Sex gaps in intelligence in the UK

About

Reanalysis of this paper https://www.sciencedirect.com/science/article/pii/S0160289622000484

Init

library(kirkegaard)

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##     +

load_packages(
  mirt
)

## Loading required package: stats4

theme_set(theme_bw())

options(
    digits = 3
)

Data

d1 = read_csv("data/Study 1/[Data] Study 1.csv")

## Rows: 656 Columns: 125
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr  (11): CountryofBirth, CurrentCountryofResidence, EmploymentStatus, Ethn...
## dbl (114): Durationinseconds, VR1, VR2, VR3, VR4, VR5, VR6, VR7, VR8, VR9, V...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

d1_scoring_key = read_tsv("data/scoring key.tsv")

## Rows: 81 Columns: 2
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: "\t"
## chr (1): item
## dbl (1): key
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

Analyses

Study 1

#get items, score them
d1_items = d1 %>% select(VR1:EC40, FLS1:FLS5)

#same order
assert_that(all(names(d1_items) == d1_scoring_key$item))

## [1] TRUE

#score to 1-0
d1_items_scored = score_items(d1_items, d1_scoring_key$key)

#g EFA IRT
d1_mirt_g = mirt(
  d1_items_scored %>% select(VR1:MR11),
  model = 1
)

## 
Iteration: 1, Log-Lik: -12574.758, Max-Change: 0.54531
Iteration: 2, Log-Lik: -12402.175, Max-Change: 0.29987
Iteration: 3, Log-Lik: -12381.561, Max-Change: 0.15589
Iteration: 4, Log-Lik: -12375.557, Max-Change: 0.08896
Iteration: 5, Log-Lik: -12372.865, Max-Change: 0.05674
Iteration: 6, Log-Lik: -12371.572, Max-Change: 0.04036
Iteration: 7, Log-Lik: -12370.673, Max-Change: 0.02076
Iteration: 8, Log-Lik: -12370.429, Max-Change: 0.01612
Iteration: 9, Log-Lik: -12370.289, Max-Change: 0.01180
Iteration: 10, Log-Lik: -12370.133, Max-Change: 0.00364
Iteration: 11, Log-Lik: -12370.124, Max-Change: 0.00245
Iteration: 12, Log-Lik: -12370.120, Max-Change: 0.00198
Iteration: 13, Log-Lik: -12370.114, Max-Change: 0.00089
Iteration: 14, Log-Lik: -12370.113, Max-Change: 0.00031
Iteration: 15, Log-Lik: -12370.113, Max-Change: 0.00025
Iteration: 16, Log-Lik: -12370.113, Max-Change: 0.00023
Iteration: 17, Log-Lik: -12370.113, Max-Change: 0.00021
Iteration: 18, Log-Lik: -12370.113, Max-Change: 0.00019
Iteration: 19, Log-Lik: -12370.113, Max-Change: 0.00045
Iteration: 20, Log-Lik: -12370.113, Max-Change: 0.00007

summary(d1_mirt_g)

##         F1     h2
## VR1  0.633 0.4005
## VR2  0.302 0.0913
## VR3  0.405 0.1638
## VR4  0.463 0.2142
## VR5  0.699 0.4889
## VR6  0.324 0.1050
## VR7  0.634 0.4022
## VR8  0.419 0.1756
## VR9  0.463 0.2144
## VR10 0.463 0.2145
## VR11 0.145 0.0210
## VR12 0.578 0.3339
## VR13 0.509 0.2593
## VR14 0.486 0.2366
## VR15 0.385 0.1485
## VR16 0.292 0.0850
## LN1  0.648 0.4193
## LN2  0.677 0.4585
## LN3  0.718 0.5159
## LN4  0.696 0.4848
## LN5  0.684 0.4684
## LN6  0.764 0.5838
## LN7  0.781 0.6096
## LN8  0.662 0.4379
## LN9  0.697 0.4853
## MR1  0.539 0.2904
## MR2  0.503 0.2528
## MR3  0.422 0.1779
## MR4  0.578 0.3339
## MR5  0.656 0.4300
## MR6  0.532 0.2827
## MR7  0.450 0.2025
## MR8  0.588 0.3456
## MR9  0.376 0.1411
## MR10 0.505 0.2554
## MR11 0.488 0.2382
## 
## SS loadings:  11 
## Proportion Var:  0.305 
## 
## Factor correlations: 
## 
##    F1
## F1  1

#scores
d1_mirt_g_scores = fscores(d1_mirt_g, full.scores = T, full.scores.SE = T)
d1$g = d1_mirt_g_scores[, 1] %>% standardize(focal_group = (d1$EthnicitySimplified == "White"))

#reliability
empirical_rxx(d1_mirt_g_scores)

##    F1 
## 0.887

#sex gap
cohen.d(d1 %>% select(g), d1$Sex)

## Call: cohen.d(x = d1 %>% select(g), group = d1$Sex)
## Cohen d statistic of difference between two means
##   lower effect upper
## g  0.08   0.25  0.42
## 
## Multivariate (Mahalanobis) distance between groups
## [1] 0.25
## r equivalent of difference between two means
##    g 
## 0.11

kirkegaard::adj_d_reliability(cohen.d(d1 %>% select(g), d1$Sex)$cohen.d[2], empirical_rxx(d1_mirt_g_scores))

##    F1 
## 0.265

#DIF test
d1_DIF = DIF_test(
  items = d1_items_scored %>% select(VR1:MR11),
  model = 1,
  group = d1$Sex
)

## There are 8 steps

## Step 1: Initial joint fit

## 
Iteration: 1, Log-Lik: -12574.758, Max-Change: 0.54531
Iteration: 2, Log-Lik: -12402.175, Max-Change: 0.29987
Iteration: 3, Log-Lik: -12381.561, Max-Change: 0.15589
Iteration: 4, Log-Lik: -12375.557, Max-Change: 0.08896
Iteration: 5, Log-Lik: -12372.865, Max-Change: 0.05674
Iteration: 6, Log-Lik: -12371.572, Max-Change: 0.04036
Iteration: 7, Log-Lik: -12370.673, Max-Change: 0.02076
Iteration: 8, Log-Lik: -12370.429, Max-Change: 0.01612
Iteration: 9, Log-Lik: -12370.289, Max-Change: 0.01180
Iteration: 10, Log-Lik: -12370.133, Max-Change: 0.00364
Iteration: 11, Log-Lik: -12370.124, Max-Change: 0.00245
Iteration: 12, Log-Lik: -12370.120, Max-Change: 0.00198
Iteration: 13, Log-Lik: -12370.114, Max-Change: 0.00089
Iteration: 14, Log-Lik: -12370.113, Max-Change: 0.00031
Iteration: 15, Log-Lik: -12370.113, Max-Change: 0.00025
Iteration: 16, Log-Lik: -12370.113, Max-Change: 0.00023
Iteration: 17, Log-Lik: -12370.113, Max-Change: 0.00021
Iteration: 18, Log-Lik: -12370.113, Max-Change: 0.00019
Iteration: 19, Log-Lik: -12370.113, Max-Change: 0.00045
Iteration: 20, Log-Lik: -12370.113, Max-Change: 0.00007

## 
## Step 2: Initial MI fit

## 
Iteration: 1, Log-Lik: -12574.758, Max-Change: 0.54275
Iteration: 2, Log-Lik: -12390.884, Max-Change: 0.24814
Iteration: 3, Log-Lik: -12375.445, Max-Change: 0.12740
Iteration: 4, Log-Lik: -12371.737, Max-Change: 0.07401
Iteration: 5, Log-Lik: -12369.867, Max-Change: 0.05910
Iteration: 6, Log-Lik: -12368.672, Max-Change: 0.04838
Iteration: 7, Log-Lik: -12366.791, Max-Change: 0.10827
Iteration: 8, Log-Lik: -12366.315, Max-Change: 0.03132
Iteration: 9, Log-Lik: -12366.179, Max-Change: 0.01612
Iteration: 10, Log-Lik: -12365.985, Max-Change: 0.02436
Iteration: 11, Log-Lik: -12365.936, Max-Change: 0.00924
Iteration: 12, Log-Lik: -12365.909, Max-Change: 0.00572
Iteration: 13, Log-Lik: -12365.850, Max-Change: 0.01613
Iteration: 14, Log-Lik: -12365.834, Max-Change: 0.00389
Iteration: 15, Log-Lik: -12365.831, Max-Change: 0.00151
Iteration: 16, Log-Lik: -12365.825, Max-Change: 0.00173
Iteration: 17, Log-Lik: -12365.824, Max-Change: 0.00093
Iteration: 18, Log-Lik: -12365.823, Max-Change: 0.00086
Iteration: 19, Log-Lik: -12365.819, Max-Change: 0.00210
Iteration: 20, Log-Lik: -12365.818, Max-Change: 0.00042
Iteration: 21, Log-Lik: -12365.818, Max-Change: 0.00040
Iteration: 22, Log-Lik: -12365.817, Max-Change: 0.00104
Iteration: 23, Log-Lik: -12365.817, Max-Change: 0.00020
Iteration: 24, Log-Lik: -12365.817, Max-Change: 0.00019
Iteration: 25, Log-Lik: -12365.817, Max-Change: 0.00052
Iteration: 26, Log-Lik: -12365.817, Max-Change: 0.00010

## 
## Step 3: Leave one out MI testing

## 
## Step 4: Fit without DIF items, liberal threshold

## 
Iteration: 1, Log-Lik: -12973.818, Max-Change: 0.53420
Iteration: 2, Log-Lik: -12862.670, Max-Change: 0.31140
Iteration: 3, Log-Lik: -12845.492, Max-Change: 0.17862
Iteration: 4, Log-Lik: -12840.327, Max-Change: 0.09945
Iteration: 5, Log-Lik: -12838.387, Max-Change: 0.05662
Iteration: 6, Log-Lik: -12837.603, Max-Change: 0.03808
Iteration: 7, Log-Lik: -12837.176, Max-Change: 0.02120
Iteration: 8, Log-Lik: -12837.046, Max-Change: 0.01343
Iteration: 9, Log-Lik: -12836.983, Max-Change: 0.00983
Iteration: 10, Log-Lik: -12836.922, Max-Change: 0.00196
Iteration: 11, Log-Lik: -12836.919, Max-Change: 0.00165
Iteration: 12, Log-Lik: -12836.918, Max-Change: 0.00134
Iteration: 13, Log-Lik: -12836.916, Max-Change: 0.00018
Iteration: 14, Log-Lik: -12836.916, Max-Change: 0.00016
Iteration: 15, Log-Lik: -12836.916, Max-Change: 0.00074
Iteration: 16, Log-Lik: -12836.916, Max-Change: 0.00037
Iteration: 17, Log-Lik: -12836.916, Max-Change: 0.00015
Iteration: 18, Log-Lik: -12836.916, Max-Change: 0.00027
Iteration: 19, Log-Lik: -12836.916, Max-Change: 0.00016
Iteration: 20, Log-Lik: -12836.916, Max-Change: 0.00004

## 
## Step 5: Fit without DIF items, conservative threshold

## 
Iteration: 1, Log-Lik: -12574.758, Max-Change: 0.54531
Iteration: 2, Log-Lik: -12402.175, Max-Change: 0.29987
Iteration: 3, Log-Lik: -12381.561, Max-Change: 0.15589
Iteration: 4, Log-Lik: -12375.557, Max-Change: 0.08896
Iteration: 5, Log-Lik: -12372.865, Max-Change: 0.05674
Iteration: 6, Log-Lik: -12371.572, Max-Change: 0.04036
Iteration: 7, Log-Lik: -12370.673, Max-Change: 0.02076
Iteration: 8, Log-Lik: -12370.429, Max-Change: 0.01612
Iteration: 9, Log-Lik: -12370.289, Max-Change: 0.01180
Iteration: 10, Log-Lik: -12370.133, Max-Change: 0.00364
Iteration: 11, Log-Lik: -12370.124, Max-Change: 0.00245
Iteration: 12, Log-Lik: -12370.120, Max-Change: 0.00198
Iteration: 13, Log-Lik: -12370.114, Max-Change: 0.00089
Iteration: 14, Log-Lik: -12370.113, Max-Change: 0.00031
Iteration: 15, Log-Lik: -12370.113, Max-Change: 0.00025
Iteration: 16, Log-Lik: -12370.113, Max-Change: 0.00023
Iteration: 17, Log-Lik: -12370.113, Max-Change: 0.00021
Iteration: 18, Log-Lik: -12370.113, Max-Change: 0.00019
Iteration: 19, Log-Lik: -12370.113, Max-Change: 0.00045
Iteration: 20, Log-Lik: -12370.113, Max-Change: 0.00007

## 
## Step 6: Fit with anchor items, liberal threshold

## 
Iteration: 1, Log-Lik: -12574.758, Max-Change: 0.69910
Iteration: 2, Log-Lik: -12364.941, Max-Change: 0.33010
Iteration: 3, Log-Lik: -12348.378, Max-Change: 0.16366
Iteration: 4, Log-Lik: -12344.399, Max-Change: 0.08893
Iteration: 5, Log-Lik: -12342.500, Max-Change: 0.05836
Iteration: 6, Log-Lik: -12341.305, Max-Change: 0.05005
Iteration: 7, Log-Lik: -12339.464, Max-Change: 0.11388
Iteration: 8, Log-Lik: -12338.950, Max-Change: 0.03213
Iteration: 9, Log-Lik: -12338.791, Max-Change: 0.01915
Iteration: 10, Log-Lik: -12338.561, Max-Change: 0.03509
Iteration: 11, Log-Lik: -12338.489, Max-Change: 0.01029
Iteration: 12, Log-Lik: -12338.462, Max-Change: 0.00660
Iteration: 13, Log-Lik: -12338.411, Max-Change: 0.01867
Iteration: 14, Log-Lik: -12338.392, Max-Change: 0.00394
Iteration: 15, Log-Lik: -12338.389, Max-Change: 0.00198
Iteration: 16, Log-Lik: -12338.384, Max-Change: 0.00317
Iteration: 17, Log-Lik: -12338.382, Max-Change: 0.00095
Iteration: 18, Log-Lik: -12338.381, Max-Change: 0.00076
Iteration: 19, Log-Lik: -12338.379, Max-Change: 0.00220
Iteration: 20, Log-Lik: -12338.378, Max-Change: 0.00052
Iteration: 21, Log-Lik: -12338.378, Max-Change: 0.00038
Iteration: 22, Log-Lik: -12338.377, Max-Change: 0.00064
Iteration: 23, Log-Lik: -12338.377, Max-Change: 0.00026
Iteration: 24, Log-Lik: -12338.377, Max-Change: 0.00022
Iteration: 25, Log-Lik: -12338.377, Max-Change: 0.00052
Iteration: 26, Log-Lik: -12338.377, Max-Change: 0.00013
Iteration: 27, Log-Lik: -12338.377, Max-Change: 0.00014
Iteration: 28, Log-Lik: -12338.377, Max-Change: 0.00028
Iteration: 29, Log-Lik: -12338.377, Max-Change: 0.00006

## 
## Step 7: Fit with anchor items, conservative threshold

## 
Iteration: 1, Log-Lik: -12574.758, Max-Change: 0.54275
Iteration: 2, Log-Lik: -12390.884, Max-Change: 0.24814
Iteration: 3, Log-Lik: -12375.445, Max-Change: 0.12740
Iteration: 4, Log-Lik: -12371.737, Max-Change: 0.07401
Iteration: 5, Log-Lik: -12369.867, Max-Change: 0.05910
Iteration: 6, Log-Lik: -12368.672, Max-Change: 0.04838
Iteration: 7, Log-Lik: -12366.791, Max-Change: 0.10827
Iteration: 8, Log-Lik: -12366.315, Max-Change: 0.03132
Iteration: 9, Log-Lik: -12366.179, Max-Change: 0.01612
Iteration: 10, Log-Lik: -12365.985, Max-Change: 0.02436
Iteration: 11, Log-Lik: -12365.936, Max-Change: 0.00924
Iteration: 12, Log-Lik: -12365.909, Max-Change: 0.00572
Iteration: 13, Log-Lik: -12365.850, Max-Change: 0.01613
Iteration: 14, Log-Lik: -12365.834, Max-Change: 0.00389
Iteration: 15, Log-Lik: -12365.831, Max-Change: 0.00151
Iteration: 16, Log-Lik: -12365.825, Max-Change: 0.00173
Iteration: 17, Log-Lik: -12365.824, Max-Change: 0.00093
Iteration: 18, Log-Lik: -12365.823, Max-Change: 0.00086
Iteration: 19, Log-Lik: -12365.819, Max-Change: 0.00210
Iteration: 20, Log-Lik: -12365.818, Max-Change: 0.00042
Iteration: 21, Log-Lik: -12365.818, Max-Change: 0.00040
Iteration: 22, Log-Lik: -12365.817, Max-Change: 0.00104
Iteration: 23, Log-Lik: -12365.817, Max-Change: 0.00020
Iteration: 24, Log-Lik: -12365.817, Max-Change: 0.00019
Iteration: 25, Log-Lik: -12365.817, Max-Change: 0.00052
Iteration: 26, Log-Lik: -12365.817, Max-Change: 0.00010

## 
## Step 8: Get scores

d1_DIF$effect_size_test

## $liberal
##           Effect Size  Value
## 1                STDS 0.2513
## 2                UTDS 0.6764
## 3              UETSDS 0.2896
## 4               ETSSD 0.0377
## 5         Starks.DTFR 0.2586
## 6               UDTFR 0.6816
## 7              UETSDN 0.3042
## 8 theta.of.max.test.D 0.2620
## 9           Test.Dmax 0.4556
## 
## $conservative
##           Effect Size Value
## 1                STDS  0.00
## 2                UTDS  0.00
## 3              UETSDS  0.00
## 4               ETSSD  0.00
## 5         Starks.DTFR  0.00
## 6               UDTFR  0.00
## 7              UETSDN  0.00
## 8 theta.of.max.test.D  0.12
## 9           Test.Dmax  0.00

d1_DIF$effect_size_items

## $liberal
##           SIDS  UIDS   SIDN  UIDN   ESSD theta.of.max.D  max.D mean.ES.foc
## item.1   0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.693
## item.2  -0.103 0.103 -0.102 0.102 -1.152         -1.986 -0.166       0.739
## item.3   0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.858
## item.4   0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.125
## item.5   0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.770
## item.6   0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.645
## item.7   0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.738
## item.8   0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.989
## item.9  -0.073 0.074 -0.071 0.072 -0.440         -1.790 -0.188       0.691
## item.10  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.496
## item.11  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.214
## item.12  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.821
## item.13  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.610
## item.14  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.492
## item.15  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.926
## item.16  0.101 0.102  0.101 0.103  0.848          1.574  0.146       0.679
## item.17  0.101 0.101  0.100 0.100  0.449         -0.262  0.151       0.770
## item.18  0.110 0.110  0.113 0.113  0.393          0.323  0.164       0.570
## item.19  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.693
## item.20  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.316
## item.21  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.548
## item.22  0.018 0.083  0.014 0.081  0.057          1.288 -0.119       0.443
## item.23  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.554
## item.24  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.336
## item.25  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.338
## item.26  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.726
## item.27  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.581
## item.28  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.526
## item.29  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.501
## item.30  0.097 0.104  0.103 0.110  0.343          0.714  0.191       0.559
## item.31  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.476
## item.32  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.227
## item.33  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.491
## item.34  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.273
## item.35  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.302
## item.36  0.000 0.000  0.000 0.000  0.000          0.047  0.000       0.390
##         mean.ES.ref
## item.1        0.693
## item.2        0.842
## item.3        0.858
## item.4        0.125
## item.5        0.770
## item.6        0.645
## item.7        0.738
## item.8        0.989
## item.9        0.764
## item.10       0.496
## item.11       0.214
## item.12       0.821
## item.13       0.610
## item.14       0.492
## item.15       0.926
## item.16       0.578
## item.17       0.669
## item.18       0.460
## item.19       0.693
## item.20       0.316
## item.21       0.548
## item.22       0.425
## item.23       0.554
## item.24       0.336
## item.25       0.338
## item.26       0.726
## item.27       0.581
## item.28       0.526
## item.29       0.501
## item.30       0.462
## item.31       0.476
## item.32       0.227
## item.33       0.491
## item.34       0.273
## item.35       0.302
## item.36       0.390
## 
## $conservative
##         SIDS UIDS SIDN UIDN ESSD theta.of.max.D max.D mean.ES.foc mean.ES.ref
## item.1     0    0    0    0    0           0.12     0       0.701       0.701
## item.2     0    0    0    0    0           0.12     0       0.816       0.816
## item.3     0    0    0    0    0           0.12     0       0.861       0.861
## item.4     0    0    0    0    0           0.12     0       0.128       0.128
## item.5     0    0    0    0    0           0.12     0       0.777       0.777
## item.6     0    0    0    0    0           0.12     0       0.649       0.649
## item.7     0    0    0    0    0           0.12     0       0.745       0.745
## item.8     0    0    0    0    0           0.12     0       0.990       0.990
## item.9     0    0    0    0    0           0.12     0       0.751       0.751
## item.10    0    0    0    0    0           0.12     0       0.504       0.504
## item.11    0    0    0    0    0           0.12     0       0.215       0.215
## item.12    0    0    0    0    0           0.12     0       0.826       0.826
## item.13    0    0    0    0    0           0.12     0       0.617       0.617
## item.14    0    0    0    0    0           0.12     0       0.499       0.499
## item.15    0    0    0    0    0           0.12     0       0.928       0.928
## item.16    0    0    0    0    0           0.12     0       0.613       0.613
## item.17    0    0    0    0    0           0.12     0       0.704       0.704
## item.18    0    0    0    0    0           0.12     0       0.502       0.502
## item.19    0    0    0    0    0           0.12     0       0.702       0.702
## item.20    0    0    0    0    0           0.12     0       0.325       0.325
## item.21    0    0    0    0    0           0.12     0       0.558       0.558
## item.22    0    0    0    0    0           0.12     0       0.438       0.438
## item.23    0    0    0    0    0           0.12     0       0.566       0.566
## item.24    0    0    0    0    0           0.12     0       0.345       0.345
## item.25    0    0    0    0    0           0.12     0       0.348       0.348
## item.26    0    0    0    0    0           0.12     0       0.732       0.732
## item.27    0    0    0    0    0           0.12     0       0.588       0.588
## item.28    0    0    0    0    0           0.12     0       0.532       0.532
## item.29    0    0    0    0    0           0.12     0       0.509       0.509
## item.30    0    0    0    0    0           0.12     0       0.502       0.502
## item.31    0    0    0    0    0           0.12     0       0.484       0.484
## item.32    0    0    0    0    0           0.12     0       0.232       0.232
## item.33    0    0    0    0    0           0.12     0       0.499       0.499
## item.34    0    0    0    0    0           0.12     0       0.278       0.278
## item.35    0    0    0    0    0           0.12     0       0.308       0.308
## item.36    0    0    0    0    0           0.12     0       0.397       0.397

d1_DIF$fits$anchor_liberal %>% empirical_ES(plot = T)

#race gaps
table2(d1$EthnicitySimplified)

SMD_matrix(
  d1$g,
  d1$EthnicitySimplified %>% fct_relevel("White")
)

##         White   Asian  Black   Mixed  Other
## White      NA  0.1319  0.547  0.0432 -0.670
## Asian  0.1319      NA  0.415 -0.0887 -0.802
## Black  0.5469  0.4150     NA -0.5036 -1.217
## Mixed  0.0432 -0.0887 -0.504      NA -0.713
## Other -0.6701 -0.8020 -1.217 -0.7133     NA

Study 2

d2 = read_csv("data/Study 2/[Data] Study 2.csv")

## Rows: 700 Columns: 267
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr  (14): CountryofBirth, CurrentCountryofResidence, EmploymentStatus, Ethn...
## dbl (253): Durationinseconds, PFA_timer_FirstClick, PFA_timer_LastClick, PFA...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

d2_scoring_key = read_tsv("data/scoring key 2.tsv")

## Rows: 112 Columns: 2
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: "\t"
## chr (1): item
## dbl (1): key
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

#get items, score them
d2_items = d2 %>% select(PFA1:Q33, !!str_glue("SynA{1:25}"), EC1:FLS5)

#same order
assert_that(all(names(d2_items) == d2_scoring_key$item))

## [1] TRUE

#score to 1-0
d2_items_scored = score_items(d2_items, d2_scoring_key$key)

#g EFA IRT
d2_mirt_g = mirt(
  d2_items_scored %>% select(PFA1:SynA25),
  model = 1
)

## 
Iteration: 1, Log-Lik: -15842.005, Max-Change: 2.16548
Iteration: 2, Log-Lik: -15284.250, Max-Change: 0.62057
Iteration: 3, Log-Lik: -15229.195, Max-Change: 0.59708
Iteration: 4, Log-Lik: -15212.238, Max-Change: 0.26665
Iteration: 5, Log-Lik: -15206.736, Max-Change: 0.36171
Iteration: 6, Log-Lik: -15203.918, Max-Change: 0.23001
Iteration: 7, Log-Lik: -15202.496, Max-Change: 0.15650
Iteration: 8, Log-Lik: -15201.538, Max-Change: 0.12404
Iteration: 9, Log-Lik: -15200.836, Max-Change: 0.13606
Iteration: 10, Log-Lik: -15199.656, Max-Change: 0.04100
Iteration: 11, Log-Lik: -15199.374, Max-Change: 0.01571
Iteration: 12, Log-Lik: -15199.208, Max-Change: 0.01597
Iteration: 13, Log-Lik: -15198.824, Max-Change: 0.00672
Iteration: 14, Log-Lik: -15198.781, Max-Change: 0.00913
Iteration: 15, Log-Lik: -15198.745, Max-Change: 0.00605
Iteration: 16, Log-Lik: -15198.694, Max-Change: 0.00895
Iteration: 17, Log-Lik: -15198.673, Max-Change: 0.00295
Iteration: 18, Log-Lik: -15198.661, Max-Change: 0.00516
Iteration: 19, Log-Lik: -15198.648, Max-Change: 0.00350
Iteration: 20, Log-Lik: -15198.640, Max-Change: 0.00286
Iteration: 21, Log-Lik: -15198.634, Max-Change: 0.00217
Iteration: 22, Log-Lik: -15198.629, Max-Change: 0.00365
Iteration: 23, Log-Lik: -15198.626, Max-Change: 0.00177
Iteration: 24, Log-Lik: -15198.623, Max-Change: 0.00125
Iteration: 25, Log-Lik: -15198.619, Max-Change: 0.00266
Iteration: 26, Log-Lik: -15198.617, Max-Change: 0.00229
Iteration: 27, Log-Lik: -15198.615, Max-Change: 0.00223
Iteration: 28, Log-Lik: -15198.612, Max-Change: 0.00070
Iteration: 29, Log-Lik: -15198.611, Max-Change: 0.00034
Iteration: 30, Log-Lik: -15198.611, Max-Change: 0.00025
Iteration: 31, Log-Lik: -15198.611, Max-Change: 0.00022
Iteration: 32, Log-Lik: -15198.611, Max-Change: 0.00022
Iteration: 33, Log-Lik: -15198.611, Max-Change: 0.00107
Iteration: 34, Log-Lik: -15198.611, Max-Change: 0.00101
Iteration: 35, Log-Lik: -15198.610, Max-Change: 0.00088
Iteration: 36, Log-Lik: -15198.610, Max-Change: 0.00046
Iteration: 37, Log-Lik: -15198.610, Max-Change: 0.00025
Iteration: 38, Log-Lik: -15198.610, Max-Change: 0.00074
Iteration: 39, Log-Lik: -15198.610, Max-Change: 0.00046
Iteration: 40, Log-Lik: -15198.610, Max-Change: 0.00024
Iteration: 41, Log-Lik: -15198.610, Max-Change: 0.00060
Iteration: 42, Log-Lik: -15198.610, Max-Change: 0.00044
Iteration: 43, Log-Lik: -15198.610, Max-Change: 0.00023
Iteration: 44, Log-Lik: -15198.610, Max-Change: 0.00050
Iteration: 45, Log-Lik: -15198.610, Max-Change: 0.00042
Iteration: 46, Log-Lik: -15198.610, Max-Change: 0.00021
Iteration: 47, Log-Lik: -15198.610, Max-Change: 0.00046
Iteration: 48, Log-Lik: -15198.610, Max-Change: 0.00039
Iteration: 49, Log-Lik: -15198.610, Max-Change: 0.00019
Iteration: 50, Log-Lik: -15198.610, Max-Change: 0.00043
Iteration: 51, Log-Lik: -15198.610, Max-Change: 0.00036
Iteration: 52, Log-Lik: -15198.610, Max-Change: 0.00018
Iteration: 53, Log-Lik: -15198.610, Max-Change: 0.00041
Iteration: 54, Log-Lik: -15198.610, Max-Change: 0.00033
Iteration: 55, Log-Lik: -15198.610, Max-Change: 0.00016
Iteration: 56, Log-Lik: -15198.610, Max-Change: 0.00039
Iteration: 57, Log-Lik: -15198.610, Max-Change: 0.00030
Iteration: 58, Log-Lik: -15198.610, Max-Change: 0.00015
Iteration: 59, Log-Lik: -15198.610, Max-Change: 0.00038
Iteration: 60, Log-Lik: -15198.610, Max-Change: 0.00028
Iteration: 61, Log-Lik: -15198.610, Max-Change: 0.00014
Iteration: 62, Log-Lik: -15198.610, Max-Change: 0.00037
Iteration: 63, Log-Lik: -15198.610, Max-Change: 0.00025
Iteration: 64, Log-Lik: -15198.610, Max-Change: 0.00013
Iteration: 65, Log-Lik: -15198.610, Max-Change: 0.00036
Iteration: 66, Log-Lik: -15198.610, Max-Change: 0.00024
Iteration: 67, Log-Lik: -15198.610, Max-Change: 0.00012
Iteration: 68, Log-Lik: -15198.610, Max-Change: 0.00035
Iteration: 69, Log-Lik: -15198.610, Max-Change: 0.00022
Iteration: 70, Log-Lik: -15198.610, Max-Change: 0.00011
Iteration: 71, Log-Lik: -15198.610, Max-Change: 0.00034
Iteration: 72, Log-Lik: -15198.610, Max-Change: 0.00021
Iteration: 73, Log-Lik: -15198.610, Max-Change: 0.00011
Iteration: 74, Log-Lik: -15198.610, Max-Change: 0.00034
Iteration: 75, Log-Lik: -15198.610, Max-Change: 0.00020
Iteration: 76, Log-Lik: -15198.610, Max-Change: 0.00010
Iteration: 77, Log-Lik: -15198.610, Max-Change: 0.00033
Iteration: 78, Log-Lik: -15198.610, Max-Change: 0.00019
Iteration: 79, Log-Lik: -15198.610, Max-Change: 0.00010

summary(d2_mirt_g)

##            F1       h2
## PFA1   0.5340 0.285187
## PFA2   0.4834 0.233678
## PFA3   0.3994 0.159517
## PFA4   0.3278 0.107426
## PFA5   0.4455 0.198435
## PFA6   0.6672 0.445185
## PFA7   0.4021 0.161657
## PFA8   0.4078 0.166293
## PFA9   0.2972 0.088320
## PFA10  0.5054 0.255439
## Q2     0.4355 0.189624
## Q3     0.3019 0.091153
## Q4     0.4421 0.195452
## Q5     0.7774 0.604305
## Q6     0.2256 0.050901
## Q7     0.3795 0.144007
## Q8     0.2579 0.066508
## Q9     0.5273 0.278064
## Q10    0.8709 0.758394
## Q11    0.7302 0.533151
## Q12    0.5059 0.255931
## Q13    0.5116 0.261769
## Q14    0.6648 0.442007
## Q15    0.5198 0.270177
## Q16    0.7071 0.500010
## Q17    0.8137 0.662062
## Q18    0.4850 0.235204
## Q19    0.7593 0.576495
## Q20    0.8634 0.745431
## Q21    0.4995 0.249471
## Q22    0.6236 0.388878
## Q23    0.8769 0.768906
## Q24    0.0615 0.003780
## Q25    0.8141 0.662733
## Q26    0.6407 0.410558
## Q27    0.6831 0.466584
## Q28    0.3260 0.106275
## Q29    0.7604 0.578133
## Q30    0.8715 0.759468
## Q31    0.7024 0.493312
## Q32    0.9277 0.860656
## Q33    0.9003 0.810464
## SynA1  0.0129 0.000167
## SynA2  0.2900 0.084111
## SynA3  0.3081 0.094923
## SynA4  0.4579 0.209666
## SynA5  0.3502 0.122657
## SynA6  0.2730 0.074509
## SynA7  0.4598 0.211449
## SynA8  0.3055 0.093307
## SynA9  0.3158 0.099702
## SynA10 0.3676 0.135120
## SynA11 0.2026 0.041044
## SynA12 0.1277 0.016300
## SynA13 0.2433 0.059181
## SynA14 0.5549 0.307913
## SynA15 0.4844 0.234661
## SynA16 0.2687 0.072174
## SynA17 0.7506 0.563441
## SynA18 0.2734 0.074767
## SynA19 0.2495 0.062244
## SynA20 0.1267 0.016044
## SynA21 0.2751 0.075656
## SynA22 0.2972 0.088320
## SynA23 0.4907 0.240824
## SynA24 0.3226 0.104051
## SynA25 0.1311 0.017187
## 
## SS loadings:  18.6 
## Proportion Var:  0.278 
## 
## Factor correlations: 
## 
##    F1
## F1  1

#scores
d2_mirt_g_scores = fscores(d2_mirt_g, full.scores = T, full.scores.SE = T)
d2$g = d2_mirt_g_scores[, 1] %>% standardize(focal_group = (d2$EthnicitySimplified == "White"))

#reliability
empirical_rxx(d2_mirt_g_scores)

##    F1 
## 0.813

#sex gap
cohen.d(d2 %>% select(g), d2$Sex)

## Call: cohen.d(x = d2 %>% select(g), group = d2$Sex)
## Cohen d statistic of difference between two means
##   lower effect upper
## g  0.11   0.26  0.41
## 
## Multivariate (Mahalanobis) distance between groups
## [1] 0.26
## r equivalent of difference between two means
##    g 
## 0.13

kirkegaard::adj_d_reliability(cohen.d(d2 %>% select(g), d2$Sex)$cohen.d[2], empirical_rxx(d2_mirt_g_scores))

##    F1 
## 0.293

#DIF test
d2_DIF = DIF_test(
  items = d2_items_scored %>% select(PFA1:SynA25),
  model = 1,
  group = d2$Sex
)

## There are 8 steps
## Step 1: Initial joint fit

## 
Iteration: 1, Log-Lik: -15842.005, Max-Change: 2.16548
Iteration: 2, Log-Lik: -15284.250, Max-Change: 0.62057
Iteration: 3, Log-Lik: -15229.195, Max-Change: 0.59708
Iteration: 4, Log-Lik: -15212.238, Max-Change: 0.26665
Iteration: 5, Log-Lik: -15206.736, Max-Change: 0.36171
Iteration: 6, Log-Lik: -15203.918, Max-Change: 0.23001
Iteration: 7, Log-Lik: -15202.496, Max-Change: 0.15650
Iteration: 8, Log-Lik: -15201.538, Max-Change: 0.12404
Iteration: 9, Log-Lik: -15200.836, Max-Change: 0.13606
Iteration: 10, Log-Lik: -15199.656, Max-Change: 0.04100
Iteration: 11, Log-Lik: -15199.374, Max-Change: 0.01571
Iteration: 12, Log-Lik: -15199.208, Max-Change: 0.01597
Iteration: 13, Log-Lik: -15198.824, Max-Change: 0.00672
Iteration: 14, Log-Lik: -15198.781, Max-Change: 0.00913
Iteration: 15, Log-Lik: -15198.745, Max-Change: 0.00605
Iteration: 16, Log-Lik: -15198.694, Max-Change: 0.00895
Iteration: 17, Log-Lik: -15198.673, Max-Change: 0.00295
Iteration: 18, Log-Lik: -15198.661, Max-Change: 0.00516
Iteration: 19, Log-Lik: -15198.648, Max-Change: 0.00350
Iteration: 20, Log-Lik: -15198.640, Max-Change: 0.00286
Iteration: 21, Log-Lik: -15198.634, Max-Change: 0.00217
Iteration: 22, Log-Lik: -15198.629, Max-Change: 0.00365
Iteration: 23, Log-Lik: -15198.626, Max-Change: 0.00177
Iteration: 24, Log-Lik: -15198.623, Max-Change: 0.00125
Iteration: 25, Log-Lik: -15198.619, Max-Change: 0.00266
Iteration: 26, Log-Lik: -15198.617, Max-Change: 0.00229
Iteration: 27, Log-Lik: -15198.615, Max-Change: 0.00223
Iteration: 28, Log-Lik: -15198.612, Max-Change: 0.00070
Iteration: 29, Log-Lik: -15198.611, Max-Change: 0.00034
Iteration: 30, Log-Lik: -15198.611, Max-Change: 0.00025
Iteration: 31, Log-Lik: -15198.611, Max-Change: 0.00022
Iteration: 32, Log-Lik: -15198.611, Max-Change: 0.00022
Iteration: 33, Log-Lik: -15198.611, Max-Change: 0.00107
Iteration: 34, Log-Lik: -15198.611, Max-Change: 0.00101
Iteration: 35, Log-Lik: -15198.610, Max-Change: 0.00088
Iteration: 36, Log-Lik: -15198.610, Max-Change: 0.00046
Iteration: 37, Log-Lik: -15198.610, Max-Change: 0.00025
Iteration: 38, Log-Lik: -15198.610, Max-Change: 0.00074
Iteration: 39, Log-Lik: -15198.610, Max-Change: 0.00046
Iteration: 40, Log-Lik: -15198.610, Max-Change: 0.00024
Iteration: 41, Log-Lik: -15198.610, Max-Change: 0.00060
Iteration: 42, Log-Lik: -15198.610, Max-Change: 0.00044
Iteration: 43, Log-Lik: -15198.610, Max-Change: 0.00023
Iteration: 44, Log-Lik: -15198.610, Max-Change: 0.00050
Iteration: 45, Log-Lik: -15198.610, Max-Change: 0.00042
Iteration: 46, Log-Lik: -15198.610, Max-Change: 0.00021
Iteration: 47, Log-Lik: -15198.610, Max-Change: 0.00046
Iteration: 48, Log-Lik: -15198.610, Max-Change: 0.00039
Iteration: 49, Log-Lik: -15198.610, Max-Change: 0.00019
Iteration: 50, Log-Lik: -15198.610, Max-Change: 0.00043
Iteration: 51, Log-Lik: -15198.610, Max-Change: 0.00036
Iteration: 52, Log-Lik: -15198.610, Max-Change: 0.00018
Iteration: 53, Log-Lik: -15198.610, Max-Change: 0.00041
Iteration: 54, Log-Lik: -15198.610, Max-Change: 0.00033
Iteration: 55, Log-Lik: -15198.610, Max-Change: 0.00016
Iteration: 56, Log-Lik: -15198.610, Max-Change: 0.00039
Iteration: 57, Log-Lik: -15198.610, Max-Change: 0.00030
Iteration: 58, Log-Lik: -15198.610, Max-Change: 0.00015
Iteration: 59, Log-Lik: -15198.610, Max-Change: 0.00038
Iteration: 60, Log-Lik: -15198.610, Max-Change: 0.00028
Iteration: 61, Log-Lik: -15198.610, Max-Change: 0.00014
Iteration: 62, Log-Lik: -15198.610, Max-Change: 0.00037
Iteration: 63, Log-Lik: -15198.610, Max-Change: 0.00025
Iteration: 64, Log-Lik: -15198.610, Max-Change: 0.00013
Iteration: 65, Log-Lik: -15198.610, Max-Change: 0.00036
Iteration: 66, Log-Lik: -15198.610, Max-Change: 0.00024
Iteration: 67, Log-Lik: -15198.610, Max-Change: 0.00012
Iteration: 68, Log-Lik: -15198.610, Max-Change: 0.00035
Iteration: 69, Log-Lik: -15198.610, Max-Change: 0.00022
Iteration: 70, Log-Lik: -15198.610, Max-Change: 0.00011
Iteration: 71, Log-Lik: -15198.610, Max-Change: 0.00034
Iteration: 72, Log-Lik: -15198.610, Max-Change: 0.00021
Iteration: 73, Log-Lik: -15198.610, Max-Change: 0.00011
Iteration: 74, Log-Lik: -15198.610, Max-Change: 0.00034
Iteration: 75, Log-Lik: -15198.610, Max-Change: 0.00020
Iteration: 76, Log-Lik: -15198.610, Max-Change: 0.00010
Iteration: 77, Log-Lik: -15198.610, Max-Change: 0.00033
Iteration: 78, Log-Lik: -15198.610, Max-Change: 0.00019
Iteration: 79, Log-Lik: -15198.610, Max-Change: 0.00010

## 
## Step 2: Initial MI fit

## 
Iteration: 1, Log-Lik: -15842.005, Max-Change: 1.77887
Iteration: 2, Log-Lik: -15270.755, Max-Change: 0.53899
Iteration: 3, Log-Lik: -15226.133, Max-Change: 0.32387
Iteration: 4, Log-Lik: -15212.434, Max-Change: 0.22231
Iteration: 5, Log-Lik: -15206.702, Max-Change: 0.17458
Iteration: 6, Log-Lik: -15203.626, Max-Change: 0.15057
Iteration: 7, Log-Lik: -15199.321, Max-Change: 0.08738
Iteration: 8, Log-Lik: -15198.166, Max-Change: 0.14893
Iteration: 9, Log-Lik: -15197.226, Max-Change: 0.10145
Iteration: 10, Log-Lik: -15195.325, Max-Change: 0.03846
Iteration: 11, Log-Lik: -15194.864, Max-Change: 0.09010
Iteration: 12, Log-Lik: -15194.452, Max-Change: 0.07359
Iteration: 13, Log-Lik: -15193.325, Max-Change: 0.03457
Iteration: 14, Log-Lik: -15193.159, Max-Change: 0.05340
Iteration: 15, Log-Lik: -15193.009, Max-Change: 0.02350
Iteration: 16, Log-Lik: -15192.830, Max-Change: 0.02543
Iteration: 17, Log-Lik: -15192.727, Max-Change: 0.02440
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## 
## Step 3: Leave one out MI testing

## Warning: Log-likelihood was decreasing near the ML solution. EM method may be
## unstable

## 
## Step 4: Fit without DIF items, liberal threshold

## 
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## EM cycles terminated after 500 iterations.
## 
## Step 5: Fit without DIF items, conservative threshold

## 
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Iteration: 86, Log-Lik: -15288.054, Max-Change: 0.00043
Iteration: 87, Log-Lik: -15288.054, Max-Change: 0.00024
Iteration: 88, Log-Lik: -15288.054, Max-Change: 0.00012
Iteration: 89, Log-Lik: -15288.054, Max-Change: 0.00043
Iteration: 90, Log-Lik: -15288.054, Max-Change: 0.00023
Iteration: 91, Log-Lik: -15288.054, Max-Change: 0.00012
Iteration: 92, Log-Lik: -15288.054, Max-Change: 0.00043
Iteration: 93, Log-Lik: -15288.054, Max-Change: 0.00023
Iteration: 94, Log-Lik: -15288.054, Max-Change: 0.00012
Iteration: 95, Log-Lik: -15288.054, Max-Change: 0.00043
Iteration: 96, Log-Lik: -15288.054, Max-Change: 0.00023
Iteration: 97, Log-Lik: -15288.054, Max-Change: 0.00012
Iteration: 98, Log-Lik: -15288.054, Max-Change: 0.00043
Iteration: 99, Log-Lik: -15288.054, Max-Change: 0.00022
Iteration: 100, Log-Lik: -15288.054, Max-Change: 0.00011
Iteration: 101, Log-Lik: -15288.054, Max-Change: 0.00043
Iteration: 102, Log-Lik: -15288.054, Max-Change: 0.00022
Iteration: 103, Log-Lik: -15288.054, Max-Change: 0.00011
Iteration: 104, Log-Lik: -15288.054, Max-Change: 0.00042
Iteration: 105, Log-Lik: -15288.054, Max-Change: 0.00022
Iteration: 106, Log-Lik: -15288.054, Max-Change: 0.00011
Iteration: 107, Log-Lik: -15288.054, Max-Change: 0.00042
Iteration: 108, Log-Lik: -15288.054, Max-Change: 0.00021
Iteration: 109, Log-Lik: -15288.054, Max-Change: 0.00011
Iteration: 110, Log-Lik: -15288.054, Max-Change: 0.00042
Iteration: 111, Log-Lik: -15288.054, Max-Change: 0.00021
Iteration: 112, Log-Lik: -15288.054, Max-Change: 0.00011
Iteration: 113, Log-Lik: -15288.054, Max-Change: 0.00042
Iteration: 114, Log-Lik: -15288.054, Max-Change: 0.00021
Iteration: 115, Log-Lik: -15288.054, Max-Change: 0.00011
Iteration: 116, Log-Lik: -15288.054, Max-Change: 0.00042
Iteration: 117, Log-Lik: -15288.054, Max-Change: 0.00020
Iteration: 118, Log-Lik: -15288.054, Max-Change: 0.00011
Iteration: 119, Log-Lik: -15288.054, Max-Change: 0.00042
Iteration: 120, Log-Lik: -15288.054, Max-Change: 0.00020
Iteration: 121, Log-Lik: -15288.054, Max-Change: 0.00010
Iteration: 122, Log-Lik: -15288.054, Max-Change: 0.00041
Iteration: 123, Log-Lik: -15288.054, Max-Change: 0.00020
Iteration: 124, Log-Lik: -15288.054, Max-Change: 0.00010
Iteration: 125, Log-Lik: -15288.054, Max-Change: 0.00041
Iteration: 126, Log-Lik: -15288.054, Max-Change: 0.00020
Iteration: 127, Log-Lik: -15288.054, Max-Change: 0.00010
Iteration: 128, Log-Lik: -15288.054, Max-Change: 0.00041
Iteration: 129, Log-Lik: -15288.054, Max-Change: 0.00019
Iteration: 130, Log-Lik: -15288.054, Max-Change: 0.00010
Iteration: 131, Log-Lik: -15288.054, Max-Change: 0.00041
Iteration: 132, Log-Lik: -15288.054, Max-Change: 0.00019
Iteration: 133, Log-Lik: -15288.054, Max-Change: 0.00010

## 
## Step 6: Fit with anchor items, liberal threshold

## 
Iteration: 1, Log-Lik: -15842.005, Max-Change: 1.80792
Iteration: 2, Log-Lik: -15194.651, Max-Change: 0.53821
Iteration: 3, Log-Lik: -15147.015, Max-Change: 0.32467
Iteration: 4, Log-Lik: -15132.900, Max-Change: 0.23455
Iteration: 5, Log-Lik: -15127.266, Max-Change: 0.19012
Iteration: 6, Log-Lik: -15124.361, Max-Change: 0.21618
Iteration: 7, Log-Lik: -15119.596, Max-Change: 0.08964
Iteration: 8, Log-Lik: -15118.495, Max-Change: 0.08852
Iteration: 9, Log-Lik: -15117.849, Max-Change: 0.22553
Iteration: 10, Log-Lik: -15116.873, Max-Change: 0.03500
Iteration: 11, Log-Lik: -15116.514, Max-Change: 0.12082
Iteration: 12, Log-Lik: -15116.173, Max-Change: 0.10358
Iteration: 13, Log-Lik: -15115.377, Max-Change: 0.03142
Iteration: 14, Log-Lik: -15115.228, Max-Change: 0.07684
Iteration: 15, Log-Lik: -15115.066, Max-Change: 0.04054
Iteration: 16, Log-Lik: -15114.835, Max-Change: 0.02504
Iteration: 17, Log-Lik: -15114.735, Max-Change: 0.03026
Iteration: 18, Log-Lik: -15114.636, Max-Change: 0.02309
Iteration: 19, Log-Lik: -15114.268, Max-Change: 0.01933
Iteration: 20, Log-Lik: -15114.266, Max-Change: 0.02124
Iteration: 21, Log-Lik: -15114.233, Max-Change: 0.01682
Iteration: 22, Log-Lik: -15114.088, Max-Change: 0.01156
Iteration: 23, Log-Lik: -15114.106, Max-Change: 0.00637
Iteration: 24, Log-Lik: -15114.095, Max-Change: 0.00770
Iteration: 25, Log-Lik: -15114.015, Max-Change: 0.01012
Iteration: 26, Log-Lik: -15114.045, Max-Change: 0.00694
Iteration: 27, Log-Lik: -15114.044, Max-Change: 0.00819
Iteration: 28, Log-Lik: -15114.015, Max-Change: 0.00665
Iteration: 29, Log-Lik: -15114.040, Max-Change: 0.00241
Iteration: 30, Log-Lik: -15114.042, Max-Change: 0.00232
Iteration: 31, Log-Lik: -15114.034, Max-Change: 0.00422
Iteration: 32, Log-Lik: -15114.051, Max-Change: 0.00326
Iteration: 33, Log-Lik: -15114.053, Max-Change: 0.00127
Iteration: 34, Log-Lik: -15114.054, Max-Change: 0.00387
Iteration: 35, Log-Lik: -15114.056, Max-Change: 0.00113
Iteration: 36, Log-Lik: -15114.057, Max-Change: 0.00115
Iteration: 37, Log-Lik: -15114.056, Max-Change: 0.00328
Iteration: 38, Log-Lik: -15114.065, Max-Change: 0.00073
Iteration: 39, Log-Lik: -15114.066, Max-Change: 0.00062
Iteration: 40, Log-Lik: -15114.066, Max-Change: 0.00285
Iteration: 41, Log-Lik: -15114.072, Max-Change: 0.00046
Iteration: 42, Log-Lik: -15114.072, Max-Change: 0.00046
Iteration: 43, Log-Lik: -15114.073, Max-Change: 0.00067
Iteration: 44, Log-Lik: -15114.076, Max-Change: 0.00027
Iteration: 45, Log-Lik: -15114.076, Max-Change: 0.00024
Iteration: 46, Log-Lik: -15114.077, Max-Change: 0.00038
Iteration: 47, Log-Lik: -15114.079, Max-Change: 0.00027
Iteration: 48, Log-Lik: -15114.079, Max-Change: 0.00024
Iteration: 49, Log-Lik: -15114.079, Max-Change: 0.00022
Iteration: 50, Log-Lik: -15114.080, Max-Change: 0.00013
Iteration: 51, Log-Lik: -15114.080, Max-Change: 0.00040
Iteration: 52, Log-Lik: -15114.080, Max-Change: 0.00011
Iteration: 53, Log-Lik: -15114.081, Max-Change: 0.00013
Iteration: 54, Log-Lik: -15114.081, Max-Change: 0.00012
Iteration: 55, Log-Lik: -15114.081, Max-Change: 0.00011
Iteration: 56, Log-Lik: -15114.081, Max-Change: 0.00010
Iteration: 57, Log-Lik: -15114.081, Max-Change: 0.00006

## 
## Step 7: Fit with anchor items, conservative threshold

## 
Iteration: 1, Log-Lik: -15842.005, Max-Change: 1.77473
Iteration: 2, Log-Lik: -15228.477, Max-Change: 0.53139
Iteration: 3, Log-Lik: -15182.413, Max-Change: 0.32881
Iteration: 4, Log-Lik: -15168.713, Max-Change: 0.20590
Iteration: 5, Log-Lik: -15163.268, Max-Change: 0.32943
Iteration: 6, Log-Lik: -15160.280, Max-Change: 0.12401
Iteration: 7, Log-Lik: -15158.879, Max-Change: 0.11349
Iteration: 8, Log-Lik: -15157.444, Max-Change: 0.09024
Iteration: 9, Log-Lik: -15156.314, Max-Change: 0.13540
Iteration: 10, Log-Lik: -15153.517, Max-Change: 0.04883
Iteration: 11, Log-Lik: -15152.963, Max-Change: 0.16115
Iteration: 12, Log-Lik: -15152.525, Max-Change: 0.14274
Iteration: 13, Log-Lik: -15151.636, Max-Change: 0.03046
Iteration: 14, Log-Lik: -15151.420, Max-Change: 0.06433
Iteration: 15, Log-Lik: -15151.203, Max-Change: 0.05265
Iteration: 16, Log-Lik: -15150.489, Max-Change: 0.02657
Iteration: 17, Log-Lik: -15150.419, Max-Change: 0.01663
Iteration: 18, Log-Lik: -15150.339, Max-Change: 0.01319
Iteration: 19, Log-Lik: -15150.042, Max-Change: 0.02431
Iteration: 20, Log-Lik: -15150.039, Max-Change: 0.01292
Iteration: 21, Log-Lik: -15150.010, Max-Change: 0.01450
Iteration: 22, Log-Lik: -15149.840, Max-Change: 0.01580
Iteration: 23, Log-Lik: -15149.866, Max-Change: 0.00578
Iteration: 24, Log-Lik: -15149.863, Max-Change: 0.00709
Iteration: 25, Log-Lik: -15149.812, Max-Change: 0.00866
Iteration: 26, Log-Lik: -15149.838, Max-Change: 0.00361
Iteration: 27, Log-Lik: -15149.840, Max-Change: 0.00452
Iteration: 28, Log-Lik: -15149.825, Max-Change: 0.00463
Iteration: 29, Log-Lik: -15149.843, Max-Change: 0.00190
Iteration: 30, Log-Lik: -15149.845, Max-Change: 0.00175
Iteration: 31, Log-Lik: -15149.840, Max-Change: 0.00515
Iteration: 32, Log-Lik: -15149.853, Max-Change: 0.00113
Iteration: 33, Log-Lik: -15149.855, Max-Change: 0.00297
Iteration: 34, Log-Lik: -15149.855, Max-Change: 0.00085
Iteration: 35, Log-Lik: -15149.857, Max-Change: 0.00085
Iteration: 36, Log-Lik: -15149.858, Max-Change: 0.00078
Iteration: 37, Log-Lik: -15149.858, Max-Change: 0.00318
Iteration: 38, Log-Lik: -15149.864, Max-Change: 0.00063
Iteration: 39, Log-Lik: -15149.865, Max-Change: 0.00045
Iteration: 40, Log-Lik: -15149.865, Max-Change: 0.00102
Iteration: 41, Log-Lik: -15149.868, Max-Change: 0.00036
Iteration: 42, Log-Lik: -15149.868, Max-Change: 0.00036
Iteration: 43, Log-Lik: -15149.869, Max-Change: 0.00051
Iteration: 44, Log-Lik: -15149.871, Max-Change: 0.00031
Iteration: 45, Log-Lik: -15149.871, Max-Change: 0.00025
Iteration: 46, Log-Lik: -15149.872, Max-Change: 0.00028
Iteration: 47, Log-Lik: -15149.873, Max-Change: 0.00014
Iteration: 48, Log-Lik: -15149.873, Max-Change: 0.00024
Iteration: 49, Log-Lik: -15149.873, Max-Change: 0.00009

## Warning: Log-likelihood was decreasing near the ML solution. EM method may be
## unstable

## 
## Step 8: Get scores

d2_DIF$effect_size_test

## $liberal
##           Effect Size  Value
## 1                STDS 0.5066
## 2                UTDS 1.0729
## 3              UETSDS 0.5066
## 4               ETSSD 0.0789
## 5         Starks.DTFR 0.5093
## 6               UDTFR 1.0824
## 7              UETSDN 0.5093
## 8 theta.of.max.test.D 2.6254
## 9           Test.Dmax 0.7969
## 
## $conservative
##           Effect Size  Value
## 1                STDS 0.2956
## 2                UTDS 0.4509
## 3              UETSDS 0.2956
## 4               ETSSD 0.0461
## 5         Starks.DTFR 0.2969
## 6               UDTFR 0.4483
## 7              UETSDN 0.2969
## 8 theta.of.max.test.D 0.4046
## 9           Test.Dmax 0.3654

d2_DIF$effect_size_items

## $liberal
##           SIDS  UIDS   SIDN  UIDN    ESSD theta.of.max.D  max.D mean.ES.foc
## item.1   0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.889
## item.2   0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.624
## item.3   0.024 0.073  0.025 0.074   0.152         -1.820  0.169       0.558
## item.4   0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.615
## item.5   0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.557
## item.6   0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.839
## item.7   0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.290
## item.8   0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.708
## item.9   0.032 0.103  0.035 0.107   0.333          2.625  0.492       0.193
## item.10  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.551
## item.11  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.983
## item.12  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.887
## item.13  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.595
## item.14  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.861
## item.15  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.771
## item.16  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.863
## item.17  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.918
## item.18  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.964
## item.19  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.906
## item.20  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.824
## item.21  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.971
## item.22  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.753
## item.23 -0.062 0.092 -0.061 0.089  -0.289         -1.407 -0.333       0.756
## item.24  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.968
## item.25  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.762
## item.26  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.861
## item.27 -0.056 0.056 -0.057 0.057  -0.607         -1.820 -0.254       0.860
## item.28  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.836
## item.29 -0.036 0.042 -0.038 0.045  -0.188         -0.737 -0.134       0.878
## item.30  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.860
## item.31  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.740
## item.32  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.995
## item.33  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.941
## item.34  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.857
## item.35  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.778
## item.36  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.970
## item.37  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.861
## item.38  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.943
## item.39  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.989
## item.40  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.805
## item.41  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.933
## item.42  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.932
## item.43 -0.036 0.036 -0.036 0.036 -10.534         -1.820 -0.047       0.946
## item.44  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.961
## item.45  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.885
## item.46  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.975
## item.47  0.052 0.056  0.054 0.058   0.784         -1.820  0.252       0.904
## item.48  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.741
## item.49  0.059 0.059  0.060 0.060   1.131         -1.820  0.198       0.960
## item.50  0.091 0.091  0.091 0.091   0.832         -1.820  0.158       0.642
## item.51  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.858
## item.52  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.849
## item.53  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.816
## item.54  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.488
## item.55  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.467
## item.56  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.966
## item.57  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.963
## item.58  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.971
## item.59  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.995
## item.60  0.095 0.095  0.095 0.096   1.618         -1.820  0.258       0.893
## item.61  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.744
## item.62  0.073 0.100  0.072 0.101   1.321          2.625  0.247       0.778
## item.63  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.868
## item.64  0.270 0.270  0.269 0.269   2.914         -0.532  0.289       0.758
## item.65  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.810
## item.66  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.585
## item.67  0.000 0.000  0.000 0.000   0.000          1.655  0.000       0.600
##         mean.ES.ref
## item.1        0.889
## item.2        0.624
## item.3        0.533
## item.4        0.615
## item.5        0.557
## item.6        0.839
## item.7        0.290
## item.8        0.708
## item.9        0.162
## item.10       0.551
## item.11       0.983
## item.12       0.887
## item.13       0.595
## item.14       0.861
## item.15       0.771
## item.16       0.863
## item.17       0.918
## item.18       0.964
## item.19       0.906
## item.20       0.824
## item.21       0.971
## item.22       0.753
## item.23       0.818
## item.24       0.968
## item.25       0.762
## item.26       0.861
## item.27       0.916
## item.28       0.836
## item.29       0.914
## item.30       0.860
## item.31       0.740
## item.32       0.995
## item.33       0.941
## item.34       0.857
## item.35       0.778
## item.36       0.970
## item.37       0.861
## item.38       0.943
## item.39       0.989
## item.40       0.805
## item.41       0.933
## item.42       0.932
## item.43       0.982
## item.44       0.961
## item.45       0.885
## item.46       0.975
## item.47       0.851
## item.48       0.741
## item.49       0.902
## item.50       0.551
## item.51       0.858
## item.52       0.849
## item.53       0.816
## item.54       0.488
## item.55       0.467
## item.56       0.966
## item.57       0.963
## item.58       0.971
## item.59       0.995
## item.60       0.799
## item.61       0.744
## item.62       0.705
## item.63       0.868
## item.64       0.489
## item.65       0.810
## item.66       0.585
## item.67       0.600
## 
## $conservative
##           SIDS  UIDS   SIDN  UIDN   ESSD theta.of.max.D  max.D mean.ES.foc
## item.1   0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.890
## item.2   0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.626
## item.3   0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.542
## item.4   0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.616
## item.5   0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.559
## item.6   0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.841
## item.7   0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.291
## item.8   0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.709
## item.9   0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.192
## item.10  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.552
## item.11  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.983
## item.12  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.887
## item.13  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.597
## item.14  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.862
## item.15  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.772
## item.16  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.863
## item.17  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.918
## item.18  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.964
## item.19  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.908
## item.20  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.826
## item.21  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.971
## item.22  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.754
## item.23 -0.064 0.092 -0.062 0.089 -0.297         -1.388 -0.334       0.757
## item.24  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.969
## item.25  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.764
## item.26  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.863
## item.27  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.891
## item.28  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.838
## item.29  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.898
## item.30  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.860
## item.31  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.741
## item.32  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.995
## item.33  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.941
## item.34  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.859
## item.35  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.780
## item.36  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.971
## item.37  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.862
## item.38  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.944
## item.39  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.989
## item.40  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.807
## item.41  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.934
## item.42  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.935
## item.43  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.964
## item.44  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.961
## item.45  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.885
## item.46  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.975
## item.47  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.875
## item.48  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.742
## item.49  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.930
## item.50  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.596
## item.51  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.859
## item.52  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.850
## item.53  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.817
## item.54  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.488
## item.55  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.468
## item.56  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.967
## item.57  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.964
## item.58  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.972
## item.59  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.995
## item.60  0.093 0.093  0.094 0.094  1.590         -1.803  0.258       0.893
## item.61  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.745
## item.62  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.748
## item.63  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.869
## item.64  0.266 0.266  0.266 0.266  2.830         -0.717  0.291       0.758
## item.65  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.812
## item.66  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.587
## item.67  0.000 0.000  0.000 0.000  0.000          1.614  0.000       0.601
##         mean.ES.ref
## item.1        0.890
## item.2        0.626
## item.3        0.542
## item.4        0.616
## item.5        0.559
## item.6        0.841
## item.7        0.291
## item.8        0.709
## item.9        0.192
## item.10       0.552
## item.11       0.983
## item.12       0.887
## item.13       0.597
## item.14       0.862
## item.15       0.772
## item.16       0.863
## item.17       0.918
## item.18       0.964
## item.19       0.908
## item.20       0.826
## item.21       0.971
## item.22       0.754
## item.23       0.820
## item.24       0.969
## item.25       0.764
## item.26       0.863
## item.27       0.891
## item.28       0.838
## item.29       0.898
## item.30       0.860
## item.31       0.741
## item.32       0.995
## item.33       0.941
## item.34       0.859
## item.35       0.780
## item.36       0.971
## item.37       0.862
## item.38       0.944
## item.39       0.989
## item.40       0.807
## item.41       0.934
## item.42       0.935
## item.43       0.964
## item.44       0.961
## item.45       0.885
## item.46       0.975
## item.47       0.875
## item.48       0.742
## item.49       0.930
## item.50       0.596
## item.51       0.859
## item.52       0.850
## item.53       0.817
## item.54       0.488
## item.55       0.468
## item.56       0.967
## item.57       0.964
## item.58       0.972
## item.59       0.995
## item.60       0.800
## item.61       0.745
## item.62       0.748
## item.63       0.869
## item.64       0.492
## item.65       0.812
## item.66       0.587
## item.67       0.601

d2_DIF$fits$anchor_liberal %>% empirical_ES(plot = T)

d2_DIF$fits$anchor_conservative %>% empirical_ES(plot = T)

#gap after bias removed
cohen.d(d2 %>% select(g), d2$Sex)$cohen.d[2] - (d2_DIF$effect_size_test$conservative %>% filter(`Effect Size`=="ETSSD") %>% pull(Value))

## [1] 0.217

kirkegaard::adj_d_reliability(
  cohen.d(d2 %>% select(g), d2$Sex)$cohen.d[2] - (d2_DIF$effect_size_test$conservative %>% filter(`Effect Size`=="ETSSD") %>% pull(Value))
  ,
  empirical_rxx(d2_mirt_g_scores)
  )

##    F1 
## 0.241

#race gaps
table2(d2$EthnicitySimplified)

SMD_matrix(
  d2$g,
  d2$EthnicitySimplified %>% fct_relevel("White")
)

##        White    Asian  Black    Mixed  Other
## White     NA  0.28073  0.862  0.28624 -0.742
## Asian  0.281       NA  0.581  0.00552 -1.023
## Black  0.862  0.58083     NA -0.57531 -1.603
## Mixed  0.286  0.00552 -0.575       NA -1.028
## Other -0.742 -1.02266 -1.603 -1.02818     NA