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Item fit statistics

Source: R/itemfit.R
itemfit.Rd

Computes item-fit statistics for a variety of unidimensional and multidimensional models. Poorly fitting items should be inspected with the empirical plots/tables for unidimensional models, otherwise itemGAM can be used to diagnose where the functional form of the IRT model was misspecified, or models can be refit using more flexible semi-parametric response models (e.g., itemtype = 'spline'). If the latent trait density was approximated (e.g., Davidian curves, Empirical histograms, etc) then passing use_dentype_estimate = TRUE will use the internally saved quadrature and density components (where applicable). Currently, only S-X2 statistic supported for mixture IRT models. Finally, where applicable the root mean-square error of approximation (RMSEA) is reported to help gauge the magnitude of item misfit.

Usage

itemfit(
  x,
  fit_stats = "S_X2",
  which.items = 1:extract.mirt(x, "nitems"),
  na.rm = FALSE,
  p.adjust = "none",
  group.bins = 10,
  group.size = NA,
  group.fun = mean,
  mincell = 1,
  mincell.X2 = 2,
  return.tables = FALSE,
  pv_draws = 30,
  boot = 1000,
  boot_dfapprox = 200,
  S_X2.plot = NULL,
  S_X2.plot_raw.score = TRUE,
  ETrange = c(-2, 2),
  ETpoints = 11,
  empirical.plot = NULL,
  empirical.CI = 0.95,
  empirical.poly.collapse = FALSE,
  method = "EAP",
  Theta = NULL,
  par.strip.text = list(cex = 0.7),
  par.settings = list(strip.background = list(col = "#9ECAE1"), strip.border = list(col =
    "black")),
  auto.key = list(space = "right", points = FALSE, lines = TRUE),
  ...
)

Arguments

x

a computed model object of class SingleGroupClass, MultipleGroupClass, or DiscreteClass

fit_stats

a character vector indicating which fit statistics should be computed. Supported inputs are:

  • 'S_X2' : Orlando and Thissen (2000, 2003) and Kang and Chen's (2007) signed chi-squared test (default)

  • 'Zh' : Drasgow, Levine, & Williams (1985) Zh

  • 'X2' : Bock's (1972) chi-squared method. The default inputs compute Yen's (1981) Q1 variant of the X2 statistic (i.e., uses a fixed group.bins = 10). However, Bock's group-size variable median-based method can be computed by passing group.fun = median and modifying the group.size input to the desired number of bins

  • 'G2' : McKinley & Mills (1985) G2 statistic (similar method to Q1, but with the likelihood-ratio test).

  • 'PV_Q1' : Chalmers and Ng's (2017) plausible-value variant of the Q1 statistic.

  • 'PV_Q1*' : Chalmers and Ng's (2017) plausible-value variant of the Q1 statistic that uses parametric bootstrapping to obtain a suitable empirical distribution.

  • 'X2*' : Stone's (2000) fit statistics that require parametric bootstrapping

  • 'X2*_df' : Stone's (2000) fit statistics that require parametric bootstrapping to obtain scaled versions of the X2* and degrees of freedom

  • 'infit' : Compute the infit and outfit statistics

Note that 'S_X2' and 'Zh' cannot be computed when there are missing response data (i.e., will require multiple-imputation/row-removal techniques).

which.items

an integer vector indicating which items to test for fit. Default tests all possible items

na.rm

logical; remove rows with any missing values? This is required for methods such as S-X2 because they require the "EAPsum" method from fscores

p.adjust

method to use for adjusting all p-values for each respective item fit statistic (see p.adjust for available options). Default is 'none'

group.bins

the number of bins to use for X2 and G2. For example, setting group.bins = 10 will will compute Yen's (1981) Q1 statistic when 'X2' is requested

group.size

approximate size of each group to be used in calculating the \(\chi^2\) statistic. The default NA disables this command and instead uses the group.bins input to try and construct equally sized bins

group.fun

function used when 'X2' or 'G2' are computed. Determines the central tendency measure within each partitioned group. E.g., setting group.fun = median will obtain the median of each respective ability estimate in each subgroup (this is what was used by Bock, 1972)

mincell

the minimum expected cell size to be used in the S-X2 computations. Tables will be collapsed across items first if polytomous, and then across scores if necessary

mincell.X2

the minimum expected cell size to be used in the X2 computations. Tables will be collapsed if polytomous, however if this condition can not be met then the group block will be omitted in the computations

return.tables

logical; return tables when investigating 'X2', 'S_X2', and 'X2*'?

pv_draws

number of plausible-value draws to obtain for PV_Q1 and PV_Q1*

boot

number of parametric bootstrap samples to create for PV_Q1* and X2*

boot_dfapprox

number of parametric bootstrap samples to create for the X2*_df statistic to approximate the scaling factor for X2* as well as the scaled degrees of freedom estimates

S_X2.plot

argument input is the same as empirical.plot, however the resulting image is constructed according to the S-X2 statistic's conditional sum-score information

S_X2.plot_raw.score

logical; use the raw-score information in the plot in stead of the latent trait scale score? Default is FALSE

ETrange

range of integration nodes for Stone's X2* statistic

ETpoints

number of integration nodes to use for Stone's X2* statistic

empirical.plot

a single numeric value or character of the item name indicating which item to plot (via itemplot) and overlay with the empirical \(\theta\) groupings (see empirical.CI). Useful for plotting the expected bins based on the 'X2' or 'G2' method

empirical.CI

a numeric value indicating the width of the empirical confidence interval ranging between 0 and 1 (default of 0 plots not interval). For example, a 95 interval would be plotted when empirical.CI = .95. Only applicable to dichotomous items

empirical.poly.collapse

logical; collapse polytomous item categories to for expected scoring functions for empirical plots? Default is FALSE

method

type of factor score estimation method. See fscores for more detail

Theta

a matrix of factor scores for each person used for statistics that require empirical estimates. If supplied, arguments typically passed to fscores() will be ignored and these values will be used instead. Also required when estimating statistics with missing data via imputation

par.strip.text

plotting argument passed to lattice

par.settings

plotting argument passed to lattice

auto.key

plotting argument passed to lattice

...

additional arguments to be passed to fscores() and lattice

References

Bock, R. D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37, 29-51.

Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29. doi:10.18637/jss.v048.i06

Chalmers, R. P. & Ng, V. (2017). Plausible-Value Imputation Statistics for Detecting Item Misfit. Applied Psychological Measurement, 41, 372-387. doi:10.1177/0146621617692079

Drasgow, F., Levine, M. V., & Williams, E. A. (1985). Appropriateness measurement with polychotomous item response models and standardized indices. British Journal of Mathematical and Statistical Psychology, 38, 67-86.

Kang, T. & Chen, Troy, T. (2007). An investigation of the performance of the generalized S-X2 item-fit index for polytomous IRT models. ACT

McKinley, R., & Mills, C. (1985). A comparison of several goodness-of-fit statistics. Applied Psychological Measurement, 9, 49-57.

Orlando, M. & Thissen, D. (2000). Likelihood-based item fit indices for dichotomous item response theory models. Applied Psychological Measurement, 24, 50-64.

Reise, S. P. (1990). A comparison of item- and person-fit methods of assessing model-data fit in IRT. Applied Psychological Measurement, 14, 127-137.

Stone, C. A. (2000). Monte Carlo Based Null Distribution for an Alternative Goodness-of-Fit Test Statistics in IRT Models. Journal of Educational Measurement, 37, 58-75.

Wright B. D. & Masters, G. N. (1982). Rating scale analysis. MESA Press.

Yen, W. M. (1981). Using simulation results to choose a latent trait model. Applied Psychological Measurement, 5, 245-262.

See also

personfit, itemGAM

Author

Phil Chalmers rphilip.chalmers@gmail.com

Examples


# \donttest{

P <- function(Theta){exp(Theta^2 * 1.2 - 1) / (1 + exp(Theta^2 * 1.2 - 1))}

#make some data
set.seed(1234)
a <- matrix(rlnorm(20, meanlog=0, sdlog = .1),ncol=1)
d <- matrix(rnorm(20),ncol=1)
Theta <- matrix(rnorm(2000))
items <- rep('2PL', 20)
ps <- P(Theta)
baditem <- numeric(2000)
for(i in 1:2000)
   baditem[i] <- sample(c(0,1), 1, prob = c(1-ps[i], ps[i]))
data <- cbind(simdata(a,d, 2000, items, Theta=Theta), baditem=baditem)

x <- mirt(data, 1)
#> 
Iteration: 1, Log-Lik: -24870.308, Max-Change: 0.66114
Iteration: 2, Log-Lik: -24710.080, Max-Change: 0.15084
Iteration: 3, Log-Lik: -24698.673, Max-Change: 0.03218
Iteration: 4, Log-Lik: -24697.464, Max-Change: 0.01365
Iteration: 5, Log-Lik: -24697.140, Max-Change: 0.00704
Iteration: 6, Log-Lik: -24697.026, Max-Change: 0.00402
Iteration: 7, Log-Lik: -24696.953, Max-Change: 0.00135
Iteration: 8, Log-Lik: -24696.942, Max-Change: 0.00093
Iteration: 9, Log-Lik: -24696.935, Max-Change: 0.00067
Iteration: 10, Log-Lik: -24696.930, Max-Change: 0.00036
Iteration: 11, Log-Lik: -24696.929, Max-Change: 0.00045
Iteration: 12, Log-Lik: -24696.928, Max-Change: 0.00019
Iteration: 13, Log-Lik: -24696.928, Max-Change: 0.00016
Iteration: 14, Log-Lik: -24696.927, Max-Change: 0.00015
Iteration: 15, Log-Lik: -24696.927, Max-Change: 0.00013
Iteration: 16, Log-Lik: -24696.927, Max-Change: 0.00006
raschfit <- mirt(data, 1, itemtype='Rasch')
#> 
Iteration: 1, Log-Lik: -24883.311, Max-Change: 0.12205
Iteration: 2, Log-Lik: -24869.680, Max-Change: 0.05401
Iteration: 3, Log-Lik: -24866.428, Max-Change: 0.02591
Iteration: 4, Log-Lik: -24865.523, Max-Change: 0.01316
Iteration: 5, Log-Lik: -24865.246, Max-Change: 0.00680
Iteration: 6, Log-Lik: -24865.148, Max-Change: 0.00361
Iteration: 7, Log-Lik: -24865.088, Max-Change: 0.00215
Iteration: 8, Log-Lik: -24865.077, Max-Change: 0.00105
Iteration: 9, Log-Lik: -24865.072, Max-Change: 0.00069
Iteration: 10, Log-Lik: -24865.067, Max-Change: 0.00038
Iteration: 11, Log-Lik: -24865.067, Max-Change: 0.00018
Iteration: 12, Log-Lik: -24865.067, Max-Change: 0.00013
Iteration: 13, Log-Lik: -24865.067, Max-Change: 0.00006
fit <- itemfit(x)
fit
#>       item    S_X2 df.S_X2 RMSEA.S_X2 p.S_X2
#> 1   Item_1  16.519      15      0.007  0.348
#> 2   Item_2  11.718      15      0.000  0.700
#> 3   Item_3  22.835      15      0.016  0.088
#> 4   Item_4  11.703      16      0.000  0.764
#> 5   Item_5  15.241      15      0.003  0.434
#> 6   Item_6  11.983      16      0.000  0.745
#> 7   Item_7  23.912      16      0.016  0.091
#> 8   Item_8  12.744      15      0.000  0.622
#> 9   Item_9  16.931      15      0.008  0.323
#> 10 Item_10   9.199      16      0.000  0.905
#> 11 Item_11  17.630      15      0.009  0.283
#> 12 Item_12  12.198      15      0.000  0.664
#> 13 Item_13  17.487      15      0.009  0.291
#> 14 Item_14  19.117      15      0.012  0.208
#> 15 Item_15  11.542      16      0.000  0.775
#> 16 Item_16  12.534      16      0.000  0.706
#> 17 Item_17  29.453      15      0.022  0.014
#> 18 Item_18  15.064      16      0.000  0.520
#> 19 Item_19  17.125      15      0.008  0.311
#> 20 Item_20  10.064      15      0.000  0.816
#> 21 baditem 233.224      18      0.077  0.000

# p-value adjustment
itemfit(x, p.adjust='fdr')
#>       item    S_X2 df.S_X2 RMSEA.S_X2 p.S_X2
#> 1   Item_1  16.519      15      0.007  0.732
#> 2   Item_2  11.718      15      0.000  0.856
#> 3   Item_3  22.835      15      0.016  0.480
#> 4   Item_4  11.703      16      0.000  0.856
#> 5   Item_5  15.241      15      0.003  0.829
#> 6   Item_6  11.983      16      0.000  0.856
#> 7   Item_7  23.912      16      0.016  0.480
#> 8   Item_8  12.744      15      0.000  0.856
#> 9   Item_9  16.931      15      0.008  0.732
#> 10 Item_10   9.199      16      0.000  0.905
#> 11 Item_11  17.630      15      0.009  0.732
#> 12 Item_12  12.198      15      0.000  0.856
#> 13 Item_13  17.487      15      0.009  0.732
#> 14 Item_14  19.117      15      0.012  0.732
#> 15 Item_15  11.542      16      0.000  0.856
#> 16 Item_16  12.534      16      0.000  0.856
#> 17 Item_17  29.453      15      0.022  0.148
#> 18 Item_18  15.064      16      0.000  0.856
#> 19 Item_19  17.125      15      0.008  0.732
#> 20 Item_20  10.064      15      0.000  0.856
#> 21 baditem 233.224      18      0.077  0.000

# two different fit stats (with/without p-value adjustment)
itemfit(x, c('S_X2' ,'X2'), p.adjust='fdr')
#>       item      X2 df.X2 RMSEA.X2  p.X2    S_X2 df.S_X2 RMSEA.S_X2 p.S_X2
#> 1   Item_1  30.842     8    0.038 0.000  16.519      15      0.007  0.732
#> 2   Item_2  27.970     8    0.035 0.001  11.718      15      0.000  0.856
#> 3   Item_3  43.995     8    0.047 0.000  22.835      15      0.016  0.480
#> 4   Item_4  33.272     8    0.040 0.000  11.703      16      0.000  0.856
#> 5   Item_5  29.469     8    0.037 0.001  15.241      15      0.003  0.829
#> 6   Item_6  21.325     8    0.029 0.007  11.983      16      0.000  0.856
#> 7   Item_7  23.127     8    0.031 0.004  23.912      16      0.016  0.480
#> 8   Item_8  25.332     8    0.033 0.002  12.744      15      0.000  0.856
#> 9   Item_9  33.778     8    0.040 0.000  16.931      15      0.008  0.732
#> 10 Item_10  22.972     8    0.031 0.004   9.199      16      0.000  0.905
#> 11 Item_11  27.300     8    0.035 0.001  17.630      15      0.009  0.732
#> 12 Item_12  23.256     8    0.031 0.004  12.198      15      0.000  0.856
#> 13 Item_13  31.523     8    0.038 0.000  17.487      15      0.009  0.732
#> 14 Item_14  27.924     8    0.035 0.001  19.117      15      0.012  0.732
#> 15 Item_15  18.462     8    0.026 0.020  11.542      16      0.000  0.856
#> 16 Item_16  25.057     8    0.033 0.002  12.534      16      0.000  0.856
#> 17 Item_17  14.828     8    0.021 0.063  29.453      15      0.022  0.148
#> 18 Item_18  17.676     8    0.025 0.025  15.064      16      0.000  0.856
#> 19 Item_19  32.585     8    0.039 0.000  17.125      15      0.008  0.732
#> 20 Item_20  37.207     8    0.043 0.000  10.064      15      0.000  0.856
#> 21 baditem 228.367     8    0.117 0.000 233.224      18      0.077  0.000
itemfit(x, c('S_X2' ,'X2'))
#>       item      X2 df.X2 RMSEA.X2  p.X2    S_X2 df.S_X2 RMSEA.S_X2 p.S_X2
#> 1   Item_1  30.842     8    0.038 0.000  16.519      15      0.007  0.348
#> 2   Item_2  27.970     8    0.035 0.000  11.718      15      0.000  0.700
#> 3   Item_3  43.995     8    0.047 0.000  22.835      15      0.016  0.088
#> 4   Item_4  33.272     8    0.040 0.000  11.703      16      0.000  0.764
#> 5   Item_5  29.469     8    0.037 0.000  15.241      15      0.003  0.434
#> 6   Item_6  21.325     8    0.029 0.006  11.983      16      0.000  0.745
#> 7   Item_7  23.127     8    0.031 0.003  23.912      16      0.016  0.091
#> 8   Item_8  25.332     8    0.033 0.001  12.744      15      0.000  0.622
#> 9   Item_9  33.778     8    0.040 0.000  16.931      15      0.008  0.323
#> 10 Item_10  22.972     8    0.031 0.003   9.199      16      0.000  0.905
#> 11 Item_11  27.300     8    0.035 0.001  17.630      15      0.009  0.283
#> 12 Item_12  23.256     8    0.031 0.003  12.198      15      0.000  0.664
#> 13 Item_13  31.523     8    0.038 0.000  17.487      15      0.009  0.291
#> 14 Item_14  27.924     8    0.035 0.000  19.117      15      0.012  0.208
#> 15 Item_15  18.462     8    0.026 0.018  11.542      16      0.000  0.775
#> 16 Item_16  25.057     8    0.033 0.002  12.534      16      0.000  0.706
#> 17 Item_17  14.828     8    0.021 0.063  29.453      15      0.022  0.014
#> 18 Item_18  17.676     8    0.025 0.024  15.064      16      0.000  0.520
#> 19 Item_19  32.585     8    0.039 0.000  17.125      15      0.008  0.311
#> 20 Item_20  37.207     8    0.043 0.000  10.064      15      0.000  0.816
#> 21 baditem 228.367     8    0.117 0.000 233.224      18      0.077  0.000

# Conditional sum-score plot from S-X2 information
itemfit(x, S_X2.plot = 1) # good fit

itemfit(x, S_X2.plot = 2) # good fit

itemfit(x, S_X2.plot = 21) # bad fit


itemfit(x, 'X2') # just X2
#>       item      X2 df.X2 RMSEA.X2  p.X2
#> 1   Item_1  30.842     8    0.038 0.000
#> 2   Item_2  27.970     8    0.035 0.000
#> 3   Item_3  43.995     8    0.047 0.000
#> 4   Item_4  33.272     8    0.040 0.000
#> 5   Item_5  29.469     8    0.037 0.000
#> 6   Item_6  21.325     8    0.029 0.006
#> 7   Item_7  23.127     8    0.031 0.003
#> 8   Item_8  25.332     8    0.033 0.001
#> 9   Item_9  33.778     8    0.040 0.000
#> 10 Item_10  22.972     8    0.031 0.003
#> 11 Item_11  27.300     8    0.035 0.001
#> 12 Item_12  23.256     8    0.031 0.003
#> 13 Item_13  31.523     8    0.038 0.000
#> 14 Item_14  27.924     8    0.035 0.000
#> 15 Item_15  18.462     8    0.026 0.018
#> 16 Item_16  25.057     8    0.033 0.002
#> 17 Item_17  14.828     8    0.021 0.063
#> 18 Item_18  17.676     8    0.025 0.024
#> 19 Item_19  32.585     8    0.039 0.000
#> 20 Item_20  37.207     8    0.043 0.000
#> 21 baditem 228.367     8    0.117 0.000
itemfit(x, 'X2', method = 'ML') # X2 with maximum-likelihood estimates for traits
#> Warning: The following factor score estimates failed to converge successfully:
#>     311,315,352,518,677,748,909,927,1081,1243,1277,1305,1415,1480,1620,1893
#>       item      X2 df.X2 RMSEA.X2  p.X2
#> 1   Item_1  35.941     8    0.042 0.000
#> 2   Item_2  53.226     8    0.053 0.000
#> 3   Item_3  47.010     8    0.049 0.000
#> 4   Item_4  85.852     8    0.070 0.000
#> 5   Item_5  85.280     8    0.070 0.000
#> 6   Item_6   8.632     8    0.006 0.374
#> 7   Item_7  57.623     8    0.056 0.000
#> 8   Item_8  42.952     8    0.047 0.000
#> 9   Item_9  55.180     8    0.054 0.000
#> 10 Item_10  32.456     8    0.039 0.000
#> 11 Item_11 131.613     8    0.088 0.000
#> 12 Item_12  50.094     8    0.051 0.000
#> 13 Item_13  55.846     8    0.055 0.000
#> 14 Item_14  18.717     8    0.026 0.016
#> 15 Item_15  12.402     8    0.017 0.134
#> 16 Item_16  38.229     8    0.043 0.000
#> 17 Item_17   4.413     8    0.000 0.818
#> 18 Item_18  16.165     8    0.023 0.040
#> 19 Item_19  14.190     8    0.020 0.077
#> 20 Item_20  21.215     8    0.029 0.007
#> 21 baditem 227.191     8    0.117 0.000
itemfit(x, group.bins=15, empirical.plot = 1, method = 'ML') #empirical item plot with 15 points
#> Warning: The following factor score estimates failed to converge successfully:
#>     311,315,352,518,677,748,909,927,1081,1243,1277,1305,1415,1480,1620,1893

itemfit(x, group.bins=15, empirical.plot = 21, method = 'ML')
#> Warning: The following factor score estimates failed to converge successfully:
#>     311,315,352,518,677,748,909,927,1081,1243,1277,1305,1415,1480,1620,1893


# PV and X2* statistics (parametric bootstrap stats not run to save time)
itemfit(x, 'PV_Q1')
#>       item   PV_Q1 df.PV_Q1 RMSEA.PV_Q1 p.PV_Q1
#> 1   Item_1   8.984        8       0.008   0.344
#> 2   Item_2   9.441        8       0.009   0.306
#> 3   Item_3   7.162        8       0.000   0.519
#> 4   Item_4   8.463        8       0.005   0.390
#> 5   Item_5   8.755        8       0.007   0.363
#> 6   Item_6   9.411        8       0.009   0.309
#> 7   Item_7   8.678        8       0.007   0.370
#> 8   Item_8   8.269        8       0.004   0.408
#> 9   Item_9   9.005        8       0.008   0.342
#> 10 Item_10   6.873        8       0.000   0.550
#> 11 Item_11   9.871        8       0.011   0.274
#> 12 Item_12   9.214        8       0.009   0.325
#> 13 Item_13   8.889        8       0.007   0.352
#> 14 Item_14   9.088        8       0.008   0.335
#> 15 Item_15   8.583        8       0.006   0.379
#> 16 Item_16   8.848        8       0.007   0.355
#> 17 Item_17   8.408        8       0.005   0.395
#> 18 Item_18   8.000        8       0.000   0.433
#> 19 Item_19   8.742        8       0.007   0.365
#> 20 Item_20   7.823        8       0.000   0.451
#> 21 baditem 118.597        8       0.083   0.000

if(interactive()) mirtCluster() # improve speed of bootstrap samples by running in parallel
# itemfit(x, 'PV_Q1*')
# itemfit(x, 'X2*') # Stone's 1993 statistic
# itemfit(x, 'X2*_df') # Stone's 2000 scaled statistic with df estimate

# empirical tables for X2 statistic
tabs <- itemfit(x, 'X2', return.tables=TRUE, which.items = 1)
tabs
#> $`theta = -1.4531`
#>       Observed  Expected z.Residual
#> cat_0      183 158.63869   1.934176
#> cat_1       17  41.36131  -3.787943
#> 
#> $`theta = -0.9416`
#>       Observed  Expected z.Residual
#> cat_0      149 138.43172  0.8982277
#> cat_1       51  61.56828 -1.3468702
#> 
#> $`theta = -0.6475`
#>       Observed  Expected z.Residual
#> cat_0      132 124.64146  0.6591135
#> cat_1       68  75.35854 -0.8476670
#> 
#> $`theta = -0.3921`
#>       Observed  Expected  z.Residual
#> cat_0      112 111.77447  0.02133235
#> cat_1       88  88.22553 -0.02401114
#> 
#> $`theta = -0.1393`
#>       Observed  Expected z.Residual
#> cat_0       88  98.63125  -1.070476
#> cat_1      112 101.36875   1.055923
#> 
#> $`theta = 0.0936`
#>       Observed Expected  z.Residual
#> cat_0       86  86.5533 -0.05947283
#> cat_1      114 113.4467  0.05194748
#> 
#> $`theta = 0.346`
#>       Observed  Expected z.Residual
#> cat_0       61  73.91477  -1.502177
#> cat_1      139 126.08523   1.150150
#> 
#> $`theta = 0.6087`
#>       Observed  Expected z.Residual
#> cat_0       54  61.64828 -0.9740998
#> cat_1      146 138.35172  0.6502370
#> 
#> $`theta = 0.9646`
#>       Observed Expected z.Residual
#> cat_0       41  47.0127 -0.8769235
#> cat_1      159 152.9873  0.4861179
#> 
#> $`theta = 1.5621`
#>       Observed  Expected z.Residual
#> cat_0       24  28.27768 -0.8044264
#> cat_1      176 171.72232  0.3264336
#> 

#infit/outfit statistics. method='ML' agrees better with eRm package
itemfit(raschfit, 'infit', method = 'ML') #infit and outfit stats
#>       item outfit z.outfit infit z.infit
#> 1   Item_1  0.919   -2.945 0.951  -2.699
#> 2   Item_2  0.962   -1.281 0.960  -2.010
#> 3   Item_3  0.876   -4.455 0.918  -4.332
#> 4   Item_4  0.998   -0.049 1.009   0.495
#> 5   Item_5  0.982   -0.523 0.974  -1.227
#> 6   Item_6  0.890   -2.233 0.950  -1.692
#> 7   Item_7  1.008    0.259 1.003   0.171
#> 8   Item_8  0.933   -1.743 0.961  -1.631
#> 9   Item_9  0.958   -1.519 0.964  -1.999
#> 10 Item_10  1.011    0.303 1.013   0.534
#> 11 Item_11  0.898   -2.300 0.939  -2.531
#> 12 Item_12  0.988   -0.383 1.012   0.607
#> 13 Item_13  0.991   -0.263 1.002   0.093
#> 14 Item_14  0.973   -0.841 0.974  -1.256
#> 15 Item_15  0.947   -0.943 0.993  -0.210
#> 16 Item_16  0.988   -0.271 0.985  -0.546
#> 17 Item_17  0.878   -1.532 0.960  -0.872
#> 18 Item_18  0.961   -0.759 0.978  -0.742
#> 19 Item_19  0.943   -2.060 0.974  -1.352
#> 20 Item_20  0.868   -4.736 0.911  -4.687
#> 21 baditem  1.513   16.123 1.338  16.509

#same as above, but inputting ML estimates instead (saves time for re-use)
Theta <- fscores(raschfit, method = 'ML')
itemfit(raschfit, 'infit', Theta=Theta)
#>       item outfit z.outfit infit z.infit
#> 1   Item_1  0.919   -2.945 0.951  -2.699
#> 2   Item_2  0.962   -1.281 0.960  -2.010
#> 3   Item_3  0.876   -4.455 0.918  -4.332
#> 4   Item_4  0.998   -0.049 1.009   0.495
#> 5   Item_5  0.982   -0.523 0.974  -1.227
#> 6   Item_6  0.890   -2.233 0.950  -1.692
#> 7   Item_7  1.008    0.259 1.003   0.171
#> 8   Item_8  0.933   -1.743 0.961  -1.631
#> 9   Item_9  0.958   -1.519 0.964  -1.999
#> 10 Item_10  1.011    0.303 1.013   0.534
#> 11 Item_11  0.898   -2.300 0.939  -2.531
#> 12 Item_12  0.988   -0.383 1.012   0.607
#> 13 Item_13  0.991   -0.263 1.002   0.093
#> 14 Item_14  0.973   -0.841 0.974  -1.256
#> 15 Item_15  0.947   -0.943 0.993  -0.210
#> 16 Item_16  0.988   -0.271 0.985  -0.546
#> 17 Item_17  0.878   -1.532 0.960  -0.872
#> 18 Item_18  0.961   -0.759 0.978  -0.742
#> 19 Item_19  0.943   -2.060 0.974  -1.352
#> 20 Item_20  0.868   -4.736 0.911  -4.687
#> 21 baditem  1.513   16.123 1.338  16.509
itemfit(raschfit, empirical.plot=1, Theta=Theta)

itemfit(raschfit, 'X2', return.tables=TRUE, Theta=Theta, which.items=1)
#> $`theta = -1.7718`
#>       Observed  Expected z.Residual
#> cat_0      178 166.44926  0.8953008
#> cat_1       22  33.55074 -1.9941546
#> 
#> $`theta = -1.0782`
#>       Observed  Expected z.Residual
#> cat_0      147 142.51602  0.3756054
#> cat_1       53  57.48398 -0.5914121
#> 
#> $`theta = -0.7497`
#>       Observed  Expected z.Residual
#> cat_0      138 128.19072  0.8663808
#> cat_1       62  71.80928 -1.1575688
#> 
#> $`theta = -0.4577`
#>       Observed Expected z.Residual
#> cat_0      109 114.2782 -0.4937469
#> cat_1       91  85.7218  0.5700861
#> 
#> $`theta = -0.193`
#>       Observed  Expected z.Residual
#> cat_0       91 101.13957  -1.008228
#> cat_1      109  98.86043   1.019784
#> 
#> $`theta = 0.0765`
#>       Observed Expected z.Residual
#> cat_0       77  87.7275  -1.145330
#> cat_1      123 112.2725   1.012423
#> 
#> $`theta = 0.3374`
#>       Observed  Expected z.Residual
#> cat_0       74  75.15333 -0.1330391
#> cat_1      126 124.84667  0.1032203
#> 
#> $`theta = 0.6728`
#>       Observed  Expected z.Residual
#> cat_0       47  60.18187  -1.699199
#> cat_1      153 139.81813   1.114796
#> 
#> $`theta = 1.0787`
#>       Observed  Expected z.Residual
#> cat_0       47  44.57924  0.3625653
#> cat_1      153 155.42076 -0.1941771
#> 
#> $`theta = 1.9249`
#>       Observed  Expected   z.Residual
#> cat_0       22  21.91506  0.018144094
#> cat_1      178 178.08494 -0.006364921
#> 

# fit a new more flexible model for the mis-fitting item
itemtype <- c(rep('2PL', 20), 'spline')
x2 <- mirt(data, 1, itemtype=itemtype)
#> 
Iteration: 1, Log-Lik: -25123.533, Max-Change: 10.56028
Iteration: 2, Log-Lik: -24697.333, Max-Change: 9.32628
Iteration: 3, Log-Lik: -24621.907, Max-Change: 4.05808
Iteration: 4, Log-Lik: -24597.377, Max-Change: 6.07215
Iteration: 5, Log-Lik: -24585.842, Max-Change: 1.92193
Iteration: 6, Log-Lik: -24577.788, Max-Change: 3.30434
Iteration: 7, Log-Lik: -24573.466, Max-Change: 1.81113
Iteration: 8, Log-Lik: -24570.695, Max-Change: 2.04660
Iteration: 9, Log-Lik: -24568.916, Max-Change: 1.77913
Iteration: 10, Log-Lik: -24603.969, Max-Change: 0.26506
Iteration: 11, Log-Lik: -24564.250, Max-Change: 0.22687
Iteration: 12, Log-Lik: -24563.783, Max-Change: 0.08490
Iteration: 13, Log-Lik: -24563.761, Max-Change: 1.24022
Iteration: 14, Log-Lik: -24563.531, Max-Change: 0.00234
Iteration: 15, Log-Lik: -24563.528, Max-Change: 0.00210
Iteration: 16, Log-Lik: -24563.527, Max-Change: 0.00028
Iteration: 17, Log-Lik: -24563.526, Max-Change: 0.00139
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Iteration: 23, Log-Lik: -24563.525, Max-Change: 0.00046
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Iteration: 25, Log-Lik: -24563.525, Max-Change: 0.06480
Iteration: 26, Log-Lik: -24563.520, Max-Change: 0.00225
Iteration: 27, Log-Lik: -24563.514, Max-Change: 0.00030
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Iteration: 29, Log-Lik: -24563.513, Max-Change: 0.00017
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#> Warning: EM cycles terminated after 500 iterations.
itemfit(x2)
#>       item   S_X2 df.S_X2 RMSEA.S_X2 p.S_X2
#> 1   Item_1 13.109      15      0.000  0.594
#> 2   Item_2 13.513      15      0.000  0.563
#> 3   Item_3 21.887      15      0.015  0.111
#> 4   Item_4  9.894      15      0.000  0.826
#> 5   Item_5 16.248      15      0.006  0.366
#> 6   Item_6 10.218      16      0.000  0.855
#> 7   Item_7 18.279      15      0.010  0.248
#> 8   Item_8 13.587      16      0.000  0.629
#> 9   Item_9 13.485      15      0.000  0.565
#> 10 Item_10 10.569      16      0.000  0.835
#> 11 Item_11 16.325      15      0.007  0.361
#> 12 Item_12  9.663      15      0.000  0.840
#> 13 Item_13 19.394      16      0.010  0.249
#> 14 Item_14 16.357      15      0.007  0.359
#> 15 Item_15  9.410      16      0.000  0.896
#> 16 Item_16 13.578      16      0.000  0.630
#> 17 Item_17 29.945      16      0.021  0.018
#> 18 Item_18 15.058      16      0.000  0.520
#> 19 Item_19 15.663      15      0.005  0.405
#> 20 Item_20  9.333      15      0.000  0.859
#> 21 baditem 11.473      13      0.000  0.571
itemplot(x2, 21)

anova(x, x2)
#>         AIC    SABIC       HQ      BIC    logLik     X2 df p
#> x  49477.85 49579.65 49564.23 49713.09 -24696.93            
#> x2 49214.97 49321.62 49305.46 49461.41 -24563.49 266.88  2 0

#------------------------------------------------------------

#similar example to Kang and Chen 2007
a <- matrix(c(.8,.4,.7, .8, .4, .7, 1, 1, 1, 1))
d <- matrix(rep(c(2.0,0.0,-1,-1.5),10), ncol=4, byrow=TRUE)
dat <- simdata(a,d,2000, itemtype = rep('graded', 10))
head(dat)
#>      Item_1 Item_2 Item_3 Item_4 Item_5 Item_6 Item_7 Item_8 Item_9 Item_10
#> [1,]      4      0      1      4      1      4      3      2      1       4
#> [2,]      2      1      1      3      2      4      2      1      4       2
#> [3,]      2      2      3      0      0      0      4      4      4       4
#> [4,]      1      2      4      1      2      2      2      2      0       4
#> [5,]      1      3      0      2      1      4      4      4      3       1
#> [6,]      1      3      3      2      3      1      1      2      0       1

mod <- mirt(dat, 1)
#> 
Iteration: 1, Log-Lik: -29588.164, Max-Change: 0.30451
Iteration: 2, Log-Lik: -29489.581, Max-Change: 0.11473
Iteration: 3, Log-Lik: -29475.859, Max-Change: 0.04424
Iteration: 4, Log-Lik: -29473.518, Max-Change: 0.01540
Iteration: 5, Log-Lik: -29473.111, Max-Change: 0.00809
Iteration: 6, Log-Lik: -29472.983, Max-Change: 0.00372
Iteration: 7, Log-Lik: -29472.964, Max-Change: 0.00210
Iteration: 8, Log-Lik: -29472.957, Max-Change: 0.00138
Iteration: 9, Log-Lik: -29472.956, Max-Change: 0.00098
Iteration: 10, Log-Lik: -29472.954, Max-Change: 0.00091
Iteration: 11, Log-Lik: -29472.953, Max-Change: 0.00013
Iteration: 12, Log-Lik: -29472.953, Max-Change: 0.00028
Iteration: 13, Log-Lik: -29472.953, Max-Change: 0.00018
Iteration: 14, Log-Lik: -29472.953, Max-Change: 0.00008
itemfit(mod)
#>       item    S_X2 df.S_X2 RMSEA.S_X2 p.S_X2
#> 1   Item_1 143.021     103      0.014  0.006
#> 2   Item_2  85.589     109      0.000  0.953
#> 3   Item_3 110.835     105      0.005  0.330
#> 4   Item_4 121.145     103      0.009  0.107
#> 5   Item_5 107.875     111      0.000  0.566
#> 6   Item_6  93.905     102      0.000  0.704
#> 7   Item_7 113.544      99      0.009  0.151
#> 8   Item_8 100.858      99      0.003  0.429
#> 9   Item_9  83.214      98      0.000  0.857
#> 10 Item_10 104.402      99      0.005  0.336
itemfit(mod, 'X2') # less useful given inflated Type I error rates
#>       item      X2 df.X2 RMSEA.X2  p.X2
#> 1   Item_1  93.925    35    0.029 0.000
#> 2   Item_2  43.667    35    0.011 0.149
#> 3   Item_3  81.354    35    0.026 0.000
#> 4   Item_4  90.490    35    0.028 0.000
#> 5   Item_5  36.169    35    0.004 0.414
#> 6   Item_6  97.559    35    0.030 0.000
#> 7   Item_7 129.917    35    0.037 0.000
#> 8   Item_8 130.263    35    0.037 0.000
#> 9   Item_9 141.266    35    0.039 0.000
#> 10 Item_10 117.650    35    0.034 0.000
itemfit(mod, empirical.plot = 1)

itemfit(mod, empirical.plot = 1, empirical.poly.collapse=TRUE)


# collapsed tables (see mincell.X2) for X2 and G2
itemfit(mod, 'X2', return.tables = TRUE, which.items = 1)
#> $`theta = -1.4692`
#>       Observed  Expected z.Residual
#> cat_0       98 65.020718  4.0899247
#> cat_1       76 88.468143 -1.3255872
#> cat_2       12 26.774054 -2.8552400
#> cat_3        7  6.656543  0.1331215
#> cat_4        7 13.080542 -1.6812388
#> 
#> $`theta = -0.8519`
#>       Observed  Expected z.Residual
#> cat_0       65 45.508938  2.8892636
#> cat_1       87 88.222767 -0.1301827
#> cat_2       29 35.896766 -1.1511126
#> cat_3        6  9.834511 -1.2227385
#> cat_4       13 20.537019 -1.6631481
#> 
#> $`theta = -0.5476`
#>       Observed Expected z.Residual
#> cat_0       35 37.54994 -0.4161270
#> cat_1       97 85.03642  1.2973549
#> cat_2       34 40.25662 -0.9861003
#> cat_3        5 11.70198 -1.9591763
#> cat_4       29 25.45504  0.7026267
#> 
#> $`theta = -0.3145`
#>       Observed Expected z.Residual
#> cat_0       27 32.21053 -0.9180857
#> cat_1       91 81.40120  1.0639013
#> cat_2       40 43.28252 -0.4989437
#> cat_3       15 13.23174  0.4861130
#> cat_4       27 29.87400 -0.5258232
#> 
#> $`theta = -0.0993`
#>       Observed Expected z.Residual
#> cat_0       23 27.84181 -0.9176111
#> cat_1       73 77.27754 -0.4865943
#> cat_2       60 45.69537  2.1161218
#> cat_3       12 14.68759 -0.7012737
#> cat_4       32 34.49770 -0.4252515
#> 
#> $`theta = 0.1116`
#>       Observed Expected  z.Residual
#> cat_0       23 24.05321 -0.21474860
#> cat_1       73 72.66989  0.03872444
#> cat_2       50 47.59720  0.34827910
#> cat_3       16 16.11821 -0.02944308
#> cat_4       38 39.56149 -0.24825845
#> 
#> $`theta = 0.3293`
#>       Observed Expected   z.Residual
#> cat_0       18 20.61824 -0.576612407
#> cat_1       69 67.48888  0.183942450
#> cat_2       49 48.98546  0.002077898
#> cat_3       24 17.55297  1.538809131
#> cat_4       40 45.35445 -0.795069543
#> 
#> $`theta = 0.5568`
#>       Observed Expected  z.Residual
#> cat_0        6 17.49926 -2.74890777
#> cat_1       60 61.79242 -0.22801909
#> cat_2       56 49.73600  0.88821096
#> cat_3       19 18.94936  0.01163316
#> cat_4       59 52.02296  0.96732827
#> 
#> $`theta = 0.8512`
#>       Observed Expected z.Residual
#> cat_0        7 14.09896 -1.8906068
#> cat_1       45 54.28449 -1.2601441
#> cat_2       48 49.58044 -0.2244513
#> cat_3       26 20.49440  1.2161493
#> cat_4       74 61.54171  1.5880848
#> 
#> $`theta = 1.4358`
#>       Observed  Expected z.Residual
#> cat_0        6  9.087564 -1.0242177
#> cat_1       25 40.094053 -2.3837784
#> cat_2       44 45.694100 -0.2506161
#> cat_3       21 22.208083 -0.2563547
#> cat_4      104 82.916200  2.3154169
#> 

mod2 <- mirt(dat, 1, 'Rasch')
#> 
Iteration: 1, Log-Lik: -30695.766, Max-Change: 0.71655
Iteration: 2, Log-Lik: -29726.980, Max-Change: 0.07848
Iteration: 3, Log-Lik: -29643.637, Max-Change: 0.05551
Iteration: 4, Log-Lik: -29611.208, Max-Change: 0.03577
Iteration: 5, Log-Lik: -29597.409, Max-Change: 0.01191
Iteration: 6, Log-Lik: -29591.508, Max-Change: 0.01423
Iteration: 7, Log-Lik: -29588.526, Max-Change: 0.00502
Iteration: 8, Log-Lik: -29587.133, Max-Change: 0.00323
Iteration: 9, Log-Lik: -29586.467, Max-Change: 0.00498
Iteration: 10, Log-Lik: -29586.046, Max-Change: 0.00380
Iteration: 11, Log-Lik: -29585.825, Max-Change: 0.00147
Iteration: 12, Log-Lik: -29585.739, Max-Change: 0.00132
Iteration: 13, Log-Lik: -29585.690, Max-Change: 0.00062
Iteration: 14, Log-Lik: -29585.666, Max-Change: 0.00049
Iteration: 15, Log-Lik: -29585.655, Max-Change: 0.00039
Iteration: 16, Log-Lik: -29585.651, Max-Change: 0.00095
Iteration: 17, Log-Lik: -29585.646, Max-Change: 0.00021
Iteration: 18, Log-Lik: -29585.645, Max-Change: 0.00015
Iteration: 19, Log-Lik: -29585.644, Max-Change: 0.00025
Iteration: 20, Log-Lik: -29585.644, Max-Change: 0.00004
itemfit(mod2, 'infit', method = 'ML')
#>       item outfit z.outfit infit z.infit
#> 1   Item_1  0.959   -1.407 0.946  -2.141
#> 2   Item_2  1.098    3.226 1.074   2.791
#> 3   Item_3  0.962   -1.326 0.961  -1.575
#> 4   Item_4  0.946   -1.867 0.932  -2.704
#> 5   Item_5  1.121    3.943 1.094   3.496
#> 6   Item_6  0.917   -2.902 0.917  -3.296
#> 7   Item_7  0.864   -4.829 0.881  -4.899
#> 8   Item_8  0.873   -4.656 0.879  -5.025
#> 9   Item_9  0.876   -4.467 0.887  -4.696
#> 10 Item_10  0.883   -4.255 0.892  -4.519

# massive list of tables for S-X2
tables <- itemfit(mod, return.tables = TRUE)

#observed and expected total score patterns for item 1 (post collapsing)
tables$O[[1]]
#>     0  1  2  3  4
#> 4  12  3  0  0  0
#> 5   6  1  0  0  0
#> 6   8 17  1  0  0
#> 7  12 16  5  0  0
#> 8  22  8  0  0  0
#> 9  30 20  3  3  1
#> 10 19 27  9  1  7
#> 11 16 32  9  4  0
#> 12 17 40 17  1  5
#> 13 25 51 15  4  8
#> 14 22 44 14  3  8
#> 15 22 46 22  5 14
#> 16 14 41 32  8 24
#> 17 11 42 31  8 10
#> 18 11 57 25  7 25
#> 19 17 41 37 11 15
#> 20 11 35 28 12 26
#> 21 10 32 32  8 22
#> 22  5 32 18 15 29
#> 23  2 23 17  7 33
#> 24  2 30 22  9 23
#> 25  3 15 19  7 28
#> 26  3 12 16 11 23
#> 27  4 13 12  4 19
#> 28  3  6  9  5 18
#> 29  3  6  2 17  0
#> 30  3 10  2 21  0
#> 31  1  2  1 13  0
#> 32  1  4  5  6  0
#> 33  3  4  4  5  0
#> 34  1  3  1 11  0
#> 35  2  6  0  0  0
#> 36  2  6  0  0  0
tables$E[[1]]
#>            [,1]      [,2]      [,3]      [,4]      [,5]
#>  [1,] 11.023325  3.976675        NA        NA        NA
#>  [2,]  4.102366  2.897634        NA        NA        NA
#>  [3,] 13.498246 10.610902  1.890852        NA        NA
#>  [4,] 15.184304 14.492730  3.322965        NA        NA
#>  [5,] 12.249443 13.799872  3.950685        NA        NA
#>  [6,] 20.682046 26.920288  6.923239  1.157706  1.316720
#>  [7,] 20.332439 30.097150  8.830861  1.641385  2.098165
#>  [8,] 17.517441 29.135716  9.625822  1.958940  2.762080
#>  [9,] 20.446921 37.829468 13.940499  3.072836  4.710276
#> [10,] 23.437800 47.811327 19.504466  4.622495  7.623912
#> [11,] 18.436615 41.167389 18.467918  4.679944  8.248134
#> [12,] 19.651227 47.756678 23.431406  6.318731 11.841957
#> [13,] 19.076413 50.199010 26.830125  7.670547 15.223905
#> [14,] 14.528071 41.195659 23.904020  7.227464 15.144786
#> [15,] 15.799085 48.086720 30.192468  9.636968 21.284760
#> [16,] 13.544069 44.116503 29.895563 10.055666 23.388198
#> [17,] 11.078348 38.500292 28.110440  9.952500 24.358420
#> [18,]  9.068050 33.529616 26.330542  9.809752 25.262041
#> [19,]  7.581094 29.780090 25.109651  9.840833 26.688332
#> [20,]  5.489874 22.880802 20.702905  8.532437 24.393982
#> [21,]  5.010515 22.116677 21.467501  9.311108 28.094199
#> [22,]  3.626463 16.954931 17.637672  8.059013 25.721921
#> [23,]  2.805419 13.907880 15.517623  7.472196 25.296882
#> [24,]  1.907017 10.013898 12.004816  6.104317 21.969952
#> [25,]  1.261885  7.039995  9.063539  4.881523 18.753058
#> [26,]  4.944641  5.875443  3.354204 13.825711        NA
#> [27,]  5.454637  7.095249  4.313860 19.136254        NA
#> [28,]  2.176787  3.093386  2.019117  9.710709        NA
#> [29,]  1.685470  2.659415  1.858932  9.796184        NA
#> [30,]  1.334541  2.384692  1.813140 10.467628        NA
#> [31,]  1.040082  2.042086  1.733955 11.183876        NA
#> [32,]  2.050562  5.949438        NA        NA        NA
#> [33,]  1.369048  6.630952        NA        NA        NA

# can also select specific items
# itemfit(mod, return.tables = TRUE, which.items=1)

# fit stats with missing data (run in parallel using all cores)
dat[sample(1:prod(dim(dat)), 100)] <- NA
raschfit <- mirt(dat, 1, itemtype='Rasch')
#> 
Iteration: 1, Log-Lik: -30540.692, Max-Change: 0.71626
Iteration: 2, Log-Lik: -29576.074, Max-Change: 0.07969
Iteration: 3, Log-Lik: -29491.591, Max-Change: 0.06442
Iteration: 4, Log-Lik: -29459.533, Max-Change: 0.03044
Iteration: 5, Log-Lik: -29446.023, Max-Change: 0.01942
Iteration: 6, Log-Lik: -29439.988, Max-Change: 0.01013
Iteration: 7, Log-Lik: -29437.156, Max-Change: 0.00491
Iteration: 8, Log-Lik: -29435.814, Max-Change: 0.00595
Iteration: 9, Log-Lik: -29435.088, Max-Change: 0.00299
Iteration: 10, Log-Lik: -29434.756, Max-Change: 0.00360
Iteration: 11, Log-Lik: -29434.539, Max-Change: 0.00274
Iteration: 12, Log-Lik: -29434.429, Max-Change: 0.00208
Iteration: 13, Log-Lik: -29434.362, Max-Change: 0.00105
Iteration: 14, Log-Lik: -29434.332, Max-Change: 0.00051
Iteration: 15, Log-Lik: -29434.319, Max-Change: 0.00039
Iteration: 16, Log-Lik: -29434.314, Max-Change: 0.00109
Iteration: 17, Log-Lik: -29434.308, Max-Change: 0.00019
Iteration: 18, Log-Lik: -29434.306, Max-Change: 0.00020
Iteration: 19, Log-Lik: -29434.306, Max-Change: 0.00077
Iteration: 20, Log-Lik: -29434.305, Max-Change: 0.00005

# use only valid data by removing rows with missing terms
itemfit(raschfit, c('S_X2', 'infit'), na.rm = TRUE)
#> Sample size after row-wise response data removal: 1901
#>       item outfit z.outfit infit z.infit    S_X2 df.S_X2 RMSEA.S_X2 p.S_X2
#> 1   Item_1  0.906   -3.626 0.911  -3.660 155.053     102      0.017  0.001
#> 2   Item_2  0.997   -0.107 1.004   0.146 146.662     103      0.015  0.003
#> 3   Item_3  0.917   -3.282 0.919  -3.385 114.783     103      0.008  0.201
#> 4   Item_4  0.884   -4.448 0.896  -4.291 121.470     102      0.010  0.092
#> 5   Item_5  1.006    0.235 1.009   0.349 204.451     103      0.023  0.000
#> 6   Item_6  0.880   -4.515 0.895  -4.216  93.810     103      0.000  0.730
#> 7   Item_7  0.852   -5.852 0.866  -5.666 129.878     102      0.012  0.033
#> 8   Item_8  0.862   -5.635 0.870  -5.607 120.879     102      0.010  0.098
#> 9   Item_9  0.855   -5.841 0.867  -5.722  96.812     102      0.000  0.627
#> 10 Item_10  0.852   -6.127 0.863  -6.019 111.851     101      0.008  0.216

# note that X2, G2, PV-Q1, and X2* do not require complete datasets
thetas <- fscores(raschfit, method = 'ML') # save for faster computations
itemfit(raschfit, c('X2', 'G2'), Theta=thetas)
#>       item      X2 df.X2 RMSEA.X2  p.X2     G2 df.G2 RMSEA.G2  p.G2
#> 1   Item_1  56.082    36    0.017 0.018 57.138    36    0.017 0.014
#> 2   Item_2  72.433    36    0.023 0.000 68.605    36    0.021 0.001
#> 3   Item_3  51.674    36    0.015 0.044 52.944    36    0.015 0.034
#> 4   Item_4  42.209    36    0.009 0.220 40.864    36    0.008 0.265
#> 5   Item_5 108.433    36    0.032 0.000 93.285    36    0.028 0.000
#> 6   Item_6  37.478    36    0.005 0.401 39.799    36    0.007 0.305
#> 7   Item_7  61.895    36    0.019 0.005 68.502    35    0.022 0.001
#> 8   Item_8  56.125    36    0.017 0.017 59.579    36    0.018 0.008
#> 9   Item_9  66.332    36    0.021 0.002 69.041    36    0.021 0.001
#> 10 Item_10  47.281    36    0.013 0.099 51.188    36    0.015 0.048
itemfit(raschfit, empirical.plot=1, Theta=thetas)

itemfit(raschfit, 'X2', return.tables=TRUE, which.items=1, Theta=thetas)
#> $`theta = -0.9751`
#>       Observed  Expected z.Residual
#> cat_0       96 89.203274  0.7196302
#> cat_1       81 87.319279 -0.6762581
#> cat_2       14 20.552190 -1.4452982
#> cat_3        5  2.584993  1.5020654
#> cat_4        6  2.340264  2.3923098
#> 
#> $`theta = -0.4747`
#>       Observed  Expected z.Residual
#> cat_0       52 55.810605 -0.5100768
#> cat_1       98 90.111135  0.8310464
#> cat_2       34 34.983142 -0.1662214
#> cat_3        6  7.257589 -0.4668126
#> cat_4        9 10.837528 -0.5581731
#> 
#> $`theta = -0.2825`
#>       Observed Expected z.Residual
#> cat_0       45 43.95405  0.1577652
#> cat_1       95 86.00287  0.9701688
#> cat_2       34 40.46184 -1.0158593
#> cat_3        9 10.17259 -0.3676465
#> cat_4       16 18.40864 -0.5613857
#> 
#> $`theta = -0.151`
#>       Observed Expected z.Residual
#> cat_0       33 36.30398 -0.5483529
#> cat_1       74 81.02032 -0.7799379
#> cat_2       45 43.47628  0.2310896
#> cat_3       11 12.46706 -0.4154939
#> cat_4       36 25.73237  2.0240925
#> 
#> $`theta = -0.0334`
#>       Observed Expected z.Residual
#> cat_0       19 29.93222 -1.9981990
#> cat_1       90 75.13532  1.7148795
#> cat_2       48 45.34903  0.3936594
#> cat_3       12 14.62666 -0.6868010
#> cat_4       30 33.95678 -0.6790139
#> 
#> $`theta = 0.0651`
#>       Observed Expected z.Residual
#> cat_0       23 25.02007 -0.4038516
#> cat_1       62 69.30476 -0.8774538
#> cat_2       63 46.15898  2.4787928
#> cat_3       17 16.42868  0.1409549
#> cat_4       34 42.08752 -1.2466326
#> 
#> $`theta = 0.1642`
#>       Observed Expected  z.Residual
#> cat_0       19 20.52933 -0.33753058
#> cat_1       63 62.79341  0.02607073
#> cat_2       45 46.18193 -0.17392181
#> cat_3       23 18.15027  1.13834925
#> cat_4       49 51.34506 -0.32726919
#> 
#> $`theta = 0.2767`
#>       Observed Expected   z.Residual
#> cat_0        4 16.04548 -3.007099726
#> cat_1       66 54.92379  1.494551513
#> cat_2       47 45.20504  0.266969704
#> cat_3       19 19.88229 -0.197868736
#> cat_4       63 62.94340  0.007134114
#> 
#> $`theta = 0.4164`
#>       Observed Expected z.Residual
#> cat_0       11 11.43297 -0.1280506
#> cat_1       44 45.00327 -0.1495531
#> cat_2       48 42.59391  0.8283409
#> cat_3       26 21.54290  0.9602843
#> cat_4       70 78.42694 -0.9515622
#> 
#> $`theta = 0.7405`
#>       Observed   Expected z.Residual
#> cat_0        4   4.631286 -0.2933428
#> cat_1       23  25.205901 -0.4393746
#> cat_2       43  32.985379  1.7437081
#> cat_3       22  23.067149 -0.2221919
#> cat_4      110 116.110285 -0.5670562
#> 

# }