Looking for CDI Bias: WG Comprehension
Nathan, George, and Mike
2021-08-01
First, let’s get some wordbank data for American English. We’ll start with production data from the CDI: Words & Gestures (WG) form. We’ll look for DIF based on 1) sex and 2) SES (high vs. low). Questions: How do we choose a dozen anchor items (that we expect to be unbiased)?
Let’s do comprehension data.
| None | Primary | Some Secondary | Secondary | Some College | College | Some Graduate | Graduate |
|---|---|---|---|---|---|---|---|
| 0 | 2 | 68 | 254 | 266 | 292 | 41 | 140 |
| Var1 | Freq |
|---|---|
| action_words | 55 |
| animals | 36 |
| body_parts | 20 |
| clothing | 19 |
| descriptive_words | 37 |
| food_drink | 30 |
| furniture_rooms | 24 |
| games_routines | 19 |
| household | 36 |
| locations | 11 |
| outside | 27 |
| people | 20 |
| pronouns | 11 |
| quantifiers | 8 |
| question_words | 6 |
| sounds | 12 |
| time_words | 8 |
| toys | 8 |
| vehicles | 9 |
We will fit comprehension data from 2385 children for the WG form.
Fit baseline 2PL model
GLIMMER Plots
## Warning: ggrepel: 58 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps
DIF Model: Sex
## Joining, by = c("a1", "definition")
## Joining, by = c("a1", "definition")Items with DIF in difficulty
275 items show DIF based on a \(\chi^2\) test yielding \(p<.05\). Below we show the 171 items with \(p<.001\).
| AIC | BIC | X2 | p | |
|---|---|---|---|---|
| doll | -326.34 | -320.57 | 328.34 | 0 |
| dress (object) | -283.44 | -277.67 | 285.44 | 0 |
| pretty | -133.86 | -128.08 | 135.86 | 0 |
| truck | -113.42 | -107.64 | 115.42 | 0 |
| hammer | -96.28 | -90.51 | 98.28 | 0 |
| necklace | -84.62 | -78.85 | 86.62 | 0 |
| purse | -79.91 | -74.13 | 81.91 | 0 |
| same | -75.60 | -69.82 | 77.60 | 0 |
| soap | -74.63 | -68.85 | 76.63 | 0 |
| baby | -70.64 | -64.86 | 72.64 | 0 |
| wash | -69.95 | -64.17 | 71.95 | 0 |
| hair | -69.27 | -63.50 | 71.27 | 0 |
| leg | -68.75 | -62.97 | 70.75 | 0 |
| face | -67.19 | -61.41 | 69.19 | 0 |
| sleep | -66.94 | -61.16 | 68.94 | 0 |
| shoe | -66.59 | -60.82 | 68.59 | 0 |
| see | -66.16 | -60.38 | 68.16 | 0 |
| naughty | -65.89 | -60.11 | 67.89 | 0 |
| read | -65.62 | -59.85 | 67.62 | 0 |
| cute | -65.58 | -59.80 | 67.58 | 0 |
| asleep | -65.38 | -59.60 | 67.38 | 0 |
| chair | -65.22 | -59.45 | 67.22 | 0 |
| help | -65.15 | -59.38 | 67.15 | 0 |
| show | -64.98 | -59.20 | 66.98 | 0 |
| flower | -64.82 | -59.04 | 66.82 | 0 |
| put | -64.74 | -58.96 | 66.74 | 0 |
| picture | -64.48 | -58.70 | 66.48 | 0 |
| hi | -64.28 | -58.51 | 66.28 | 0 |
| clean (action) | -63.98 | -58.20 | 65.98 | 0 |
| dance | -63.97 | -58.20 | 65.97 | 0 |
| tummy | -63.84 | -58.06 | 65.84 | 0 |
| tickle | -63.77 | -58.00 | 65.77 | 0 |
| blanket | -63.52 | -57.75 | 65.52 | 0 |
| teddybear | -63.52 | -57.74 | 65.52 | 0 |
| sweater | -63.38 | -57.60 | 65.38 | 0 |
| little (description) | -63.35 | -57.57 | 65.35 | 0 |
| girl | -63.24 | -57.47 | 65.24 | 0 |
| glasses | -63.19 | -57.41 | 65.19 | 0 |
| clean (description) | -63.12 | -57.34 | 65.12 | 0 |
| school | -63.11 | -57.34 | 65.11 | 0 |
| tongue | -63.07 | -57.29 | 65.07 | 0 |
| me | -63.07 | -57.29 | 65.07 | 0 |
| eye | -62.99 | -57.21 | 64.99 | 0 |
| mouse | -62.91 | -57.13 | 64.91 | 0 |
| pen | -62.90 | -57.12 | 64.90 | 0 |
| bed | -62.77 | -56.99 | 64.77 | 0 |
| beads | -62.67 | -56.90 | 64.67 | 0 |
| cheek | -62.66 | -56.89 | 64.66 | 0 |
| when | -62.54 | -56.77 | 64.54 | 0 |
| play pen | -62.52 | -56.75 | 64.52 | 0 |
| walk | -62.37 | -56.60 | 64.37 | 0 |
| you | -62.29 | -56.51 | 64.29 | 0 |
| dirty | -62.27 | -56.50 | 64.27 | 0 |
| paper | -62.04 | -56.26 | 64.04 | 0 |
| coat | -62.01 | -56.23 | 64.01 | 0 |
| potty | -61.98 | -56.20 | 63.98 | 0 |
| bottle | -61.81 | -56.03 | 63.81 | 0 |
| knee | -61.76 | -55.98 | 63.76 | 0 |
| child | -61.74 | -55.96 | 63.74 | 0 |
| cat | -61.68 | -55.90 | 63.68 | 0 |
| happy | -61.67 | -55.89 | 63.67 | 0 |
| who | -61.63 | -55.85 | 63.63 | 0 |
| hello | -61.62 | -55.85 | 63.62 | 0 |
| meow | -61.59 | -55.81 | 63.59 | 0 |
| cry | -61.58 | -55.80 | 63.58 | 0 |
| play | -61.54 | -55.76 | 63.54 | 0 |
| fish (food) | -61.52 | -55.75 | 63.52 | 0 |
| yes | -61.52 | -55.74 | 63.52 | 0 |
| keys | -61.48 | -55.70 | 63.48 | 0 |
| take | -61.39 | -55.61 | 63.39 | 0 |
| finger | -61.36 | -55.58 | 63.36 | 0 |
| zipper | -61.35 | -55.57 | 63.35 | 0 |
| your | -61.31 | -55.54 | 63.31 | 0 |
| tooth | -61.31 | -55.53 | 63.31 | 0 |
| I | -61.27 | -55.49 | 63.27 | 0 |
| finish | -61.23 | -55.45 | 63.23 | 0 |
| cup | -61.22 | -55.45 | 63.22 | 0 |
| night night | -61.18 | -55.40 | 63.18 | 0 |
| bib | -61.10 | -55.32 | 63.10 | 0 |
| swim | -61.06 | -55.28 | 63.06 | 0 |
| babysitter’s name | -61.05 | -55.27 | 63.05 | 0 |
| bye | -60.78 | -55.00 | 62.78 | 0 |
| stroller | -60.66 | -54.88 | 62.66 | 0 |
| pattycake | -60.24 | -54.46 | 62.24 | 0 |
| bunny | -60.22 | -54.44 | 62.22 | 0 |
| comb | -60.15 | -54.37 | 62.15 | 0 |
| please | -60.13 | -54.35 | 62.13 | 0 |
| tomorrow | -60.11 | -54.33 | 62.11 | 0 |
| nice | -60.08 | -54.30 | 62.08 | 0 |
| yum yum | -60.05 | -54.28 | 62.05 | 0 |
| love | -59.96 | -54.18 | 61.96 | 0 |
| red | -59.96 | -54.18 | 61.96 | 0 |
| belly button | -59.94 | -54.17 | 61.94 | 0 |
| sing | -59.94 | -54.17 | 61.94 | 0 |
| rocking chair | -59.94 | -54.17 | 61.94 | 0 |
| mine | -59.91 | -54.13 | 61.91 | 0 |
| kiss | -59.90 | -54.12 | 61.90 | 0 |
| good | -59.89 | -54.11 | 61.89 | 0 |
| write | -59.88 | -54.10 | 61.88 | 0 |
| money | -59.84 | -54.07 | 61.84 | 0 |
| shh/shush/hush | -59.80 | -54.02 | 61.80 | 0 |
| candy | -59.80 | -54.02 | 61.80 | 0 |
| thank you | -59.77 | -54.00 | 61.77 | 0 |
| lady | -59.76 | -53.99 | 61.76 | 0 |
| later | -59.74 | -53.97 | 61.74 | 0 |
| grandma* | -59.74 | -53.97 | 61.74 | 0 |
| party | -59.71 | -53.93 | 61.71 | 0 |
| firetruck | -57.81 | -52.03 | 59.81 | 0 |
| broom | -48.77 | -43.00 | 50.77 | 0 |
| shovel | -32.80 | -27.02 | 34.80 | 0 |
| motorcycle | -30.41 | -24.64 | 32.41 | 0 |
| train | -27.11 | -21.34 | 29.11 | 0 |
| vroom | -26.20 | -20.42 | 28.20 | 0 |
| vacuum | -22.85 | -17.07 | 24.85 | 0 |
| bathroom | -20.86 | -15.09 | 22.86 | 0 |
| touch | -19.51 | -13.73 | 21.51 | 0 |
| choo choo | -19.49 | -13.71 | 21.49 | 0 |
| kitchen | -19.36 | -13.58 | 21.36 | 0 |
| towel | -19.28 | -13.50 | 21.28 | 0 |
| mouth | -16.56 | -10.78 | 18.56 | 0 |
| home | -15.94 | -10.16 | 17.94 | 0 |
| pajamas | -15.84 | -10.06 | 17.84 | 0 |
| get | -15.51 | -9.73 | 17.51 | 0 |
| arm | -15.44 | -9.67 | 17.44 | 0 |
| dry (description) | -15.15 | -9.38 | 17.15 | 0 |
| out | -14.96 | -9.18 | 16.96 | 0 |
| foot | -14.83 | -9.06 | 16.83 | 0 |
| inside | -14.67 | -8.90 | 16.67 | 0 |
| bowl | -14.52 | -8.75 | 16.52 | 0 |
| brush | -14.15 | -8.37 | 16.15 | 0 |
| open | -14.12 | -8.34 | 16.12 | 0 |
| sun | -13.73 | -7.96 | 15.73 | 0 |
| bread | -13.68 | -7.91 | 15.68 | 0 |
| stop | -13.67 | -7.89 | 15.67 | 0 |
| bear | -13.63 | -7.85 | 15.63 | 0 |
| toe | -13.24 | -7.46 | 15.24 | 0 |
| there | -13.12 | -7.35 | 15.12 | 0 |
| store | -13.05 | -7.27 | 15.05 | 0 |
| hurry | -12.78 | -7.00 | 14.78 | 0 |
| wanna/want to | -12.59 | -6.82 | 14.59 | 0 |
| big | -12.57 | -6.80 | 14.57 | 0 |
| couch | -12.54 | -6.76 | 14.54 | 0 |
| nap | -12.22 | -6.44 | 14.22 | 0 |
| button | -12.12 | -6.34 | 14.12 | 0 |
| pillow | -11.91 | -6.13 | 13.91 | 0 |
| table | -11.67 | -5.89 | 13.67 | 0 |
| airplane | -11.46 | -5.69 | 13.46 | 0 |
| bird | -11.14 | -5.36 | 13.14 | 0 |
| hungry | -11.12 | -5.35 | 13.12 | 0 |
| toy (object) | -10.96 | -5.18 | 12.96 | 0 |
| hat | -10.76 | -4.98 | 12.76 | 0 |
| plate | -10.75 | -4.97 | 12.75 | 0 |
| milk | -10.61 | -4.84 | 12.61 | 0 |
| bring | -10.55 | -4.77 | 12.55 | 0 |
| diaper | -10.54 | -4.77 | 12.54 | 0 |
| shorts | -10.48 | -4.70 | 12.48 | 0 |
| squirrel | -10.23 | -4.45 | 12.23 | 0 |
| give | -10.16 | -4.38 | 12.16 | 0 |
| all | -9.86 | -4.09 | 11.86 | 0 |
| bus | -9.84 | -4.06 | 11.84 | 0 |
| apple | -9.83 | -4.05 | 11.83 | 0 |
| ride | -9.62 | -3.85 | 11.62 | 0 |
| head | -9.57 | -3.80 | 11.57 | 0 |
| bee | -9.53 | -3.75 | 11.53 | 0 |
| pig | -9.43 | -3.65 | 11.43 | 0 |
| animal | -9.41 | -3.63 | 11.41 | 0 |
| quack quack | -9.39 | -3.61 | 11.39 | 0 |
| turtle | -9.37 | -3.60 | 11.37 | 0 |
| deer | -9.31 | -3.54 | 11.31 | 0 |
| noodles | -8.91 | -3.14 | 10.91 | 0 |
| fall | -8.91 | -3.13 | 10.91 | 0 |
Items with a large difference in difficulty across sex
| definition | a1 | d_m | d_f | d_diff | d_diff_abs |
|---|---|---|---|---|---|
| dress (object) | 2.20 | -4.58 | -1.41 | 3.17 | 3.17 |
| doll | 1.75 | -1.56 | 0.87 | 2.43 | 2.43 |
| when | 2.63 | -7.63 | -5.96 | 1.67 | 1.67 |
| pretty | 1.52 | -2.29 | -0.74 | 1.55 | 1.55 |
| hammer | 2.07 | -2.22 | -3.69 | -1.47 | 1.47 |
| necklace | 2.00 | -3.36 | -1.90 | 1.46 | 1.46 |
| purse | 2.05 | -2.17 | -0.85 | 1.32 | 1.32 |
| tomorrow | 2.59 | -7.15 | -5.91 | 1.24 | 1.24 |
| truck | 2.09 | 0.16 | -1.04 | -1.20 | 1.20 |
| old | 2.84 | -7.69 | -6.58 | 1.11 | 1.11 |
| sweater | 2.05 | -3.61 | -2.53 | 1.08 | 1.08 |
| baby | 1.72 | 0.73 | 1.76 | 1.04 | 1.04 |
| bye | 2.05 | 3.97 | 4.99 | 1.03 | 1.03 |
| firetruck | 2.12 | -1.84 | -2.85 | -1.01 | 1.01 |
| girl | 1.95 | -2.87 | -1.87 | 1.00 | 1.00 |
| chair | 3.21 | -0.48 | 0.46 | 0.94 | 0.94 |
| tonight | 1.96 | -5.49 | -4.57 | 0.92 | 0.92 |
| child | 1.72 | -4.07 | -3.15 | 0.92 | 0.92 |
| shovel | 2.08 | -2.75 | -3.66 | -0.91 | 0.91 |
| beads | 1.55 | -3.59 | -2.71 | 0.87 | 0.87 |
| cute | 1.49 | -2.52 | -1.65 | 0.87 | 0.87 |
| same | 2.85 | -6.64 | -5.78 | 0.86 | 0.86 |
| motorcycle | 1.89 | -2.57 | -3.41 | -0.84 | 0.84 |
| later | 2.17 | -4.23 | -3.39 | 0.84 | 0.84 |
| naughty | 1.16 | -3.29 | -2.45 | 0.84 | 0.84 |
| tooth | 2.54 | -0.91 | -0.07 | 0.84 | 0.84 |
| broom | 2.12 | -1.04 | -1.87 | -0.83 | 0.83 |
| hi | 1.43 | 1.66 | 2.48 | 0.82 | 0.82 |
| belly button | 2.07 | -0.60 | 0.21 | 0.81 | 0.81 |
| little (description) | 2.96 | -4.38 | -3.58 | 0.80 | 0.80 |
| leg | 3.13 | -2.52 | -1.73 | 0.79 | 0.79 |
| shoe | 3.11 | 2.16 | 2.95 | 0.78 | 0.78 |
| rocking chair | 1.94 | -2.19 | -1.41 | 0.78 | 0.78 |
| picture | 2.74 | -2.06 | -1.28 | 0.78 | 0.78 |
| bed | 2.57 | -0.03 | 0.75 | 0.78 | 0.78 |
| paper | 2.50 | -1.97 | -1.19 | 0.78 | 0.78 |
| hair | 3.10 | 0.34 | 1.12 | 0.77 | 0.77 |
| help | 2.82 | -2.67 | -1.90 | 0.77 | 0.77 |
| kiss | 1.83 | 1.71 | 2.48 | 0.76 | 0.76 |
| lady | 2.02 | -3.79 | -3.03 | 0.76 | 0.76 |
| flower | 2.67 | -0.90 | -0.14 | 0.76 | 0.76 |
| eye | 2.53 | 0.41 | 1.17 | 0.76 | 0.76 |
| red | 1.96 | -4.45 | -3.70 | 0.75 | 0.75 |
| party | 2.13 | -4.91 | -4.17 | 0.74 | 0.74 |
| write | 2.05 | -3.56 | -2.82 | 0.74 | 0.74 |
| clean (description) | 2.55 | -2.59 | -1.86 | 0.74 | 0.74 |
| clean (action) | 2.57 | -2.01 | -1.28 | 0.73 | 0.73 |
| please | 2.01 | -1.32 | -0.60 | 0.72 | 0.72 |
| money | 1.96 | -3.07 | -2.36 | 0.71 | 0.71 |
Plot item ease for males vs. females
We label the 49 items with absolute ease difference of more than median + 1SD = 0.71.
Anchor items
For our DIF analysis, let’s pick 10 anchor items that show the smallest difficulty difference in the slope-invariant free group means model (mg3).
| definition | a1 | d_f | d_m | d_diff | d_diff_abs |
|---|---|---|---|---|---|
| jeans | 2.512 | -4.489 | -4.490 | 0.001 | 0.001 |
| his | 2.300 | -4.305 | -4.302 | -0.003 | 0.003 |
| hit | 1.995 | -0.979 | -0.982 | 0.003 | 0.003 |
| plant | 2.126 | -1.915 | -1.909 | -0.006 | 0.006 |
| pants | 2.942 | -1.357 | -1.350 | -0.008 | 0.008 |
| ball | 2.812 | 3.516 | 3.507 | 0.009 | 0.009 |
| push | 2.018 | -1.199 | -1.213 | 0.014 | 0.014 |
| light | 2.324 | -0.328 | -0.311 | -0.016 | 0.016 |
| park | 1.798 | -1.698 | -1.715 | 0.017 | 0.017 |
| stairs | 2.083 | -0.636 | -0.658 | 0.022 | 0.022 |
Ability distribution comparison
What are the ability distributions by sex in the 2PL model?
## Joining, by = "data_id"
## Joining, by = "data_id"
| sex | ability_2pl | ability_sex |
|---|---|---|
| Female | 0.22 | 0.05 |
| Male | 0.02 | 0.05 |
Average male ability is slightly higher in the sex group model (i.e., there is a larger female advantage in the standard 2PL model), showing that the 36 items that are easier for females boost female ability estimates.
SES-related DIF
Now we will look for SES-based DIF, using mother’s education as a proxy for SES. Here’s the distribution of mom_ed in our data:
| Var1 | Freq |
|---|---|
| None | 0 |
| Primary | 2 |
| Some Secondary | 68 |
| Secondary | 254 |
| Some College | 266 |
| College | 292 |
| Some Graduate | 41 |
| Graduate | 140 |
We (arbitrarily) define high SES as their mother having at least some college (N=739), and low SES as having at most secondary education (N=324).
## Joining, by = c("a1", "definition")
## Joining, by = c("a1", "definition")| MEAN_1 | COV_11 | |
|---|---|---|
| par | 0.2507666 | 1 |
Items with DIF in difficulty
10 items show DIF based on a \(\chi^2\) test yielding \(p<.05\). We show these items below.
| AIC | BIC | X2 | p | |
|---|---|---|---|---|
| daddy* | -8.56 | -3.59 | 10.56 | 0.00 |
| babysitter’s name | -8.55 | -3.58 | 10.55 | 0.00 |
| quack quack | -5.23 | -0.26 | 7.23 | 0.01 |
| I | -5.16 | -0.20 | 7.16 | 0.01 |
| people | -5.11 | -0.14 | 7.11 | 0.01 |
| out | -4.83 | 0.14 | 6.83 | 0.01 |
| open | -3.68 | 1.29 | 5.68 | 0.02 |
| read | -3.33 | 1.64 | 5.33 | 0.02 |
| child’s own name | -3.03 | 1.94 | 5.03 | 0.02 |
| cheerios | -2.19 | 2.78 | 4.19 | 0.04 |
Items with a large difference in difficulty across SES
| definition | a1 | d_hi | d_lo | d_diff | d_diff_abs |
|---|---|---|---|---|---|
| why | 2.22 | -5.96 | -4.11 | -1.85 | 1.85 |
| couch | 2.85 | -2.82 | -1.19 | -1.63 | 1.63 |
| when | 3.17 | -8.78 | -7.16 | -1.63 | 1.63 |
| candy | 1.82 | -3.12 | -1.52 | -1.60 | 1.60 |
| table | 3.45 | -3.04 | -1.47 | -1.57 | 1.57 |
| window | 2.87 | -2.42 | -0.87 | -1.55 | 1.55 |
| pillow | 2.38 | -2.30 | -0.78 | -1.52 | 1.52 |
| TV | 2.54 | -1.02 | 0.46 | -1.48 | 1.48 |
| tonight | 1.75 | -5.35 | -3.87 | -1.48 | 1.48 |
| away | 2.01 | -4.04 | -2.59 | -1.45 | 1.45 |
| fish (food) | 2.89 | -4.78 | -3.33 | -1.45 | 1.45 |
| toy (object) | 1.88 | -0.71 | 0.71 | -1.42 | 1.42 |
| cake | 2.15 | -3.61 | -2.21 | -1.40 | 1.40 |
| his | 2.30 | -5.30 | -3.94 | -1.36 | 1.36 |
| penny | 2.00 | -4.71 | -3.36 | -1.35 | 1.35 |
| leg | 2.96 | -3.61 | -2.26 | -1.35 | 1.35 |
| later | 2.46 | -5.33 | -3.99 | -1.34 | 1.34 |
| run | 3.11 | -3.74 | -2.41 | -1.33 | 1.33 |
| radio | 2.08 | -3.20 | -1.89 | -1.32 | 1.32 |
| glass | 2.51 | -3.50 | -2.20 | -1.30 | 1.30 |
| bathroom | 2.58 | -1.52 | -0.22 | -1.29 | 1.29 |
| tomorrow | 2.44 | -7.26 | -6.00 | -1.27 | 1.27 |
| living room | 2.63 | -3.72 | -2.46 | -1.26 | 1.26 |
| fall | 2.75 | -2.79 | -1.53 | -1.26 | 1.26 |
| meat | 1.98 | -3.54 | -2.30 | -1.24 | 1.24 |
| money | 1.97 | -3.56 | -2.32 | -1.24 | 1.24 |
| clean (description) | 2.45 | -3.45 | -2.23 | -1.22 | 1.22 |
| hard | 3.22 | -7.02 | -5.80 | -1.22 | 1.22 |
| shorts | 2.38 | -4.07 | -2.85 | -1.22 | 1.22 |
| jeans | 2.59 | -5.75 | -4.53 | -1.21 | 1.21 |
| fine | 2.76 | -7.91 | -6.70 | -1.21 | 1.21 |
| kitchen | 3.21 | -2.24 | -1.03 | -1.21 | 1.21 |
| say | 2.08 | -2.65 | -1.45 | -1.20 | 1.20 |
| hurry | 2.31 | -4.19 | -3.00 | -1.19 | 1.19 |
| bedroom | 2.70 | -2.37 | -1.18 | -1.19 | 1.19 |
| fork | 3.42 | -3.71 | -2.53 | -1.17 | 1.17 |
| tongue | 2.16 | -2.49 | -1.34 | -1.15 | 1.15 |
| play | 2.71 | -1.94 | -0.81 | -1.13 | 1.13 |
| back | 2.24 | -3.49 | -2.36 | -1.12 | 1.12 |
| refrigerator | 2.88 | -2.45 | -1.33 | -1.12 | 1.12 |
| wait | 2.17 | -2.53 | -1.41 | -1.11 | 1.11 |
| same | 2.83 | -7.35 | -6.24 | -1.11 | 1.11 |
| bed | 2.41 | -0.88 | 0.23 | -1.11 | 1.11 |
| face | 2.24 | -2.54 | -1.44 | -1.11 | 1.11 |
| scared | 2.49 | -5.76 | -4.65 | -1.11 | 1.11 |
| bad | 1.24 | -1.61 | -0.50 | -1.11 | 1.11 |
| now | 2.18 | -3.84 | -2.74 | -1.11 | 1.11 |
| watch (action) | 2.19 | -2.91 | -1.80 | -1.10 | 1.10 |
| oven | 2.39 | -3.59 | -2.49 | -1.10 | 1.10 |
| cup | 2.75 | 0.09 | 1.18 | -1.10 | 1.10 |
| chicken (food) | 1.98 | -2.80 | -1.71 | -1.09 | 1.09 |
| egg | 2.51 | -3.35 | -2.26 | -1.09 | 1.09 |
| cheek | 2.54 | -4.10 | -3.01 | -1.09 | 1.09 |
| little (description) | 2.71 | -5.10 | -4.01 | -1.09 | 1.09 |
| some | 1.72 | -3.44 | -2.35 | -1.08 | 1.08 |
| clean (action) | 2.69 | -3.09 | -2.00 | -1.08 | 1.08 |
| box | 3.30 | -3.63 | -2.55 | -1.08 | 1.08 |
| head | 2.77 | -2.43 | -1.35 | -1.08 | 1.08 |
| stove | 2.49 | -4.09 | -3.02 | -1.07 | 1.07 |
| none | 1.88 | -4.12 | -3.07 | -1.05 | 1.05 |
| cereal | 2.13 | -1.40 | -0.34 | -1.05 | 1.05 |
| penguin | 2.77 | -5.97 | -4.93 | -1.04 | 1.04 |
| cry | 2.38 | -1.61 | -0.58 | -1.03 | 1.03 |
| orange (food) | 2.51 | -3.56 | -2.53 | -1.03 | 1.03 |
| scissors | 2.65 | -5.16 | -4.13 | -1.03 | 1.03 |
| brush | 2.90 | -1.34 | -0.31 | -1.03 | 1.03 |
| hit | 2.24 | -2.06 | -1.04 | -1.02 | 1.02 |
| knee | 3.00 | -4.80 | -3.78 | -1.02 | 1.02 |
| store | 2.74 | -3.07 | -2.06 | -1.01 | 1.01 |
| door | 3.14 | -0.84 | 0.17 | -1.01 | 1.01 |
| picture | 2.86 | -3.03 | -2.02 | -1.01 | 1.01 |
| chair | 3.31 | -1.74 | -0.73 | -1.01 | 1.01 |
| sink | 3.20 | -4.65 | -3.64 | -1.01 | 1.01 |
| aunt | 1.06 | -1.92 | -0.91 | -1.01 | 1.01 |
| happy | 1.90 | -2.60 | -1.60 | -1.00 | 1.00 |
Plot item ease for high vs. low SES
We label the 75 items with absolute ease difference of more than median + 1SD = 1.
## Warning: ggrepel: 47 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps
Anchor items
For our DIF analysis, let’s pick 10 anchor items that show the smallest difficulty difference in the slope-invariant model (mg2).
| definition | a1 | d_hi | d_lo | d_diff | d_diff_abs |
|---|---|---|---|---|---|
| pool | 1.217 | -1.700 | -1.718 | 0.018 | 0.018 |
| kitty | 1.294 | 0.186 | 0.168 | 0.018 | 0.018 |
| bear | 1.736 | -1.266 | -1.285 | 0.019 | 0.019 |
| woof woof | 1.563 | -0.101 | -0.075 | -0.025 | 0.025 |
| swim | 1.528 | -2.732 | -2.701 | -0.030 | 0.030 |
| another | 1.829 | -3.335 | -3.302 | -0.033 | 0.033 |
| zoo | 2.041 | -4.389 | -4.356 | -0.033 | 0.033 |
| slide (object) | 2.389 | -2.529 | -2.490 | -0.039 | 0.039 |
| hi | 1.436 | 1.343 | 1.304 | 0.039 | 0.039 |
| moo | 1.998 | -1.212 | -1.172 | -0.040 | 0.040 |
Ability distribution comparison
What are the ability distributions by SES in the 2PL model?
## Joining, by = c("data_id", "ability")
## Joining, by = "data_id"
| ses_group | ability_2pl | ability_ses |
|---|---|---|
| high | -0.13 | 0.24 |
| low | -0.17 | 0.05 |