582 0.2777778 0.69934641 0.017857642
#> (1.664659,1.828188] 0.00000000 0.3468900 0.65311005 0.009866868
#> (1.828188,1.991716] 0.00000000 0.0000000 1.00000000 0.007690015
#> (1.991716,2.155245] 0.00000000 0.0000000 1.00000000 0.003962699
#> exp.prob.1 exp.prob.2 exp.prob.3 raw_resid.0
#> [0.3564295,0.5199582] 0.31299790 0.3472692 0.1432210 0.803488167
#> (0.5199582,0.6834869] 0.27025065 0.3900531 0.2092649 0.469568685
#> (0.6834869,0.8470155] 0.24407213 0.4043226 0.2489738 0.230701885
#> (0.8470155,1.010544] 0.21379299 0.4127992 0.2962784 0.013779645
#> (1.010544,1.174073] 0.17398130 0.4120662 0.3627831 -0.006056613
#> (1.174073,1.337602] 0.13632441 0.3983962 0.4327853 -0.001724843
#> (1.337602,1.50113] 0.10523862 0.3756891 0.4985373 -0.020534959
#> (1.50113,1.664659] 0.09707782 0.3676106 0.5174539 -0.017857642
#> (1.664659,1.828188] 0.06836048 0.3299158 0.5918569 -0.009866868
#> (1.828188,1.991716] 0.05880602 0.3132481 0.6202558 -0.007690015
#> (1.991716,2.155245] 0.03912356 0.2690653 0.6878484 -0.003962699
#> raw_resid.1 raw_resid.2 raw_resid.3 se.0
#> [0.3564295,0.5199582] -0.312997903 -0.34726922 -0.14322104 0.397359953
#> (0.5199582,0.6834869] 0.129749354 -0.39005312 -0.20926492 0.150611412
#> (0.6834869,0.8470155] 0.422594537 -0.40432265 -0.24897378 0.078357401
#> (0.8470155,1.010544] 0.058934282 0.20538261 -0.27809653 0.035974863
#> (1.010544,1.174073] 0.126770584 -0.01356995 -0.10714402 0.019106171
#> (1.174073,1.337602] 0.005983284 0.19006531 -0.19432375 0.010996190
#> (1.337602,1.50113] 0.129455259 0.20594357 -0.31486387 0.014326112
#> (1.50113,1.664659] -0.074201998 -0.08983281 0.18189246 0.007570744
#> (1.664659,1.828188] -0.068360484 0.01697418 0.06125317 0.004834464
#> (1.828188,1.991716] -0.058806016 -0.31324812 0.37974416 0.010516294
#> (1.991716,2.155245] -0.039123555 -0.26906531 0.31215156 0.003873963
#> se.1 se.2 se.3 std_resid.0
#> [0.3564295,0.5199582] 0.46371351 0.47610220 0.35029812 2.0220663
#> (0.5199582,0.6834869] 0.19860274 0.21813376 0.18191928 3.1177497
#> (0.6834869,0.8470155] 0.11090564 0.12671381 0.11165000 2.9442258
#> (0.8470155,1.010544] 0.05528201 0.06638675 0.06156999 0.3830354
#> (1.010544,1.174073] 0.03287157 0.04267975 0.04169091 -0.3169978
#> (1.174073,1.337602] 0.02128019 0.03036171 0.03072722 -0.1568583
#> (1.337602,1.50113] 0.03099761 0.04892172 0.05050741 -1.4333937
#> (1.50113,1.664659] 0.01692484 0.02756294 0.02856568 -2.3587698
#> (1.664659,1.828188] 0.01234350 0.02299737 0.02403956 -2.0409436
#> (1.828188,1.991716] 0.02832213 0.05583668 0.05842604 -0.7312476
#> (1.991716,2.155245] 0.01195570 0.02734578 0.02857270 -1.0229057
#> std_resid.1 std_resid.2 std_resid.3 raw.resid.0
#> [0.3564295,0.5199582] -0.6749812 -0.7294006 -0.4088547 0.803488167
#> (0.5199582,0.6834869] 0.6533110 -1.7881373 -1.1503175 0.469568685
#> (0.6834869,0.8470155] 3.8103971 -3.1908333 -2.2299488 0.230701885
#> (0.8470155,1.010544] 1.0660662 3.0937290 -4.5167547 0.013779645
#> (1.010544,1.174073] 3.8565422 -0.3179482 -2.5699613 -0.006056613
#> (1.174073,1.337602] 0.2811669 6.2600333 -6.3241558 -0.001724843
#> (1.337602,1.50113] 4.1762987 4.2096551 -6.2340132 -0.020534959
#> (1.50113,1.664659] -4.3842081 -3.2591881 6.3675177 -0.017857642
#> (1.664659,1.828188] -5.5381760 0.7380923 2.5480159 -0.009866868
#> (1.828188,1.991716] -2.0763275 -5.6100775 6.4995706 -0.007690015
#> (1.991716,2.155245] -3.2723764 -9.8393733 10.9248190 -0.003962699
#> raw.resid.1 raw.resid.2 raw.resid.3 se.0.1
#> [0.3564295,0.5199582] -0.312997903 -0.34726922 -0.14322104 0.397359953
#> (0.5199582,0.6834869] 0.129749354 -0.39005312 -0.20926492 0.150611412
#> (0.6834869,0.8470155] 0.422594537 -0.40432265 -0.24897378 0.078357401
#> (0.8470155,1.010544] 0.058934282 0.20538261 -0.27809653 0.035974863
#> (1.010544,1.174073] 0.126770584 -0.01356995 -0.10714402 0.019106171
#> (1.174073,1.337602] 0.005983284 0.19006531 -0.19432375 0.010996190
#> (1.337602,1.50113] 0.129455259 0.20594357 -0.31486387 0.014326112
#> (1.50113,1.664659] -0.074201998 -0.08983281 0.18189246 0.007570744
#> (1.664659,1.828188] -0.068360484 0.01697418 0.06125317 0.004834464
#> (1.828188,1.991716] -0.058806016 -0.31324812 0.37974416 0.010516294
#> (1.991716,2.155245] -0.039123555 -0.26906531 0.31215156 0.003873963
#> se.1.1 se.2.1 se.3.1 std.resid.0
#> [0.3564295,0.5199582] 0.46371351 0.47610220 0.35029812 2.0220663
#> (0.5199582,0.6834869] 0.19860274 0.21813376 0.18191928 3.1177497
#> (0.6834869,0.8470155] 0.11090564 0.12671381 0.11165000 2.9442258
#> (0.8470155,1.010544] 0.05528201 0.06638675 0.06156999 0.3830354
#> (1.010544,1.174073] 0.03287157 0.04267975 0.04169091 -0.3169978
#> (1.174073,1.337602] 0.02128019 0.03036171 0.03072722 -0.1568583
#> (1.337602,1.50113] 0.03099761 0.04892172 0.05050741 -1.4333937
#> (1.50113,1.664659] 0.01692484 0.02756294 0.02856568 -2.3587698
#> (1.664659,1.828188] 0.01234350 0.02299737 0.02403956 -2.0409436
#> (1.828188,1.991716] 0.02832213 0.05583668 0.05842604 -0.7312476
#> (1.991716,2.155245] 0.01195570 0.02734578 0.02857270 -1.0229057
#> std.resid.1 std.resid.2 std.resid.3
#> [0.3564295,0.5199582] -0.6749812 -0.7294006 -0.4088547
#> (0.5199582,0.6834869] 0.6533110 -1.7881373 -1.1503175
#> (0.6834869,0.8470155] 3.8103971 -3.1908333 -2.2299488
#> (0.8470155,1.010544] 1.0660662 3.0937290 -4.5167547
#> (1.010544,1.174073] 3.8565422 -0.3179482 -2.5699613
#> (1.174073,1.337602] 0.2811669 6.2600333 -6.3241558
#> (1.337602,1.50113] 4.1762987 4.2096551 -6.2340132
#> (1.50113,1.664659] -4.3842081 -3.2591881 6.3675177
#> (1.664659,1.828188] -5.5381760 0.7380923 2.5480159
#> (1.828188,1.991716] -2.0763275 -5.6100775 6.4995706
#> (1.991716,2.155245] -3.2723764 -9.8393733 10.9248190