Note to self: these models take a long time to run, so, rather than estimating them each time I run the code, I’ve saved the models, commented out teh code for running the models, and included the code for opening the models. Be EXTRA CAREFUL that the saved models are the most up to date.

1 Preliminaries

library(wordbankr) # WB data
library(tidyverse) # tidy
library(mirt) # IRT models
library(ltm) # more IRT functions
library(psych) # some psychometric stuff (tests of dimensionality)
library(Gifi)# some more psychometric stuff (tests of dimensionality)
library(knitr) # some formatting, tables, etc
library(patchwork) # combining plots. 
library(GGally) # More plottinng options. 
library(lordif) # differential item functioning.

Inst <- get_instrument_data(language="English (American)", form="WS")
Admin <- get_administration_data(language="English (American)", form="WS")
N_total = nrow(Admin) # making sure things add up later
N_long = nrow(filter(Admin, longitudinal==TRUE)) # making sure things add up later
Item <- get_item_data(language="English (American)", form = "WS")

Vocab <- Admin %>%
  full_join(.,Inst, by="data_id") %>%
  full_join(., Item, by="num_item_id") %>%
  filter(longitudinal==FALSE) %>% # remove longitudinal data set
  filter(type == "word"
         ) %>%
  mutate(
    out = ifelse(value=="produces", yes=1, no =0)
    )

N_vocab = nrow(filter(Item, type == "word")) 

nrow(Vocab) == (N_total - N_long)*N_vocab

## [1] TRUE

Vocab %>%
  filter(is.na(out)) %>%
  group_by(definition) %>%
  count()

Number of missing items differs by word. How can this be??

Check distribution of missing values by source.

Vocab %>%
  filter(is.na(out)) %>%
  group_by(source_name) %>%
  count()

These all seem to come from a single study (- 1).

Vocab %>%
  group_by(source_name) %>%
  count()

Vocab %>%
 filter(is.na(out)) %>%
 filter(source_name=="Marchman (Outreach1)")

No idea why this word is missing. I’m removing all these participants from the IRT models.

N_missing <- Vocab %>%
  filter(is.na(out)) %>%
  group_by(data_id) %>%
  slice(1) %>%
  ungroup(data_id) %>%
  count()

Vocab %>% 
  filter(!is.na(out)) %>%
  group_by(definition) %>%
  summarise(
    mean=mean(out), 
    sd=sd(out),
    category = first(lexical_category)
  ) %>%
  arrange(category) %>%
  kable(caption="Means and SDs for Each Item (Arranged by Item)")

Means and SDs for Each Item (Arranged by Item)
definition	mean	sd	category
a	0.2880992	0.4529315	function_words
a lot	0.1881848	0.3909063	function_words
about	0.0732872	0.2606384	function_words
above	0.0909308	0.2875450	function_words
all	0.3041925	0.4601194	function_words
am	0.1834009	0.3870410	function_words
an	0.0663643	0.2489475	function_words
and	0.2560191	0.4364845	function_words
another	0.2240229	0.4169869	function_words
any	0.1541766	0.3611611	function_words
are	0.1529103	0.3599440	function_words
around	0.1664679	0.3725446	function_words
at	0.2131617	0.4095898	function_words
away	0.2717961	0.4449383	function_words
back	0.3266667	0.4690500	function_words
be	0.1469466	0.3540949	function_words
because	0.1382191	0.3451711	function_words
behind	0.1869783	0.3899406	function_words
beside	0.0822996	0.2748534	function_words
but	0.0945333	0.2926042	function_words
by	0.1967096	0.3975583	function_words
can (auxiliary)	0.2479182	0.4318554	function_words
could	0.0761518	0.2652725	function_words
did/did ya	0.2269368	0.4189013	function_words
do	0.4020937	0.4903790	function_words
does	0.1195419	0.3244638	function_words
don’t	0.3340481	0.4717128	function_words
down	0.6519981	0.4763933	function_words
each	0.0591885	0.2360054	function_words
every	0.0983294	0.2977950	function_words
for	0.1870229	0.3899764	function_words
gonna/going to	0.2437574	0.4293991	function_words
gotta/got to	0.1350191	0.3417847	function_words
hafta/have to	0.1704057	0.3760337	function_words
he	0.2185115	0.4132855	function_words
her	0.1667860	0.3728292	function_words
here	0.3775607	0.4848346	function_words
hers	0.1147971	0.3188150	function_words
him	0.1550942	0.3620377	function_words
his	0.1400620	0.3470928	function_words
how	0.1537178	0.3607210	function_words
I	0.4377825	0.4961729	function_words
if	0.0603963	0.2382480	function_words
inside/in	0.4440210	0.4969157	function_words
into	0.1004534	0.3006394	function_words
is	0.2211883	0.4150965	function_words
it	0.3263409	0.4689296	function_words
lemme/let me	0.3024309	0.4593656	function_words
me	0.5405663	0.4984110	function_words
mine	0.6595340	0.4739223	function_words
more	0.6362340	0.4811396	function_words
much	0.1293556	0.3356332	function_words
my	0.3974756	0.4894342	function_words
myself	0.1390744	0.3460655	function_words
need/need to	0.2291369	0.4203276	function_words
next to	0.1212121	0.3264126	function_words
none	0.1499404	0.3570556	function_words
not	0.2356870	0.4244781	function_words
of	0.1002387	0.3003538	function_words
off	0.5752318	0.4943665	function_words
on	0.5615037	0.4962619	function_words
on top of	0.1905669	0.3927950	function_words
other	0.1967096	0.3975583	function_words
our	0.1071088	0.3092884	function_words
out	0.5418848	0.4983019	function_words
over	0.2550704	0.4359528	function_words
same	0.1370026	0.3438911	function_words
she	0.1881708	0.3908951	function_words
so	0.1137882	0.3175917	function_words
some	0.3160906	0.4650042	function_words
that	0.4465094	0.4971898	function_words
the	0.2462419	0.4308725	function_words
their	0.0835322	0.2767180	function_words
them	0.1216893	0.3269657	function_words
then	0.0887828	0.2844640	function_words
there	0.3482611	0.4764760	function_words
these	0.2051037	0.4038256	function_words
they	0.1150358	0.3191032	function_words
this	0.4040476	0.4907652	function_words
those	0.1500119	0.3571257	function_words
to	0.2435592	0.4292809	function_words
too	0.3306356	0.4704980	function_words
try/try to	0.2199190	0.4142409	function_words
under	0.2818680	0.4499630	function_words
up	0.6628653	0.4727875	function_words
us	0.0902363	0.2865543	function_words
wanna/want to	0.3738696	0.4838872	function_words
was	0.1100239	0.3129569	function_words
we	0.1528738	0.3599088	function_words
were	0.0701503	0.2554307	function_words
what	0.4424631	0.4967375	function_words
when	0.1067938	0.3088877	function_words
where	0.3529272	0.4779372	function_words
which	0.0765744	0.2659467	function_words
who	0.2293949	0.4204938	function_words
why	0.2638724	0.4407834	function_words
will	0.1321880	0.3387355	function_words
with	0.2200763	0.4143473	function_words
would	0.0601576	0.2378069	function_words
you	0.4323103	0.4954559	function_words
your	0.1764425	0.3812417	function_words
yourself	0.0611124	0.2395650	function_words
airplane	0.6494772	0.4771904	nouns
alligator	0.3564286	0.4790009	nouns
animal	0.4225553	0.4940247	nouns
ankle	0.1731044	0.3783826	nouns
ant	0.3986663	0.4896821	nouns
apple	0.7561728	0.4294406	nouns
applesauce	0.3798523	0.4854077	nouns
arm	0.5634506	0.4960166	nouns
backyard	0.2776454	0.4478909	nouns
ball	0.9344729	0.2474829	nouns
balloon	0.7591449	0.4276533	nouns
banana	0.8015195	0.3989032	nouns
basement	0.1137068	0.3174927	nouns
basket	0.3689228	0.4825705	nouns
bat	0.3419170	0.4744085	nouns
bathroom	0.4662387	0.4989182	nouns
bathtub	0.5354256	0.4988027	nouns
beads	0.2361641	0.4247748	nouns
beans	0.4151393	0.4928047	nouns
bear	0.6807701	0.4662337	nouns
bed	0.6421953	0.4794112	nouns
bedroom	0.3618844	0.4806028	nouns
bee	0.5981931	0.4903216	nouns
belly button	0.6276748	0.4834819	nouns
belt	0.3370653	0.4727637	nouns
bench	0.1424141	0.3495161	nouns
bib	0.4611905	0.4985509	nouns
bicycle	0.5744529	0.4944845	nouns
bird	0.7736342	0.4185283	nouns
blanket	0.6408551	0.4798068	nouns
block	0.5700690	0.4951249	nouns
boat	0.6286258	0.4832297	nouns
book	0.8252612	0.3797887	nouns
boots	0.5310050	0.4990971	nouns
bottle	0.6626277	0.4728693	nouns
bowl	0.5142653	0.4998559	nouns
box	0.5393392	0.4985093	nouns
bread	0.5680684	0.4954039	nouns
broom	0.4469553	0.4972374	nouns
brush	0.5483718	0.4977138	nouns
bubbles	0.7375297	0.4400291	nouns
bucket	0.3326185	0.4712073	nouns
bug	0.5823417	0.4932319	nouns
bunny	0.6228300	0.4847357	nouns
bus	0.6181430	0.4858995	nouns
butter	0.4138095	0.4925738	nouns
butterfly	0.4919163	0.4999941	nouns
buttocks/bottom*	0.5435093	0.4981626	nouns
button	0.5203329	0.4996458	nouns
cake	0.5509865	0.4974527	nouns
camera	0.3567349	0.4790926	nouns
can (object)	0.2736164	0.4458676	nouns
candy	0.5248632	0.4994409	nouns
car	0.8015195	0.3989032	nouns
carrots	0.4493581	0.4974879	nouns
cat	0.7432914	0.4368691	nouns
cereal	0.5509039	0.4974612	nouns
chair	0.6222381	0.4848853	nouns
chalk	0.2784538	0.4482915	nouns
cheek	0.4803805	0.4996743	nouns
cheerios	0.4682219	0.4990485	nouns
cheese	0.7418665	0.4376598	nouns
chicken (animal)	0.5065367	0.5000167	nouns
chicken (food)	0.5152091	0.4998280	nouns
chin	0.4496788	0.4975205	nouns
chocolate	0.3837016	0.4863444	nouns
clock	0.5005951	0.5000592	nouns
closet	0.3162027	0.4650484	nouns
cloud	0.3620567	0.4806523	nouns
coat	0.5299857	0.4991594	nouns
coffee	0.3933413	0.4885496	nouns
coke	0.2531011	0.4348403	nouns
comb	0.3961905	0.4891631	nouns
cookie	0.7491686	0.4335431	nouns
corn	0.4412955	0.4966010	nouns
couch	0.4124079	0.4923264	nouns
cow	0.6623901	0.4729509	nouns
cracker	0.6775268	0.4674786	nouns
crayon	0.4967880	0.5000492	nouns
crib	0.3540181	0.4782715	nouns
cup	0.6927096	0.4614256	nouns
deer	0.3295969	0.4701229	nouns
diaper	0.6907535	0.4622379	nouns
dish	0.2905840	0.4540860	nouns
dog	0.8717949	0.3343578	nouns
doll	0.5446535	0.4980614	nouns
donkey	0.2458899	0.4306649	nouns
donut	0.3157644	0.4648750	nouns
door	0.6521739	0.4763371	nouns
drawer	0.2594620	0.4383916	nouns
dress (object)	0.3691355	0.4826282	nouns
drink (beverage)	0.5915258	0.4916102	nouns
dryer	0.2338652	0.4233379	nouns
duck	0.7712589	0.4200720	nouns
ear	0.7695415	0.4211764	nouns
egg	0.5504631	0.4975060	nouns
elephant	0.5130703	0.4998885	nouns
eye	0.7957730	0.4031835	nouns
face	0.4549132	0.4980223	nouns
finger	0.5783591	0.4938804	nouns
firetruck	0.4208522	0.4937547	nouns
fish (animal)	0.7146591	0.4516303	nouns
fish (food)	0.5414785	0.4983358	nouns
flag	0.3171197	0.4654100	nouns
flower	0.6351962	0.4814324	nouns
food	0.4759638	0.4994814	nouns
foot	0.6146898	0.4867264	nouns
fork	0.5604944	0.4963859	nouns
french fries	0.4996431	0.5000594	nouns
frog	0.5521429	0.4973329	nouns
game	0.3192857	0.4662554	nouns
garage	0.2960667	0.4565752	nouns
garbage	0.3408605	0.4740549	nouns
garden	0.2079161	0.4058648	nouns
giraffe	0.4244587	0.4943194	nouns
glass	0.3580776	0.4794922	nouns
glasses	0.4750238	0.4994352	nouns
gloves	0.2803805	0.4492385	nouns
glue	0.1801287	0.3843404	nouns
goose	0.2875536	0.4526758	nouns
grapes	0.5568236	0.4968197	nouns
grass	0.4738344	0.4993743	nouns
green beans	0.2828211	0.4504239	nouns
gum	0.3044100	0.4602120	nouns
hair	0.6860603	0.4641473	nouns
hamburger	0.3956149	0.4890406	nouns
hammer	0.3424690	0.4745921	nouns
hand	0.6040380	0.4891144	nouns
hat	0.7295821	0.4442284	nouns
head	0.5828381	0.4931487	nouns
helicopter	0.3828218	0.4861332	nouns
hen	0.1760496	0.3809078	nouns
high chair	0.3623810	0.4807453	nouns
horse	0.6391067	0.4803167	nouns
hose	0.2711016	0.4445814	nouns
ice	0.5113015	0.4999317	nouns
ice cream	0.5624257	0.4961467	nouns
jacket	0.4549774	0.4980280	nouns
jar	0.3068480	0.4612408	nouns
jeans	0.2605382	0.4389806	nouns
jello	0.2449905	0.4301328	nouns
jelly	0.3033413	0.4597562	nouns
juice	0.7488129	0.4337474	nouns
keys	0.5450440	0.4980261	nouns
kitchen	0.4399524	0.4964402	nouns
kitty	0.7184004	0.4498327	nouns
knee	0.5183246	0.4997236	nouns
knife	0.3726190	0.4835595	nouns
ladder	0.2650775	0.4414271	nouns
lamb	0.2948321	0.4560216	nouns
lamp	0.2573267	0.4372130	nouns
lawn mower	0.3077290	0.4616088	nouns
leg	0.5023798	0.5000538	nouns
light	0.6280285	0.4833883	nouns
lion	0.4963139	0.5000459	nouns
lips	0.3697359	0.4827906	nouns
living room	0.2560076	0.4364780	nouns
lollipop	0.2740935	0.4461096	nouns
meat	0.3506308	0.4772243	nouns
medicine	0.4221429	0.4939599	nouns
melon	0.2656027	0.4417062	nouns
milk	0.7565899	0.4291915	nouns
mittens	0.2788484	0.4484862	nouns
money	0.4702664	0.4991745	nouns
monkey	0.5874109	0.4923585	nouns
moon	0.6044244	0.4890321	nouns
moose	0.2189659	0.4135947	nouns
mop	0.1989516	0.3992591	nouns
motorcycle	0.3676436	0.4822211	nouns
mouse	0.4954762	0.5000391	nouns
mouth	0.6562871	0.4750031	nouns
muffin	0.3313497	0.4707545	nouns
nail	0.2336271	0.4231880	nouns
napkin	0.3977137	0.4894840	nouns
necklace	0.3558677	0.4788324	nouns
noodles	0.4462672	0.4971635	nouns
nose	0.8000950	0.3999762	nouns
nuts	0.2777513	0.4479434	nouns
orange (food)	0.5114068	0.4999293	nouns
oven	0.2948596	0.4560339	nouns
owie/boo boo	0.6778332	0.4673620	nouns
owl	0.4559733	0.4981172	nouns
pajamas	0.4845385	0.4998203	nouns
pancake	0.4289116	0.4949796	nouns
pants	0.5471833	0.4978279	nouns
paper	0.5161674	0.4997980	nouns
peanut butter	0.4073810	0.4914053	nouns
peas	0.4185714	0.4933836	nouns
pen	0.4506070	0.4976136	nouns
pencil	0.3704145	0.4829732	nouns
penguin	0.3013568	0.4589020	nouns
penis*	0.3288128	0.4698377	nouns
penny	0.2992370	0.4579784	nouns
pickle	0.3379442	0.4730658	nouns
picture	0.4351654	0.4958376	nouns
pig	0.6202471	0.4853830	nouns
pillow	0.5320817	0.4990290	nouns
pizza	0.5870753	0.4924180	nouns
plant	0.3149119	0.4645361	nouns
plate	0.4399239	0.4964368	nouns
play dough	0.2932349	0.4552994	nouns
play pen	0.1038434	0.3050937	nouns
pony	0.2598951	0.4386291	nouns
pool	0.4626190	0.4986601	nouns
popcorn	0.4464030	0.4971783	nouns
popsicle	0.3614688	0.4804832	nouns
porch	0.1699284	0.3756147	nouns
potato	0.3719933	0.4833942	nouns
potato chip	0.4204004	0.4936821	nouns
potty	0.6090369	0.4880242	nouns
present	0.3602381	0.4801265	nouns
pretzel	0.3295184	0.4700944	nouns
pudding	0.2128370	0.4093622	nouns
pumpkin	0.3634849	0.4810600	nouns
puppy	0.6105163	0.4876912	nouns
purse	0.3965722	0.4892440	nouns
puzzle	0.4194623	0.4935298	nouns
radio	0.2714932	0.4447828	nouns
rain	0.5482414	0.4977265	nouns
raisin	0.4431223	0.4968135	nouns
refrigerator	0.3361085	0.4724327	nouns
rock	0.5506073	0.4974916	nouns
rocking chair	0.3219652	0.4672854	nouns
roof	0.1909871	0.3931258	nouns
room	0.3956698	0.4890523	nouns
rooster	0.2502383	0.4332018	nouns
salt	0.2187277	0.4134327	nouns
sandbox	0.2675888	0.4427548	nouns
sandwich	0.3955259	0.4890216	nouns
sauce	0.2488688	0.4324091	nouns
scarf	0.1403383	0.3473791	nouns
scissors	0.3413473	0.4742181	nouns
sheep	0.4704065	0.4991828	nouns
shirt	0.5708512	0.4950135	nouns
shoe	0.8566002	0.3505217	nouns
shorts	0.3854216	0.4867527	nouns
shoulder	0.2709078	0.4444815	nouns
shovel	0.3355545	0.4722401	nouns
shower	0.4426736	0.4967619	nouns
sidewalk	0.2502980	0.4332362	nouns
sink	0.3630952	0.4809492	nouns
sky	0.4303376	0.4951822	nouns
sled	0.2291369	0.4203276	nouns
slide (object)	0.4940561	0.5000241	nouns
slipper	0.3030736	0.4596415	nouns
sneaker	0.1923169	0.3941677	nouns
snow	0.4007606	0.4901109	nouns
snowman	0.2750832	0.4466093	nouns
snowsuit	0.0924690	0.2897214	nouns
soap	0.5214082	0.4996009	nouns
sock	0.5849370	0.4927914	nouns
soda/pop	0.3278454	0.4694842	nouns
sofa	0.1728248	0.3781408	nouns
soup	0.3962444	0.4891745	nouns
spaghetti	0.4167659	0.4930821	nouns
spoon	0.6611256	0.4733833	nouns
sprinkler	0.2004773	0.4004053	nouns
squirrel	0.3954318	0.4890014	nouns
stairs	0.3771116	0.4847209	nouns
star	0.5228245	0.4995382	nouns
stick	0.4180562	0.4932983	nouns
stone	0.1685742	0.3744200	nouns
story	0.3909631	0.4880242	nouns
stove	0.3399952	0.4737635	nouns
strawberry	0.4414843	0.4966232	nouns
street	0.3465841	0.4759385	nouns
stroller	0.3573638	0.4792803	nouns
sun	0.5001190	0.5000595	nouns
sweater	0.4615751	0.4985807	nouns
swing (object)	0.5610278	0.4963207	nouns
table	0.4639715	0.4987596	nouns
tape	0.3211818	0.4669861	nouns
teddybear	0.4754879	0.4994582	nouns
telephone	0.5985263	0.4902547	nouns
tiger	0.4462161	0.4971580	nouns
tights	0.1463996	0.3535485	nouns
tissue/kleenex	0.3886245	0.4874957	nouns
toast	0.4727576	0.4993167	nouns
toe	0.6043251	0.4890533	nouns
tongue	0.4879848	0.4999151	nouns
tooth	0.5522814	0.4973182	nouns
toothbrush	0.5775719	0.4940046	nouns
towel	0.4853885	0.4998458	nouns
toy (object)	0.5885714	0.4921512	nouns
tractor	0.3786870	0.4851176	nouns
train	0.6135932	0.4869835	nouns
trash	0.4232514	0.4941335	nouns
tray	0.1245526	0.3302503	nouns
tree	0.6509030	0.4767413	nouns
tricycle	0.2079657	0.4059005	nouns
truck	0.7133349	0.4522575	nouns
tummy	0.5853137	0.4927264	nouns
tuna	0.1726687	0.3780057	nouns
turkey	0.3153003	0.4646907	nouns
turtle	0.5105877	0.4999474	nouns
TV	0.5713946	0.4949354	nouns
underpants	0.2497617	0.4329266	nouns
vacuum	0.4149012	0.4927636	nouns
vagina*	0.1793893	0.3837237	nouns
vanilla	0.1302481	0.3366163	nouns
vitamins	0.2785595	0.4483437	nouns
walker	0.0866348	0.2813328	nouns
washing machine	0.2921830	0.4548202	nouns
watch (object)	0.4146225	0.4927154	nouns
water (beverage)	0.7003087	0.4581771	nouns
water (not beverage)	0.6805984	0.4663002	nouns
wind	0.3337298	0.4716006	nouns
window	0.3780314	0.4849532	nouns
wolf	0.2246066	0.4173727	nouns
yogurt	0.4806275	0.4996840	nouns
zebra	0.3829686	0.4861686	nouns
zipper	0.4020937	0.4903790	nouns
after	0.1699595	0.3756420	other
aunt	0.3533191	0.4780576	other
baa baa	0.7287411	0.4446622	other
baby	0.8380817	0.3684196	other
babysitter	0.1183488	0.3230593	other
babysitter’s name	0.4131936	0.4924656	other
bath	0.7432304	0.4369031	other
beach	0.2987601	0.4577690	other
before	0.0990453	0.2987585	other
boy	0.4841704	0.4998089	other
breakfast	0.4298976	0.4951202	other
brother	0.3183333	0.4658851	other
bye	0.9054856	0.2925777	other
call (on phone)	0.4613739	0.4985650	other
camping	0.1088305	0.3114637	other
child	0.1243746	0.3300477	other
child’s own name	0.6618380	0.4731402	other
choo choo	0.6794202	0.4667549	other
church*	0.3188648	0.4660921	other
circus	0.1276850	0.3337785	other
clown	0.2729008	0.4455034	other
cockadoodledoo	0.3926190	0.4883914	other
country	0.0515144	0.2210709	other
cowboy	0.1372315	0.3441327	other
daddy*	0.9648623	0.1841497	other
day	0.2262443	0.4184490	other
dinner	0.4125208	0.4923465	other
doctor	0.4054247	0.4910325	other
downtown	0.0930565	0.2905463	other
farm	0.2417896	0.4282184	other
fireman	0.2301644	0.4209881	other
friend	0.2901690	0.4538943	other
gas station	0.1976633	0.3982843	other
girl	0.4431223	0.4968135	other
give me five!	0.3927212	0.4884138	other
go potty	0.5183159	0.4997239	other
gonna get you!	0.4020029	0.4903610	other
grandma*	0.7577773	0.4284793	other
grandpa*	0.7015918	0.4576139	other
grrr	0.7302569	0.4438791	other
hello	0.6792587	0.4668170	other
hi	0.8012821	0.3990826	other
home	0.5773343	0.4940419	other
house	0.5154468	0.4998207	other
lady	0.2540515	0.4353786	other
later	0.2443385	0.4297455	other
lunch	0.4192244	0.4934909	other
mailman	0.2196518	0.4140601	other
man	0.3696118	0.4827571	other
meow	0.7923990	0.4056376	other
mommy*	0.9705603	0.1690556	other
moo	0.8180523	0.3858473	other
morning	0.2954059	0.4562793	other
movie	0.2785442	0.4483360	other
nap	0.5176023	0.4997495	other
night	0.4167460	0.4930787	other
night night	0.7487521	0.4337824	other
no	0.8765139	0.3290334	other
now	0.3493689	0.4768275	other
nurse	0.1098114	0.3126919	other
ouch	0.7516029	0.4321346	other
outside	0.6558117	0.4751593	other
park	0.4903732	0.4999667	other
party	0.3216667	0.4671715	other
pattycake	0.3786038	0.4850969	other
peekaboo	0.6747388	0.4685280	other
people	0.2880952	0.4529296	other
person	0.1027659	0.3036890	other
pet’s name	0.5483103	0.4977199	other
picnic	0.2074392	0.4055211	other
playground	0.2530408	0.4348060	other
please	0.7264957	0.4458104	other
police	0.1993807	0.3995823	other
quack quack	0.7276616	0.4452160	other
school	0.4652712	0.4988518	other
shh/shush/hush	0.6975529	0.4593724	other
shopping	0.3358742	0.4723514	other
sister	0.3280171	0.4695470	other
snack	0.4508450	0.4976372	other
so big!	0.3299214	0.4702403	other
store	0.4527943	0.4978258	other
teacher	0.2279657	0.4195703	other
thank you	0.7466762	0.4349664	other
this little piggy	0.3048548	0.4604007	other
time	0.1298020	0.3361255	other
today	0.1891827	0.3917004	other
tomorrow	0.1934176	0.3950246	other
tonight	0.1309325	0.3373668	other
turn around	0.3199334	0.4665059	other
uh oh	0.8981481	0.3024893	other
uncle	0.3387250	0.4733325	other
vroom	0.6611905	0.4733614	other
woods	0.1059160	0.3077668	other
woof woof	0.8007126	0.3995120	other
work (place)	0.4351345	0.4958336	other
yard	0.2588263	0.4380423	other
yes	0.7515439	0.4321690	other
yesterday	0.0894775	0.2854657	other
yum yum	0.6779258	0.4673268	other
zoo	0.3522267	0.4777211	other
all gone	0.6881388	0.4633085	predicates
asleep	0.4006189	0.4900822	predicates
awake	0.3227803	0.4675951	predicates
bad	0.3896289	0.4877241	predicates
better	0.2772749	0.4477067	predicates
big	0.5260404	0.4993808	predicates
bite	0.5424495	0.4982540	predicates
black	0.3264335	0.4689637	predicates
blow	0.4316290	0.4953623	predicates
blue	0.4983365	0.5000567	predicates
break	0.3884789	0.4874624	predicates
bring	0.2901308	0.4538765	predicates
broken	0.4642093	0.4987767	predicates
brown	0.2874822	0.4526422	predicates
build	0.2670793	0.4424868	predicates
bump	0.3404762	0.4739258	predicates
buy	0.2512503	0.4337838	predicates
careful	0.3187991	0.4660665	predicates
carry	0.3573130	0.4792652	predicates
catch	0.3560894	0.4788991	predicates
chase	0.2345091	0.4237421	predicates
clap	0.4636061	0.4987330	predicates
clean (action)	0.4282319	0.4948813	predicates
clean (description)	0.4492754	0.4974795	predicates
climb	0.3463554	0.4758648	predicates
close	0.4105063	0.4919842	predicates
cold	0.6041815	0.4890839	predicates
cook	0.3773810	0.4847892	predicates
cover	0.2289731	0.4202219	predicates
cry	0.4798004	0.4996512	predicates
cut	0.2956708	0.4563980	predicates
cute	0.2876549	0.4527233	predicates
dance	0.4749108	0.4994295	predicates
dark	0.3337301	0.4716007	predicates
dirty	0.5362491	0.4987435	predicates
draw	0.3559362	0.4788530	predicates
drink (action)	0.5935791	0.4912233	predicates
drive	0.3802616	0.4855088	predicates
drop	0.3289693	0.4698947	predicates
dry (action)	0.2999762	0.4583018	predicates
dry (description)	0.3220501	0.4673177	predicates
dump	0.1879323	0.3907047	predicates
eat	0.6677757	0.4710669	predicates
empty	0.3127533	0.4636700	predicates
fall	0.4714829	0.4992454	predicates
fast	0.3359505	0.4723779	predicates
feed	0.2880629	0.4529145	predicates
find	0.3425309	0.4746125	predicates
fine	0.1484747	0.3556123	predicates
finish	0.2315189	0.4218533	predicates
first	0.2107773	0.4079092	predicates
fit	0.1986171	0.3990066	predicates
fix	0.3751189	0.4842112	predicates
full	0.2733556	0.4457350	predicates
gentle	0.2666032	0.4422358	predicates
get	0.4378867	0.4961860	predicates
give	0.3334127	0.4714887	predicates
go	0.6885246	0.4631516	predicates
good	0.4463734	0.4971750	predicates
green	0.4156956	0.4929001	predicates
happy	0.4344106	0.4957383	predicates
hard	0.2401716	0.4272384	predicates
hate	0.0756202	0.2644210	predicates
have	0.3242857	0.4681631	predicates
hear	0.2852724	0.4515978	predicates
heavy	0.3832421	0.4862344	predicates
help	0.5134300	0.4998790	predicates
hide	0.3578396	0.4794216	predicates
high	0.3018823	0.4591292	predicates
hit	0.4074250	0.4914136	predicates
hold	0.3707758	0.4830700	predicates
hot	0.7430473	0.4370050	predicates
hug	0.5676576	0.4954602	predicates
hungry	0.4234706	0.4941674	predicates
hurry	0.2589328	0.4381008	predicates
hurt	0.4079010	0.4915031	predicates
jump	0.4939387	0.5000227	predicates
kick	0.4166072	0.4930552	predicates
kiss	0.6005706	0.4898394	predicates
knock	0.3545390	0.4784304	predicates
last	0.1111906	0.3144056	predicates
lick	0.2514884	0.4339203	predicates
like	0.3291290	0.4699528	predicates
listen	0.2366667	0.4250866	predicates
little (description)	0.3582658	0.4795479	predicates
long	0.1536260	0.3606328	predicates
look	0.4405611	0.4965135	predicates
loud	0.3029293	0.4595796	predicates
love	0.4964354	0.5000467	predicates
mad	0.2211905	0.4150979	predicates
make	0.2789148	0.4485189	predicates
naughty	0.1334129	0.3400610	predicates
new	0.2278571	0.4194999	predicates
nice	0.3726190	0.4835595	predicates
noisy	0.2248450	0.4175300	predicates
old	0.1711969	0.3767259	predicates
open	0.5611784	0.4963020	predicates
orange (description)	0.4218156	0.4939081	predicates
paint	0.3121277	0.4634168	predicates
pick	0.2222222	0.4157893	predicates
play	0.5127229	0.4998975	predicates
poor	0.0809262	0.2727544	predicates
pour	0.2326579	0.4225764	predicates
pretend	0.1358760	0.3426977	predicates
pretty	0.4186324	0.4933937	predicates
pull	0.3208671	0.4668654	predicates
push	0.4059005	0.4911239	predicates
put	0.2888095	0.4532632	predicates
quiet	0.2880952	0.4529296	predicates
read	0.5184392	0.4997193	predicates
red	0.4394011	0.4963732	predicates
ride	0.4271429	0.4947223	predicates
rip	0.1364178	0.3432727	predicates
run	0.4604950	0.4984962	predicates
sad	0.3032105	0.4597000	predicates
say	0.2728139	0.4454590	predicates
scared	0.2863604	0.4521137	predicates
see	0.5043995	0.5000401	predicates
shake	0.2776588	0.4478975	predicates
share	0.3030014	0.4596106	predicates
show	0.2612011	0.4393417	predicates
sick	0.2899000	0.4537698	predicates
sing	0.4096099	0.4918203	predicates
sit	0.5562158	0.4968888	predicates
skate	0.1334923	0.3401465	predicates
sleep	0.5014265	0.5000574	predicates
sleepy	0.3601049	0.4800878	predicates
slide (action)	0.4233698	0.4941517	predicates
slow	0.1975220	0.3981769	predicates
smile	0.2900691	0.4538481	predicates
soft	0.3267445	0.4690788	predicates
spill	0.2945385	0.4558894	predicates
splash	0.3590660	0.4797838	predicates
stand	0.3130062	0.4637721	predicates
stay	0.3027130	0.4594868	predicates
sticky	0.3206470	0.4667808	predicates
stop	0.5101022	0.4999574	predicates
stuck	0.3497020	0.4769326	predicates
sweep	0.3095068	0.4623454	predicates
swim	0.4080952	0.4915395	predicates
swing (action)	0.4974994	0.5000533	predicates
take	0.2797903	0.4489496	predicates
talk	0.3221429	0.4673530	predicates
taste	0.2305311	0.4212229	predicates
tear	0.1624523	0.3689092	predicates
think	0.1340010	0.3406940	predicates
thirsty	0.3374613	0.4729000	predicates
throw	0.4114707	0.4921587	predicates
tickle	0.4728701	0.4993228	predicates
tiny	0.1459575	0.3531058	predicates
tired	0.3302381	0.4703547	predicates
touch	0.3318247	0.4709245	predicates
wait	0.3117409	0.4632598	predicates
wake	0.2804384	0.4492670	predicates
walk	0.5175856	0.4997500	predicates
wash	0.4499167	0.4975445	predicates
watch (action)	0.3356360	0.4722686	predicates
wet	0.5241379	0.4994764	predicates
white	0.2816667	0.4498652	predicates
windy	0.2769048	0.4475223	predicates
wipe	0.3461172	0.4757878	predicates
wish	0.0858984	0.2802473	predicates
work (action)	0.3802951	0.4855171	predicates
write	0.2884707	0.4531051	predicates
yellow	0.4290805	0.4950037	predicates
yucky	0.5406949	0.4984005	predicates

Vocab %>% 
  filter(!is.na(out)) %>%
  group_by(definition) %>%
  summarise(
    mean=mean(out), 
    sd=sd(out),
    category = first(lexical_category)
  ) %>%
  ggplot(aes(x=mean, fill=category)) + geom_histogram()

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Stick to just nouns and predicates as these are relatively clearly not grammatical items.

Vocab_short_with_ids <- Vocab %>% 
  filter(lexical_category == "nouns" | lexical_category == "predicates") %>%
  dplyr::select(data_id, value, out, definition) %>%
  pivot_wider(id_cols=data_id, names_from = "definition", values_from="out") %>%
  drop_na() # drop participants with missing data


Vocab_short <- Vocab_short_with_ids %>%
  dplyr::select(-"data_id") # dataset for IRT can't have IDs

nrow(Vocab_short_with_ids) == N_total - N_long - N_missing # Looks good

##         n
## [1,] TRUE

2 Dimensionality assessment

I’m not going to bother with the correlation plot because I think it will be too difficult to visualize.

Complex_poly <- tetrachoric(Vocab_short)

## For i = 131 j = 58  A cell entry of 0 was replaced with correct =  0.5.  Check your data!

## For i = 160 j = 58  A cell entry of 0 was replaced with correct =  0.5.  Check your data!

## For i = 225 j = 58  A cell entry of 0 was replaced with correct =  0.5.  Check your data!

## For i = 387 j = 58  A cell entry of 0 was replaced with correct =  0.5.  Check your data!

## For i = 448 j = 445  A cell entry of 0 was replaced with correct =  0.5.  Check your data!

## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was done

rho <- Complex_poly$rho

These will not run.

#pc <- princals(rho)

#plot(pc)

fa.parallel(rho, fa="fa", fm="minres", cor="poly", n.obs = 4186)

## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined.
## Chi square is based upon observed residuals.

## The determinant of the smoothed correlation was zero.
## This means the objective function is not defined for the null model either.
## The Chi square is thus based upon observed correlations.

## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.

## Parallel analysis suggests that the number of factors =  22  and the number of components =  NA

3 One dimension

3.1 2PL Model

#m1 <- mirt(Vocab_short, 1, itemtype="2PL") 
#saveRDS(m1, "vocab_output/m1.rds")
m1 <-  readRDS("vocab_output/m1.rds")

Looking at item misfit statistics

#itf <- itemfit(m1)
#saveRDS(itf, "vocab_output/itf.rds")
itf <- readRDS("vocab_output/itf.rds")

misfit <- itf  %>% # Get labels of mis-fitting items. 
  filter(p.S_X2 <= .01) %>%
  dplyr::select(item) %>%
  as.vector()

items_good <- dplyr::select(Vocab_short, -all_of(misfit$item)) # Well fitting items
items_bad <- dplyr::select(Vocab_short, all_of(misfit$item)) # Poorly fitting items

mod_fit <- mirt(items_good, 1, "2PL", verbose=FALSE) # Calculate factor scores using only the well fitting items. 
Theta <- fscores(mod_fit)

plot(itemGAM(items_bad$dog, Theta)) %>% update(main = "dog")
plot(itemGAM(items_bad$donkey,Theta)) %>% update(main = "donkey")
plot(itemGAM(items_bad$teddybear,Theta)) %>% update(main = "teddybear")
plot(itemGAM(items_bad$block,Theta)) %>% update(main = "block")
plot(itemGAM(items_bad$doll,Theta)) %>% update(main = "doll")
plot(itemGAM(items_bad$`toy (object)`,Theta)) %>% update(main = "toy (object)")
plot(itemGAM(items_bad$beans,Theta)) %>% update(main = "beans") 
plot(itemGAM(items_bad$raisin,Theta)) %>% update(main = "raisin") 
plot(itemGAM(items_bad$underpants,Theta)) %>% update(main = "underpants") 
plot(itemGAM(items_bad$`penis*`,Theta)) %>% update(main = "penis") 
plot(itemGAM(items_bad$`vagina*`,Theta)) %>% update(main = "vagina")
plot(itemGAM(items_bad$clock,Theta)) %>% update(main = "clock") 
plot(itemGAM(items_bad$dish,Theta)) %>% update(main = "dish")
plot(itemGAM(items_bad$keys,Theta)) %>% update(main = "keys")
plot(itemGAM(items_bad$plate,Theta)) %>% update(main = "plate")
plot(itemGAM(items_bad$trash,Theta)) %>% update(main = "trash")
plot(itemGAM(items_bad$bathtub,Theta)) %>% update(main = "bathtub")
plot(itemGAM(items_bad$TV,Theta)) %>% update(main = "TV")

plot(itemGAM(items_bad$catch, Theta)) %>% update(main = "catch")
plot(itemGAM(items_bad$fit,Theta))  %>% update(main = "fit")
plot(itemGAM(items_bad$get,Theta)) %>% update(main = "get")
plot(itemGAM(items_bad$go,Theta)) %>% update(main = "go")
plot(itemGAM(items_bad$read,Theta)) %>% update(main = "read")

true_raw <- Vocab_short %>%
  mutate(
    Raw = rowSums(.[,1:478]), 
    Theta = fscores(m1)
  ) %>%
  ggplot(aes(x=Theta, y=Raw)) + geom_point() + stat_smooth(method="loess") + theme_minimal()

raw_score <- Vocab_short %>%
  mutate(
    Raw = rowSums(.[,1:478])
    ) %>% 
   ggplot(aes(x=Raw)) + geom_histogram() + theme_minimal()

true_score <- Vocab_short %>%
  mutate(
    Theta = fscores(m1)
    ) %>% 
   ggplot(aes(x=Theta)) + geom_histogram() + theme_minimal()

library(patchwork)

true_raw/(true_score + raw_score)

## `geom_smooth()` using formula 'y ~ x'

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

coefs_2pl <- coef(m1, as.data.frame = TRUE) %>% 
 t() %>%
  as_tibble() %>%
  dplyr::select(-c(1913:1914)) %>%
  pivot_longer(everything()) %>%
  tidyr::separate(, col=name, into=c("item", "parameter"), sep="([.])") %>%
  filter(parameter == "a1" | parameter == "d" ) %>%
  pivot_wider(id_cols=item, names_from=parameter, values_from=value)

## Warning: Expected 2 pieces. Additional pieces discarded in 180 rows [41, 42,
## 43, 44, 69, 70, 71, 72, 281, 282, 283, 284, 297, 298, 299, 300, 349, 350, 351,
## 352, ...].

ggplot(coefs_2pl,  
       aes(x = a1, y = -d)) + # Note in the book they use -d here, I think MIRT outputs a1 and an easiness rather than a difficulty. 
  geom_point(alpha = .3) + 
  ggrepel::geom_text_repel(data = coefs_2pl, 
                  aes(label = item), size = 3) + 
  xlab("Discrimination") + 
  ylab("Difficulty") + theme_minimal()

## Warning: ggrepel: 312 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps

#ggplot(coefs_2pl, aes(x=a1, fill=lexical_category)) + geom_histogram() + theme_minimal()
#ggplot(coefs_2pl, aes(x=d, fill=lexical_category)) + geom_histogram() + theme_minimal()

3.2 Try changing to a non-parametric link function

These discrimination parameters look good, but I’m not crazy about the item response functions, so I will try a spline model .

#m2 <- mirt(Vocab_short, 1, "spline", technical=list(NCYCLES = 1000)) # I can increase iterations, but it just jumps around the same few values. 
#saveRDS(m2, "vocab_output/m2.rds")
m2 <-  readRDS("vocab_output/m2.rds")

Plot latent variables of spline model against 2PL model.

Vocab_short %>%
  mutate(
    Raw = rowSums(.[,1:478]), 
    Theta_2pl = fscores(m1)[,1], 
    Theta_spline = fscores(m2)[,1]
  ) %>%
  dplyr::select("Raw", "Theta_2pl", "Theta_spline") %>%
  ggpairs()

3.3 Try other latent variable

#m3 <- mirt(Vocab_short, 1, dentype="EH",  technical=list(NCYCLES = 2000)) 
#saveRDS(m3, "vocab_output/m3.rds")
m3 <- readRDS("vocab_output/m3.rds")

Vocab_short %>%
  mutate(
    Raw = rowSums(.[,1:478]), 
    Theta_2pl = fscores(m1)[,1], 
    Theta_spline = fscores(m2)[,1], 
    Theta_EH =  fscores(m3)[,1]
  ) %>%
  dplyr::select("Raw", "Theta_2pl", "Theta_spline", "Theta_EH") %>%
  ggpairs()

Compare the shape of distribution of latent variables.

(dens_plot <- Vocab_short %>%
  mutate(
    Theta_logit = fscores(m1)[,1], # Used MAP here, but EAP gives same results. 
    Theta_spline = fscores(m2)[,1],
    Theta_EH = fscores(m3)[,1]
  ) %>%
  dplyr::select("Theta_logit", "Theta_spline", "Theta_EH") %>%
  pivot_longer(everything(), names_to="model", values_to="theta") %>%
  ggplot(aes(x=theta, fill=model)) + geom_density(alpha = .2) +
  ggtitle("Distribution of Theta"))

Theta <- matrix(seq(-4,4,.01))
m1_inf <- testinfo(m1, Theta)
#mspline_inf <- testinfo(m2, Theta)
mEH_inf <- testinfo(m3, Theta)


(info_plot <- tibble(Theta, m1_inf, mEH_inf) %>%
   pivot_longer(c("m1_inf", "mEH_inf"), names_to = "LV", values_to = "Info") %>%
  mutate(
    model = ifelse(LV == "m1_inf", yes="2PL", no ="EH")
  ) %>%
  ggplot(aes(x=Theta, y=Info, group=model, color=model)) + geom_line() +
  ggtitle("Test Information"))

coefs_2pl <- coef(m3, as.data.frame = TRUE) %>% 
 t() %>%
  as_tibble() %>%
  dplyr::select(-c(1913:1914)) %>%
  pivot_longer(everything()) %>%
  tidyr::separate(, col=name, into=c("item", "parameter"), sep="([.])") %>%
  filter(parameter == "a1" | parameter == "d" ) %>%
  pivot_wider(id_cols=item, names_from=parameter, values_from=value)

## Warning: Expected 2 pieces. Additional pieces discarded in 180 rows [41, 42,
## 43, 44, 69, 70, 71, 72, 281, 282, 283, 284, 297, 298, 299, 300, 349, 350, 351,
## 352, ...].

ggplot(coefs_2pl,  
       aes(x = a1, y = -d)) + # Note in the book they use -d here, I think MIRT outputs a1 and -d
  geom_point(alpha = .3) + 
  ggrepel::geom_text_repel(data = coefs_2pl, 
                  aes(label = item), size = 3) + 
  xlab("Discrimination") + 
  ylab("Difficulty") + theme_minimal()

## Warning: ggrepel: 306 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps

4 Add a dimension

Compare this to a model with 2 dimensions.

#m4<- mirt(Vocab_short, 2, itemtype="2PL", technical=list(NCYCLES = 4000)) 
#saveRDS(m4, "vocab_output/m4.rds")
m4 <-  readRDS("vocab_output/m4.rds")

summary(m4, "oblimin", suppress=.20)

## 
## Rotation:  oblimin 
## 
## Rotated factor loadings: 
## 
##                          F1     F2    h2
## alligator            -0.858     NA 0.784
## animal               -0.847     NA 0.737
## ant                  -0.787     NA 0.633
## bear                 -0.781 -0.213 0.666
## bee                  -0.754 -0.204 0.620
## bird                 -0.794     NA 0.676
## bug                  -0.806     NA 0.658
## bunny                -0.812     NA 0.692
## butterfly            -0.845     NA 0.764
## cat                  -0.748     NA 0.578
## chicken (animal)     -0.852     NA 0.757
## cow                  -0.810 -0.208 0.711
## deer                 -0.736 -0.236 0.608
## dog                  -0.710     NA 0.516
## donkey               -0.735 -0.261 0.621
## duck                 -0.770 -0.252 0.669
## elephant             -0.874     NA 0.813
## fish (animal)        -0.832     NA 0.727
## frog                 -0.858 -0.219 0.796
## giraffe              -0.807 -0.266 0.735
## goose                -0.752 -0.237 0.633
## hen                  -0.762 -0.212 0.636
## horse                -0.871     NA 0.792
## kitty                -0.709     NA 0.508
## lamb                 -0.810 -0.201 0.707
## lion                 -0.863 -0.216 0.803
## monkey               -0.865     NA 0.798
## moose                -0.718 -0.285 0.610
## mouse                -0.852     NA 0.770
## owl                  -0.733 -0.297 0.640
## penguin              -0.799 -0.206 0.690
## pig                  -0.868     NA 0.793
## pony                 -0.778     NA 0.637
## puppy                -0.757     NA 0.578
## rooster              -0.826 -0.232 0.749
## sheep                -0.811 -0.266 0.742
## squirrel             -0.808 -0.202 0.704
## teddybear            -0.801     NA 0.645
## tiger                -0.846     NA 0.760
## turkey               -0.807     NA 0.689
## turtle               -0.836 -0.231 0.765
## wolf                 -0.776 -0.212 0.657
## zebra                -0.829 -0.274 0.776
## airplane             -0.854     NA 0.761
## bicycle              -0.825     NA 0.704
## boat                 -0.810 -0.258 0.736
## bus                  -0.786     NA 0.666
## car                  -0.811     NA 0.700
## firetruck            -0.829     NA 0.710
## helicopter           -0.827     NA 0.724
## motorcycle           -0.827     NA 0.701
## sled                 -0.702     NA 0.530
## stroller             -0.785     NA 0.619
## tractor              -0.708 -0.240 0.570
## train                -0.862     NA 0.783
## tricycle             -0.781     NA 0.642
## truck                -0.807     NA 0.699
## ball                 -0.786 -0.304 0.725
## balloon              -0.821     NA 0.716
## bat                  -0.742     NA 0.566
## block                -0.800     NA 0.675
## book                 -0.825 -0.217 0.739
## bubbles              -0.794 -0.223 0.692
## chalk                -0.786     NA 0.641
## crayon               -0.877     NA 0.781
## doll                 -0.754     NA 0.568
## game                 -0.873     NA 0.766
## glue                 -0.835     NA 0.710
## pen                  -0.815     NA 0.666
## pencil               -0.864     NA 0.748
## play dough           -0.780     NA 0.624
## present              -0.908     NA 0.833
## puzzle               -0.879     NA 0.797
## story                -0.876     NA 0.774
## toy (object)         -0.869     NA 0.754
## apple                -0.851     NA 0.767
## applesauce           -0.820     NA 0.702
## banana               -0.758     NA 0.611
## beans                -0.790     NA 0.656
## bread                -0.879     NA 0.788
## butter               -0.853     NA 0.745
## cake                 -0.867     NA 0.761
## candy                -0.793     NA 0.631
## carrots              -0.902     NA 0.835
## cereal               -0.847     NA 0.720
## cheerios             -0.734     NA 0.563
## cheese               -0.821     NA 0.718
## chicken (food)       -0.877     NA 0.780
## chocolate            -0.850     NA 0.728
## coffee               -0.813     NA 0.678
## coke                 -0.625     NA 0.390
## cookie               -0.826     NA 0.691
## corn                 -0.878     NA 0.791
## cracker              -0.815     NA 0.699
## donut                -0.753     NA 0.568
## drink (beverage)     -0.813     NA 0.660
## egg                  -0.842     NA 0.731
## fish (food)          -0.757     NA 0.599
## food                 -0.828     NA 0.684
## french fries         -0.814     NA 0.661
## grapes               -0.860     NA 0.763
## green beans          -0.797     NA 0.664
## gum                  -0.702     NA 0.496
## hamburger            -0.862     NA 0.744
## ice                  -0.790     NA 0.632
## ice cream            -0.884     NA 0.787
## jello                -0.778     NA 0.609
## jelly                -0.867     NA 0.758
## juice                -0.772     NA 0.602
## lollipop             -0.715     NA 0.513
## meat                 -0.791     NA 0.633
## melon                -0.787     NA 0.646
## milk                 -0.796     NA 0.659
## muffin               -0.847     NA 0.749
## noodles              -0.833     NA 0.712
## nuts                 -0.843     NA 0.725
## orange (food)        -0.875     NA 0.783
## pancake              -0.850     NA 0.738
## peas                 -0.792     NA 0.666
## peanut butter        -0.843     NA 0.722
## pickle               -0.794     NA 0.636
## pizza                -0.862     NA 0.750
## popcorn              -0.795     NA 0.634
## popsicle             -0.773     NA 0.597
## potato chip          -0.813     NA 0.661
## potato               -0.837     NA 0.712
## pretzel              -0.778     NA 0.629
## pudding              -0.811     NA 0.665
## pumpkin              -0.839     NA 0.732
## raisin               -0.834     NA 0.719
## salt                 -0.843     NA 0.713
## sandwich             -0.917     NA 0.841
## sauce                -0.826     NA 0.694
## soda/pop             -0.629     NA 0.396
## soup                 -0.846     NA 0.723
## spaghetti            -0.868     NA 0.755
## strawberry           -0.853     NA 0.762
## toast                -0.813     NA 0.688
## tuna                 -0.772     NA 0.604
## vanilla              -0.864     NA 0.758
## vitamins             -0.745     NA 0.560
## water (beverage)     -0.827     NA 0.703
## yogurt               -0.771 -0.218 0.653
## beads                -0.719     NA 0.543
## belt                 -0.822     NA 0.680
## bib                  -0.761     NA 0.604
## boots                -0.784     NA 0.642
## button               -0.841     NA 0.732
## coat                 -0.812     NA 0.671
## diaper               -0.843     NA 0.716
## dress (object)       -0.852     NA 0.726
## gloves               -0.840     NA 0.717
## hat                  -0.849     NA 0.747
## jacket               -0.823     NA 0.683
## jeans                -0.834     NA 0.706
## mittens              -0.806     NA 0.684
## necklace             -0.853     NA 0.733
## pajamas              -0.897     NA 0.810
## pants                -0.903     NA 0.821
## scarf                -0.840     NA 0.730
## shirt                -0.901     NA 0.824
## shoe                 -0.852     NA 0.742
## shorts               -0.874     NA 0.770
## slipper              -0.808     NA 0.660
## sneaker              -0.754     NA 0.570
## snowsuit             -0.791     NA 0.631
## sock                 -0.704     NA 0.496
## sweater              -0.691     NA 0.516
## tights               -0.783     NA 0.618
## underpants           -0.819     NA 0.670
## zipper               -0.864     NA 0.766
## ankle                -0.832     NA 0.711
## arm                  -0.910     NA 0.830
## belly button         -0.801     NA 0.666
## buttocks/bottom*     -0.836     NA 0.701
## cheek                -0.844     NA 0.727
## chin                 -0.857     NA 0.746
## ear                  -0.844     NA 0.747
## eye                  -0.859     NA 0.744
## face                 -0.898     NA 0.806
## finger               -0.901     NA 0.821
## foot                 -0.904     NA 0.816
## hair                 -0.898     NA 0.814
## hand                 -0.916     NA 0.841
## head                 -0.907     NA 0.824
## knee                 -0.835     NA 0.723
## leg                  -0.935     NA 0.876
## lips                 -0.877     NA 0.769
## mouth                -0.873     NA 0.768
## nose                 -0.849     NA 0.749
## owie/boo boo         -0.673     NA 0.454
## penis*               -0.550     NA 0.317
## shoulder             -0.874     NA 0.776
## toe                  -0.825     NA 0.698
## tongue               -0.837     NA 0.712
## tooth                -0.843     NA 0.714
## tummy                -0.880     NA 0.774
## vagina*              -0.605     NA 0.366
## basket               -0.893     NA 0.804
## blanket              -0.869     NA 0.755
## bottle               -0.730     NA 0.532
## bowl                 -0.870     NA 0.764
## box                  -0.864     NA 0.757
## broom                -0.833     NA 0.694
## brush                -0.873     NA 0.765
## bucket               -0.880     NA 0.784
## camera               -0.906     NA 0.824
## can (object)         -0.858     NA 0.736
## clock                -0.795     NA 0.663
## comb                 -0.846     NA 0.718
## cup                  -0.868     NA 0.754
## dish                 -0.853     NA 0.729
## fork                 -0.905     NA 0.828
## garbage              -0.802     NA 0.644
## glass                -0.863     NA 0.745
## glasses              -0.864     NA 0.753
## hammer               -0.847     NA 0.733
## jar                  -0.615     NA 0.401
## keys                 -0.659     NA 0.436
## knife                -0.909     NA 0.831
## lamp                 -0.859     NA 0.745
## light                -0.849     NA 0.728
## medicine             -0.887     NA 0.787
## money                -0.841     NA 0.708
## mop                  -0.803     NA 0.644
## nail                 -0.865     NA 0.753
## napkin               -0.886     NA 0.785
## paper                -0.924     NA 0.854
## penny                -0.805     NA 0.647
## picture              -0.928     NA 0.860
## pillow               -0.918     NA 0.842
## plant                -0.879     NA 0.779
## plate                -0.906     NA 0.824
## purse                -0.821     NA 0.675
## radio                -0.836     NA 0.700
## scissors             -0.897     NA 0.805
## soap                 -0.899     NA 0.809
## spoon                -0.861     NA 0.759
## tape                 -0.893     NA 0.798
## telephone            -0.891     NA 0.795
## tissue/kleenex       -0.863     NA 0.743
## toothbrush           -0.889     NA 0.793
## towel                -0.911     NA 0.830
## trash                -0.723     NA 0.522
## tray                 -0.862     NA 0.746
## vacuum               -0.838     NA 0.706
## walker               -0.788     NA 0.620
## watch (object)       -0.843     NA 0.714
## basement             -0.674     NA 0.468
## bathroom             -0.927     NA 0.860
## bathtub              -0.847     NA 0.718
## bed                  -0.911     NA 0.829
## bedroom              -0.910     NA 0.828
## bench                -0.893     NA 0.805
## chair                -0.915     NA 0.839
## closet               -0.932     NA 0.869
## couch                -0.893     NA 0.797
## crib                 -0.856     NA 0.734
## door                 -0.880     NA 0.775
## drawer               -0.903     NA 0.814
## dryer                -0.910     NA 0.829
## garage               -0.875     NA 0.773
## high chair           -0.825     NA 0.682
## kitchen              -0.937     NA 0.877
## living room          -0.898     NA 0.805
## oven                 -0.898     NA 0.807
## play pen             -0.782     NA 0.610
## porch                -0.842     NA 0.708
## potty                -0.824     NA 0.680
## rocking chair        -0.861     NA 0.746
## refrigerator         -0.896     NA 0.802
## room                 -0.911     NA 0.830
## shower               -0.890     NA 0.794
## sink                 -0.919     NA 0.844
## sofa                 -0.757     NA 0.573
## stairs               -0.868     NA 0.753
## stove                -0.834     NA 0.700
## table                -0.937     NA 0.878
## TV                   -0.851     NA 0.723
## window               -0.880     NA 0.775
## washing machine      -0.848     NA 0.724
## backyard             -0.837     NA 0.700
## cloud                -0.856     NA 0.748
## flag                 -0.817     NA 0.687
## flower               -0.878     NA 0.788
## garden               -0.865     NA 0.752
## grass                -0.898     NA 0.807
## hose                 -0.852     NA 0.731
## ladder               -0.887     NA 0.804
## lawn mower           -0.784     NA 0.632
## moon                 -0.767 -0.208 0.641
## pool                 -0.779     NA 0.609
## rain                 -0.906     NA 0.825
## rock                 -0.852     NA 0.737
## roof                 -0.901     NA 0.815
## sandbox              -0.833     NA 0.702
## shovel               -0.869     NA 0.768
## sidewalk             -0.914     NA 0.836
## sky                  -0.826     NA 0.688
## slide (object)       -0.869     NA 0.762
## snow                 -0.758     NA 0.603
## snowman              -0.846     NA 0.735
## sprinkler            -0.859     NA 0.744
## star                 -0.809     NA 0.686
## stick                -0.869     NA 0.760
## stone                -0.795     NA 0.635
## street               -0.920     NA 0.846
## sun                  -0.884     NA 0.796
## swing (object)       -0.853     NA 0.737
## tree                 -0.849     NA 0.751
## water (not beverage) -0.860     NA 0.749
## wind                 -0.883     NA 0.787
## bite                 -0.831     NA 0.713
## blow                 -0.868     NA 0.760
## break                -0.902     NA 0.827
## bring                -0.889     NA 0.816
## build                -0.916     NA 0.842
## bump                 -0.826     NA 0.688
## buy                  -0.857     NA 0.752
## carry                -0.912     NA 0.844
## catch                -0.892     NA 0.813
## chase                -0.855     NA 0.739
## clap                 -0.863     NA 0.756
## clean (action)       -0.913     NA 0.844
## climb                -0.926     NA 0.863
## close                -0.878     NA 0.781
## cook                 -0.885     NA 0.786
## cover                -0.909     NA 0.849
## cry                  -0.909     NA 0.844
## cut                  -0.900     NA 0.818
## dance                -0.881     NA 0.783
## draw                 -0.873     NA 0.767
## drink (action)       -0.856     NA 0.747
## drive                -0.916     NA 0.846
## drop                 -0.922     NA 0.865
## dry (action)         -0.914     NA 0.840
## dump                 -0.828     NA 0.687
## eat                  -0.876     NA 0.790
## fall                 -0.919     NA 0.855
## feed                 -0.920     NA 0.857
## find                 -0.939     NA 0.898
## finish               -0.855     NA 0.750
## fit                  -0.910     NA 0.843
## fix                  -0.910     NA 0.834
## get                  -0.873     NA 0.787
## give                 -0.901  0.205 0.842
## go                   -0.755     NA 0.587
## hate                 -0.769  0.213 0.626
## have                 -0.924     NA 0.865
## hear                 -0.921     NA 0.859
## help                 -0.849     NA 0.728
## hide                 -0.897     NA 0.814
## hit                  -0.894     NA 0.824
## hold                 -0.915     NA 0.860
## hug                  -0.884     NA 0.796
## hurry                -0.877  0.210 0.801
## jump                 -0.905     NA 0.825
## kick                 -0.882     NA 0.794
## kiss                 -0.883     NA 0.806
## knock                -0.843     NA 0.718
## lick                 -0.911     NA 0.838
## like                 -0.924     NA 0.866
## listen               -0.893     NA 0.821
## look                 -0.855  0.227 0.770
## love                 -0.824     NA 0.696
## make                 -0.932     NA 0.883
## open                 -0.882     NA 0.790
## paint                -0.878     NA 0.771
## pick                 -0.914     NA 0.857
## play                 -0.911     NA 0.844
## pour                 -0.909     NA 0.834
## pretend              -0.876     NA 0.775
## pull                 -0.886     NA 0.799
## push                 -0.874     NA 0.775
## put                  -0.902     NA 0.838
## read                 -0.893     NA 0.798
## ride                 -0.917     NA 0.853
## rip                  -0.855     NA 0.742
## run                  -0.934     NA 0.878
## say                  -0.883  0.203 0.810
## see                  -0.825  0.208 0.713
## shake                -0.877     NA 0.776
## share                -0.902     NA 0.832
## show                 -0.927     NA 0.878
## sing                 -0.924     NA 0.865
## sit                  -0.847     NA 0.733
## skate                -0.853     NA 0.728
## sleep                -0.925     NA 0.869
## slide (action)       -0.883     NA 0.781
## smile                -0.891  0.204 0.823
## spill                -0.923     NA 0.866
## splash               -0.888     NA 0.793
## stand                -0.929     NA 0.885
## stay                 -0.880  0.208 0.806
## stop                 -0.837  0.215 0.735
## sweep                -0.885     NA 0.788
## swim                 -0.887     NA 0.786
## swing (action)       -0.873     NA 0.762
## take                 -0.918     NA 0.867
## talk                 -0.912  0.215 0.866
## taste                -0.897     NA 0.826
## tear                 -0.906     NA 0.843
## think                -0.891     NA 0.818
## throw                -0.925     NA 0.865
## tickle               -0.823     NA 0.686
## touch                -0.904     NA 0.835
## wait                 -0.849  0.227 0.759
## wake                 -0.907     NA 0.839
## walk                 -0.877     NA 0.774
## wash                 -0.912     NA 0.841
## watch (action)       -0.892     NA 0.812
## wipe                 -0.881     NA 0.789
## wish                 -0.869  0.227 0.795
## work (action)        -0.877     NA 0.772
## write                -0.861     NA 0.764
## all gone             -0.732     NA 0.536
## asleep               -0.864     NA 0.754
## awake                -0.896     NA 0.811
## bad                  -0.762  0.216 0.616
## better               -0.877     NA 0.776
## big                  -0.897     NA 0.803
## black                -0.838     NA 0.712
## blue                 -0.776     NA 0.632
## broken               -0.885     NA 0.787
## brown                -0.840     NA 0.722
## careful              -0.894     NA 0.801
## clean (description)  -0.919     NA 0.846
## cold                 -0.870     NA 0.757
## cute                 -0.796     NA 0.641
## dark                 -0.871     NA 0.759
## dirty                -0.889     NA 0.791
## dry (description)    -0.900     NA 0.810
## empty                -0.842     NA 0.709
## fast                 -0.907     NA 0.823
## fine                 -0.850     NA 0.731
## first                -0.892     NA 0.813
## full                 -0.896     NA 0.810
## gentle               -0.781     NA 0.610
## good                 -0.828     NA 0.706
## green                -0.819     NA 0.701
## happy                -0.838     NA 0.702
## hard                 -0.919     NA 0.849
## heavy                -0.914     NA 0.837
## high                 -0.890     NA 0.792
## hot                  -0.759     NA 0.576
## hungry               -0.879     NA 0.784
## hurt                 -0.878     NA 0.783
## last                 -0.898     NA 0.827
## little (description) -0.923     NA 0.853
## long                 -0.920     NA 0.856
## loud                 -0.900     NA 0.812
## mad                  -0.854     NA 0.750
## naughty              -0.689     NA 0.479
## new                  -0.898     NA 0.810
## nice                 -0.795     NA 0.640
## noisy                -0.858     NA 0.738
## old                  -0.873     NA 0.766
## orange (description) -0.816     NA 0.679
## poor                 -0.812     NA 0.675
## pretty               -0.799     NA 0.642
## quiet                -0.901     NA 0.820
## red                  -0.822     NA 0.703
## sad                  -0.890     NA 0.792
## scared               -0.890     NA 0.798
## sick                 -0.898     NA 0.815
## sleepy               -0.844     NA 0.716
## slow                 -0.895     NA 0.811
## soft                 -0.872     NA 0.761
## sticky               -0.860     NA 0.740
## stuck                -0.797     NA 0.634
## thirsty              -0.874     NA 0.771
## tiny                 -0.860     NA 0.741
## tired                -0.914     NA 0.848
## wet                  -0.884     NA 0.783
## white                -0.842     NA 0.715
## windy                -0.875     NA 0.766
## yellow               -0.776     NA 0.635
## yucky                -0.582 -0.208 0.389
## 
## Rotated SS loadings:  343.784 7.129 
## 
## Factor correlations: 
## 
##       F1    F2
## F1 1.000 0.032
## F2 0.032 1.000

anova(m4, m1)

## 
## Model 1: mirt(data = Vocab_short, model = 1, itemtype = "2PL")
## Model 2: mirt(data = Vocab_short, model = 2, itemtype = "2PL", technical = list(NCYCLES = 4000))

Vocab_short %>%
  mutate(
    Raw = rowSums(.[,1:478]), 
    Theta1 = fscores(m4)[,1], 
    Theta2 = fscores(m4)[,2]
  ) %>%
  dplyr::select(Raw, Theta1, Theta2) %>%
  ggpairs()

Second factor doesn’t look like it’s doing much work.

model.1 <- mirt.model('
                      F1 = 1 - 312
                      F2 = 313 - 478
                      COV=F1*F2')

#m5 <- mirt(Vocab_short, model.1, "2PL")


#summary(m5)

#saveRDS(m5, "vocab_output/m5.rds")
m5 <-  readRDS("vocab_output/m5.rds")

anova(m5, m1)

## 
## Model 1: mirt(data = Vocab_short, model = 1, itemtype = "2PL")
## Model 2: mirt(data = Vocab_short, model = model.1, itemtype = "2PL")

Vocab_short %>%
  mutate(
    Raw = rowSums(.[,1:478]), 
    Theta1 = fscores(m5)[,1], 
    Theta2 = fscores(m5)[,2]
  ) %>%
  dplyr::select(Raw, Theta1, Theta2) %>%
  ggpairs()

Vocab_with_predictors <- Admin %>%
  dplyr::select(data_id, age, ethnicity, sex, mom_ed) %>%
  mutate(
    female = ifelse(sex=="Female", yes=1, no=0),
   age_y = ifelse(age < 25, yes=1, no=0),
   college_grad = ifelse(mom_ed %in% c("College", "Some Graduate",  "Some Graduate"), yes=1, no=0)
   ) %>%
  right_join(., Vocab_short_with_ids, by="data_id")

Vocab_with_predictors %>%
  summarise(
    age_missing = sum(is.na(age)), 
    ethnicity_missing = sum(is.na(ethnicity)), # Some ethnicity variables missing. 
    sex_missing = sum(is.na(sex)), 
    college_grad = sum(is.na(college_grad))
  )

table(Vocab_with_predictors$age)

## 
##  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30 
## 305 271 442 327 273 203 200 261 569 324 180 194 145 197 295

table(Vocab_with_predictors$ethnicity)

## 
##    Asian    Black    Other    White Hispanic 
##       67      222       93     2202      131

table(Vocab_with_predictors$sex)

## 
## Female   Male  Other 
##   1374   1413      0

table(Vocab_with_predictors$college_grad)

## 
##    0    1 
## 3154 1032

#Vocab_short2 <- data.frame(Vocab_short) 

#dif <- lordif(Vocab_short2, 
#              Vocab_with_predictors$female,
#              criterion="Chisqr", 
#              alpha = .01)

#saveRDS(dif, "vocab_output/dif.rds")
dif  <- readRDS("vocab_output/dif.rds")

dif

## Call:
## lordif(resp.data = Vocab_short2, group = Vocab_with_predictors$female, 
##     criterion = "Chisqr", alpha = 0.01)
## 
##   Number of DIF groups: 2 
## 
##   Number of items flagged for DIF: 111 of 478 
## 
##   Items flagged: 8, 24, 25, 26, 28, 33, 34, 38, 39, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 60, 65, 66, 72, 125, 135, 144, 146, 148, 151, 155, 157, 163, 164, 168, 169, 170, 174, 175, 176, 183, 186, 192, 194, 195, 198, 200, 201, 204, 205, 210, 212, 214, 216, 217, 222, 225, 226, 230, 234, 241, 246, 250, 259, 262, 263, 269, 270, 282, 284, 285, 288, 289, 290, 295, 296, 297, 303, 305, 309, 317, 321, 324, 329, 331, 334, 337, 344, 353, 358, 360, 362, 368, 385, 387, 404, 409, 415, 418, 421, 423, 424, 429, 432, 434, 440, 441, 442, 460 
## 
##   Number of iterations for purification: 3 of 10 
## 
##   Detection criterion: Chisqr 
## 
##   Threshold: alpha = 0.01 
## 
##     item ncat  chi12  chi13  chi23
## 1      1    2 0.0266 0.0673 0.4878
## 2      2    2 0.1171 0.1625 0.2776
## 3      3    2 0.7516 0.8709 0.6747
## 4      4    2 0.8788 0.2822 0.1133
## 5      5    2 0.5130 0.1179 0.0498
## 6      6    2 0.6330 0.5192 0.2980
## 7      7    2 0.4475 0.7000 0.7118
## 8      8    2 0.0000 0.0002 0.7343
## 9      9    2 0.3965 0.5430 0.4785
## 10    10    2 0.1645 0.1413 0.1592
## 11    11    2 0.0550 0.1040 0.3578
## 12    12    2 0.5432 0.7461 0.6420
## 13    13    2 0.0964 0.2507 0.9663
## 14    14    2 0.1302 0.2948 0.6961
## 15    15    2 0.0525 0.1448 0.7442
## 16    16    2 0.4042 0.5678 0.5090
## 17    17    2 0.3617 0.3204 0.2294
## 18    18    2 0.6109 0.7630 0.5953
## 19    19    2 0.0190 0.0634 0.8920
## 20    20    2 0.0178 0.0367 0.3190
## 21    21    2 0.4410 0.7275 0.8367
## 22    22    2 0.2214 0.3948 0.5464
## 23    23    2 0.7781 0.8890 0.6929
## 24    24    2 0.0001 0.0003 0.2604
## 25    25    2 0.0000 0.0001 0.5059
## 26    26    2 0.0066 0.0144 0.2949
## 27    27    2 0.0705 0.1486 0.4619
## 28    28    2 0.0001 0.0006 0.5662
## 29    29    2 0.3039 0.5675 0.7827
## 30    30    2 0.5847 0.1767 0.0751
## 31    31    2 0.6821 0.3770 0.1818
## 32    32    2 0.0252 0.0614 0.4494
## 33    33    2 0.0025 0.0100 0.7622
## 34    34    2 0.0053 0.0199 0.7995
## 35    35    2 0.1252 0.3084 0.9674
## 36    36    2 0.5152 0.7326 0.6557
## 37    37    2 0.7115 0.0750 0.0247
## 38    38    2 0.0005 0.0023 0.8544
## 39    39    2 0.0088 0.0313 0.7903
## 40    40    2 0.1459 0.3305 0.7525
## 41    41    2 0.3774 0.6350 0.7195
## 42    42    2 0.0124 0.0200 0.2117
## 43    43    2 0.2964 0.5679 0.8392
## 44    44    2 0.0023 0.0082 0.6064
## 45    45    2 0.0007 0.0029 0.6916
## 46    46    2 0.0000 0.0000 0.2070
## 47    47    2 0.0000 0.0000 0.2261
## 48    48    2 0.0003 0.0009 0.3419
## 49    49    2 0.0000 0.0000 0.3984
## 50    50    2 0.0000 0.0000 0.1480
## 51    51    2 0.0000 0.0000 0.2213
## 52    52    2 0.7488 0.8881 0.7136
## 53    53    2 0.0000 0.0000 0.1354
## 54    54    2 0.0000 0.0000 0.0705
## 55    55    2 0.0000 0.0000 0.0869
## 56    56    2 0.0002 0.0005 0.2666
## 57    57    2 0.0000 0.0000 0.6035
## 58    58    2 0.6402 0.7805 0.5986
## 59    59    2 0.4557 0.0392 0.0149
## 60    60    2 0.0000 0.0000 0.4693
## 61    61    2 0.3072 0.5920 0.9398
## 62    62    2 0.2248 0.2228 0.2162
## 63    63    2 0.2580 0.2861 0.2687
## 64    64    2 0.8294 0.8824 0.6517
## 65    65    2 0.0005 0.0005 0.0873
## 66    66    2 0.0000 0.0000 0.0649
## 67    67    2 0.1777 0.0949 0.0889
## 68    68    2 0.4196 0.5973 0.5380
## 69    69    2 0.7198 0.9373 0.9765
## 70    70    2 0.1695 0.3889 0.9675
## 71    71    2 0.8038 0.8027 0.5388
## 72    72    2 0.0015 0.0042 0.3612
## 73    73    2 0.5787 0.8435 0.8578
## 74    74    2 0.7142 0.7153 0.4641
## 75    75    2 0.1701 0.3868 0.8952
## 76    76    2 0.5404 0.7423 0.6381
## 77    77    2 0.8005 0.4493 0.2152
## 78    78    2 0.1159 0.2717 0.7131
## 79    79    2 0.3021 0.5809 0.8840
## 80    80    2 0.1755 0.1830 0.2115
## 81    81    2 0.3079 0.0445 0.0228
## 82    82    2 0.8004 0.3604 0.1597
## 83    83    2 0.4070 0.0530 0.0227
## 84    84    2 0.9430 0.8513 0.5735
## 85    85    2 0.6526 0.5937 0.3593
## 86    86    2 0.4105 0.0700 0.0312
## 87    87    2 0.0474 0.0201 0.0488
## 88    88    2 0.0922 0.2418 0.9512
## 89    89    2 0.1912 0.3387 0.4992
## 90    90    2 0.4486 0.5036 0.3718
## 91    91    2 0.0801 0.1548 0.4135
## 92    92    2 0.7874 0.2961 0.1244
## 93    93    2 0.6095 0.5136 0.3005
## 94    94    2 0.0622 0.1579 0.6442
## 95    95    2 0.0739 0.1126 0.2786
## 96    96    2 0.3679 0.2381 0.1513
## 97    97    2 0.0430 0.1188 0.6837
## 98    98    2 0.4933 0.7284 0.6852
## 99    99    2 0.1391 0.1002 0.1202
## 100  100    2 0.7857 0.9031 0.7186
## 101  101    2 0.1369 0.3249 0.8489
## 102  102    2 0.3342 0.6271 0.9823
## 103  103    2 0.1543 0.2616 0.4191
## 104  104    2 0.3485 0.6429 0.9449
## 105  105    2 0.4592 0.3271 0.1940
## 106  106    2 0.5400 0.3838 0.2147
## 107  107    2 0.3592 0.6146 0.7154
## 108  108    2 0.7845 0.8099 0.5559
## 109  109    2 0.8039 0.1311 0.0454
## 110  110    2 0.5984 0.8074 0.6980
## 111  111    2 0.9152 0.4213 0.1900
## 112  112    2 0.3711 0.6602 0.8619
## 113  113    2 0.7638 0.8752 0.6746
## 114  114    2 0.3199 0.5853 0.7750
## 115  115    2 0.4108 0.6925 0.8090
## 116  116    2 0.2022 0.4222 0.7540
## 117  117    2 0.2383 0.3984 0.5024
## 118  118    2 0.4433 0.6456 0.5918
## 119  119    2 0.9989 0.2738 0.1075
## 120  120    2 0.7058 0.3492 0.1613
## 121  121    2 0.0629 0.1766 0.9271
## 122  122    2 0.4238 0.6291 0.5921
## 123  123    2 0.3954 0.0943 0.0455
## 124  124    2 0.0618 0.1269 0.4237
## 125  125    2 0.0012 0.0042 0.4759
## 126  126    2 0.0647 0.1747 0.7827
## 127  127    2 0.1378 0.2740 0.5340
## 128  128    2 0.8804 0.7553 0.4630
## 129  129    2 0.5702 0.3737 0.1995
## 130  130    2 0.0854 0.2111 0.6963
## 131  131    2 0.0914 0.0410 0.0599
## 132  132    2 0.3352 0.5716 0.6631
## 133  133    2 0.1768 0.3334 0.5417
## 134  134    2 0.1205 0.2946 0.8549
## 135  135    2 0.0068 0.0257 0.9455
## 136  136    2 0.7898 0.4479 0.2153
## 137  137    2 0.1673 0.2007 0.2533
## 138  138    2 0.1894 0.3976 0.7264
## 139  139    2 0.7862 0.9573 0.9069
## 140  140    2 0.3328 0.1147 0.0655
## 141  141    2 0.2959 0.4794 0.5388
## 142  142    2 0.2528 0.4631 0.6304
## 143  143    2 0.7010 0.6893 0.4398
## 144  144    2 0.0000 0.0000 0.2465
## 145  145    2 0.6366 0.8407 0.7250
## 146  146    2 0.0000 0.0000 0.8395
## 147  147    2 0.2825 0.2892 0.2495
## 148  148    2 0.0003 0.0014 0.8901
## 149  149    2 0.1493 0.0647 0.0653
## 150  150    2 0.0376 0.1076 0.7098
## 151  151    2 0.0000 0.0000 0.0057
## 152  152    2 0.2857 0.2120 0.1613
## 153  153    2 0.7495 0.5190 0.2714
## 154  154    2 0.4199 0.1515 0.0772
## 155  155    2 0.0000 0.0001 0.5549
## 156  156    2 0.6282 0.8876 0.9500
## 157  157    2 0.0000 0.0000 0.2909
## 158  158    2 0.1518 0.3258 0.6637
## 159  159    2 0.8050 0.8600 0.6237
## 160  160    2 0.0568 0.0993 0.3198
## 161  161    2 0.0798 0.1137 0.2583
## 162  162    2 0.0671 0.1861 0.9226
## 163  163    2 0.0000 0.0000 0.2339
## 164  164    2 0.0001 0.0002 0.3577
## 165  165    2 0.2794 0.5288 0.7471
## 166  166    2 0.1742 0.3970 0.9758
## 167  167    2 0.0213 0.0234 0.1374
## 168  168    2 0.0000 0.0000 0.1126
## 169  169    2 0.0000 0.0000 0.6868
## 170  170    2 0.0000 0.0000 0.2321
## 171  171    2 0.2186 0.0192 0.0114
## 172  172    2 0.1721 0.3726 0.7406
## 173  173    2 0.4417 0.7374 0.8947
## 174  174    2 0.0000 0.0000 0.2456
## 175  175    2 0.0000 0.0000 0.2660
## 176  176    2 0.0006 0.0008 0.1229
## 177  177    2 0.0165 0.0159 0.1115
## 178  178    2 0.0592 0.0126 0.0228
## 179  179    2 0.1187 0.2765 0.7124
## 180  180    2 0.1554 0.1233 0.1410
## 181  181    2 0.0187 0.0469 0.4410
## 182  182    2 0.0741 0.2024 0.9433
## 183  183    2 0.0000 0.0000 0.1613
## 184  184    2 0.2201 0.3562 0.4538
## 185  185    2 0.7847 0.6828 0.4067
## 186  186    2 0.0004 0.0020 0.8502
## 187  187    2 0.0634 0.1003 0.2827
## 188  188    2 0.0156 0.0439 0.5231
## 189  189    2 0.0181 0.0612 0.9684
## 190  190    2 0.8511 0.8384 0.5733
## 191  191    2 0.0156 0.0473 0.6166
## 192  192    2 0.0000 0.0000 0.0445
## 193  193    2 0.0130 0.0456 0.9859
## 194  194    2 0.0040 0.0109 0.3846
## 195  195    2 0.0004 0.0015 0.4653
## 196  196    2 0.0498 0.1459 0.9922
## 197  197    2 0.0129 0.0451 0.8919
## 198  198    2 0.0000 0.0000 0.0429
## 199  199    2 0.0354 0.0279 0.0983
## 200  200    2 0.0026 0.0098 0.6454
## 201  201    2 0.0304 0.0031 0.0087
## 202  202    2 0.9316 0.9624 0.7925
## 203  203    2 0.0381 0.0962 0.5362
## 204  204    2 0.0000 0.0000 0.0472
## 205  205    2 0.3348 0.0138 0.0057
## 206  206    2 0.0160 0.0280 0.2446
## 207  207    2 0.0397 0.1203 0.9616
## 208  208    2 0.0134 0.0279 0.3065
## 209  209    2 0.0423 0.1123 0.6181
## 210  210    2 0.0009 0.0036 0.7090
## 211  211    2 0.8193 0.5863 0.3135
## 212  212    2 0.0013 0.0031 0.2749
## 213  213    2 0.5733 0.8039 0.7296
## 214  214    2 0.0134 0.0014 0.0082
## 215  215    2 0.7811 0.9559 0.9093
## 216  216    2 0.0016 0.0057 0.5180
## 217  217    2 0.0000 0.0000 0.1154
## 218  218    2 0.1357 0.1263 0.1668
## 219  219    2 0.6807 0.9094 0.8858
## 220  220    2 0.0441 0.1111 0.5583
## 221  221    2 0.7777 0.8553 0.6293
## 222  222    2 0.0004 0.0001 0.0081
## 223  223    2 0.6191 0.8643 0.8330
## 224  224    2 0.4885 0.7280 0.6937
## 225  225    2 0.0000 0.0000 0.4532
## 226  226    2 0.0000 0.0000 0.5346
## 227  227    2 0.3403 0.6183 0.8194
## 228  228    2 0.2969 0.4700 0.5160
## 229  229    2 0.3603 0.6578 0.9761
## 230  230    2 0.0056 0.0215 0.9153
## 231  231    2 0.7601 0.9215 0.7910
## 232  232    2 0.7053 0.1869 0.0731
## 233  233    2 0.4324 0.6624 0.6489
## 234  234    2 0.0000 0.0000 0.3371
## 235  235    2 0.0171 0.0357 0.3229
## 236  236    2 0.2871 0.4164 0.4314
## 237  237    2 0.0443 0.1317 0.9221
## 238  238    2 0.6077 0.8387 0.7663
## 239  239    2 0.6842 0.4082 0.2022
## 240  240    2 0.0788 0.2122 0.9142
## 241  241    2 0.0001 0.0004 0.8649
## 242  242    2 0.5664 0.6408 0.4538
## 243  243    2 0.0470 0.0998 0.4151
## 244  244    2 0.3247 0.5930 0.7838
## 245  245    2 0.3494 0.6454 0.9951
## 246  246    2 0.0000 0.0000 0.6509
## 247  247    2 0.9307 0.9436 0.7418
## 248  248    2 0.0418 0.1023 0.5189
## 249  249    2 0.0907 0.2282 0.7607
## 250  250    2 0.1836 0.0128 0.0084
## 251  251    2 0.2985 0.3166 0.2695
## 252  252    2 0.4481 0.4534 0.3157
## 253  253    2 0.2749 0.5501 0.9554
## 254  254    2 0.4554 0.5218 0.3884
## 255  255    2 0.9812 0.7075 0.4056
## 256  256    2 0.5209 0.4820 0.3061
## 257  257    2 0.7480 0.2012 0.0781
## 258  258    2 0.0984 0.0811 0.1300
## 259  259    2 0.0015 0.0039 0.3013
## 260  260    2 0.2585 0.3156 0.3101
## 261  261    2 0.0340 0.0861 0.5221
## 262  262    2 0.0000 0.0000 0.2421
## 263  263    2 0.0001 0.0005 0.6299
## 264  264    2 0.3344 0.3154 0.2408
## 265  265    2 0.4366 0.6972 0.7334
## 266  266    2 0.0449 0.1000 0.4451
## 267  267    2 0.6849 0.1839 0.0726
## 268  268    2 0.6215 0.6153 0.3937
## 269  269    2 0.0000 0.0000 0.6001
## 270  270    2 0.0028 0.0090 0.4962
## 271  271    2 0.0659 0.0754 0.1811
## 272  272    2 0.3203 0.4273 0.3985
## 273  273    2 0.3278 0.5699 0.6830
## 274  274    2 0.0415 0.1248 0.9328
## 275  275    2 0.0142 0.0306 0.3251
## 276  276    2 0.9249 0.9924 0.9363
## 277  277    2 0.8070 0.8497 0.6059
## 278  278    2 0.8227 0.9254 0.7461
## 279  279    2 0.1739 0.2112 0.2615
## 280  280    2 0.2475 0.5030 0.8474
## 281  281    2 0.0768 0.2051 0.8480
## 282  282    2 0.0008 0.0011 0.1349
## 283  283    2 0.2858 0.3654 0.3498
## 284  284    2 0.0027 0.0099 0.6256
## 285  285    2 0.0002 0.0008 0.8235
## 286  286    2 0.3892 0.6631 0.7771
## 287  287    2 0.7100 0.7836 0.5545
## 288  288    2 0.0000 0.0000 0.2633
## 289  289    2 0.0000 0.0000 0.7190
## 290  290    2 0.0000 0.0000 0.7221
## 291  291    2 0.0457 0.1207 0.6258
## 292  292    2 0.7380 0.8708 0.6847
## 293  293    2 0.8223 0.6474 0.3654
## 294  294    2 0.3296 0.6100 0.8451
## 295  295    2 0.0000 0.0000 0.4965
## 296  296    2 0.0054 0.0022 0.0349
## 297  297    2 0.0000 0.0000 0.7308
## 298  298    2 0.7214 0.0345 0.0102
## 299  299    2 0.0687 0.1763 0.6915
## 300  300    2 0.2689 0.4653 0.5788
## 301  301    2 0.0432 0.0880 0.3789
## 302  302    2 0.0222 0.0659 0.6474
## 303  303    2 0.0000 0.0000 0.2905
## 304  304    2 0.9967 0.4211 0.1884
## 305  305    2 0.0000 0.0000 0.2777
## 306  306    2 0.0903 0.2025 0.5685
## 307  307    2 0.0730 0.0339 0.0594
## 308  308    2 0.9839 0.7072 0.4053
## 309  309    2 0.0017 0.0063 0.5848
## 310  310    2 0.1816 0.2489 0.3181
## 311  311    2 0.6609 0.8180 0.6473
## 312  312    2 0.1195 0.2444 0.5304
## 313  313    2 0.2444 0.4203 0.5382
## 314  314    2 0.8237 0.9676 0.8988
## 315  315    2 0.0281 0.0756 0.5577
## 316  316    2 0.7130 0.9280 0.9052
## 317  317    2 0.0000 0.0000 0.3851
## 318  318    2 0.8766 0.7978 0.5132
## 319  319    2 0.6395 0.0812 0.0284
## 320  320    2 0.1090 0.0830 0.1206
## 321  321    2 0.0001 0.0001 0.0452
## 322  322    2 0.0600 0.1421 0.5447
## 323  323    2 0.0355 0.0730 0.3668
## 324  324    2 0.0010 0.0020 0.2037
## 325  325    2 0.1296 0.2216 0.3973
## 326  326    2 0.3085 0.1477 0.0949
## 327  327    2 0.6275 0.3266 0.1570
## 328  328    2 0.4085 0.5311 0.4453
## 329  329    2 0.0025 0.0095 0.7003
## 330  330    2 0.3655 0.6533 0.8569
## 331  331    2 0.0034 0.0119 0.6128
## 332  332    2 0.0459 0.0341 0.0960
## 333  333    2 0.3809 0.1567 0.0865
## 334  334    2 0.0000 0.0000 0.2349
## 335  335    2 0.6037 0.5307 0.3179
## 336  336    2 0.0147 0.0479 0.7307
## 337  337    2 0.0000 0.0000 0.2206
## 338  338    2 0.4424 0.5647 0.4572
## 339  339    2 0.1203 0.0694 0.0874
## 340  340    2 0.0420 0.1251 0.8771
## 341  341    2 0.1285 0.2950 0.7166
## 342  342    2 0.5346 0.5154 0.3323
## 343  343    2 0.1454 0.3210 0.6960
## 344  344    2 0.0000 0.0000 0.0325
## 345  345    2 0.2251 0.4505 0.7252
## 346  346    2 0.8677 0.7598 0.4701
## 347  347    2 0.8733 0.6829 0.3905
## 348  348    2 0.0462 0.0515 0.1619
## 349  349    2 0.2156 0.3572 0.4685
## 350  350    2 0.2339 0.0924 0.0674
## 351  351    2 0.7691 0.1210 0.0419
## 352  352    2 0.0294 0.0880 0.7332
## 353  353    2 0.0000 0.0000 0.1584
## 354  354    2 0.3548 0.1446 0.0827
## 355  355    2 0.6172 0.2579 0.1167
## 356  356    2 0.2951 0.2988 0.2507
## 357  357    2 0.8159 0.8779 0.6497
## 358  358    2 0.0029 0.0119 0.8985
## 359  359    2 0.6260 0.7082 0.5012
## 360  360    2 0.0007 0.0032 0.7519
## 361  361    2 0.9845 0.9411 0.7280
## 362  362    2 0.0023 0.0079 0.5451
## 363  363    2 0.8298 0.6846 0.3989
## 364  364    2 0.8945 0.8055 0.5194
## 365  365    2 0.2580 0.1502 0.1130
## 366  366    2 0.8960 0.9061 0.6712
## 367  367    2 0.6710 0.5080 0.2786
## 368  368    2 0.0037 0.0131 0.6240
## 369  369    2 0.5703 0.2811 0.1366
## 370  370    2 0.8847 0.3299 0.1383
## 371  371    2 0.2191 0.0462 0.0312
## 372  372    2 0.9515 0.6109 0.3217
## 373  373    2 0.0478 0.0823 0.2994
## 374  374    2 0.1485 0.2528 0.4155
## 375  375    2 0.0857 0.2284 0.9823
## 376  376    2 0.1042 0.2666 0.9516
## 377  377    2 0.0923 0.1731 0.4120
## 378  378    2 0.0851 0.1406 0.3276
## 379  379    2 0.4679 0.4877 0.3404
## 380  380    2 0.9600 0.9939 0.9216
## 381  381    2 0.3335 0.2766 0.2009
## 382  382    2 0.9565 0.9222 0.6901
## 383  383    2 0.5965 0.8641 0.9132
## 384  384    2 0.6203 0.1137 0.0428
## 385  385    2 0.0004 0.0021 0.9885
## 386  386    2 0.1962 0.4254 0.8432
## 387  387    2 0.0051 0.0176 0.6253
## 388  388    2 0.5390 0.6034 0.4263
## 389  389    2 0.8955 0.4012 0.1786
## 390  390    2 0.0509 0.0147 0.0313
## 391  391    2 0.3744 0.4332 0.3471
## 392  392    2 0.1750 0.3661 0.6797
## 393  393    2 0.0318 0.0921 0.6897
## 394  394    2 0.2238 0.4675 0.8405
## 395  395    2 0.5672 0.5034 0.3065
## 396  396    2 0.0921 0.1011 0.1863
## 397  397    2 0.8707 0.6509 0.3616
## 398  398    2 0.0291 0.0920 0.9202
## 399  399    2 0.5372 0.3644 0.2006
## 400  400    2 0.4096 0.0953 0.0449
## 401  401    2 0.8364 0.6353 0.3525
## 402  402    2 0.2206 0.1261 0.1041
## 403  403    2 0.8174 0.6114 0.3347
## 404  404    2 0.0000 0.0000 0.0435
## 405  405    2 0.1942 0.3795 0.6153
## 406  406    2 0.8774 0.9874 0.9686
## 407  407    2 0.8814 0.9430 0.7577
## 408  408    2 0.7405 0.6891 0.4255
## 409  409    2 0.0097 0.0091 0.0991
## 410  410    2 0.1736 0.3435 0.5927
## 411  411    2 0.6732 0.7008 0.4653
## 412  412    2 0.3861 0.6708 0.8278
## 413  413    2 0.1281 0.1790 0.2888
## 414  414    2 0.5513 0.1420 0.0596
## 415  415    2 0.0014 0.0036 0.3065
## 416  416    2 0.4418 0.7393 0.9104
## 417  417    2 0.8449 0.6712 0.3836
## 418  418    2 0.0024 0.0065 0.3620
## 419  419    2 0.1674 0.1874 0.2297
## 420  420    2 0.5368 0.8252 0.9568
## 421  421    2 0.0041 0.0096 0.3045
## 422  422    2 0.0464 0.0723 0.2568
## 423  423    2 0.0009 0.0012 0.1275
## 424  424    2 0.0034 0.0095 0.3953
## 425  425    2 0.1539 0.3418 0.7351
## 426  426    2 0.0635 0.0739 0.1836
## 427  427    2 0.1225 0.1802 0.3073
## 428  428    2 0.5161 0.7914 0.8299
## 429  429    2 0.0030 0.0082 0.3776
## 430  430    2 0.0914 0.1897 0.4905
## 431  431    2 0.4310 0.7324 0.9584
## 432  432    2 0.0001 0.0002 0.1516
## 433  433    2 0.3358 0.1626 0.0999
## 434  434    2 0.0000 0.0002 0.7290
## 435  435    2 0.9966 0.2417 0.0919
## 436  436    2 0.0187 0.0307 0.2299
## 437  437    2 0.5523 0.5222 0.3307
## 438  438    2 0.5612 0.7273 0.5843
## 439  439    2 0.0739 0.1493 0.4352
## 440  440    2 0.0005 0.0021 0.6279
## 441  441    2 0.0004 0.0006 0.1498
## 442  442    2 0.0013 0.0028 0.2264
## 443  443    2 0.0528 0.0347 0.0848
## 444  444    2 0.9557 0.3457 0.1453
## 445  445    2 0.4518 0.1748 0.0874
## 446  446    2 0.1811 0.1593 0.1697
## 447  447    2 0.0591 0.1556 0.6910
## 448  448    2 0.8871 0.9691 0.8363
## 449  449    2 0.7455 0.8322 0.6088
## 450  450    2 0.3165 0.5978 0.8734
## 451  451    2 0.0123 0.0183 0.1875
## 452  452    2 0.9642 0.9433 0.7348
## 453  453    2 0.4879 0.6769 0.5843
## 454  454    2 0.5848 0.1398 0.0565
## 455  455    2 0.2701 0.4563 0.5526
## 456  456    2 0.0952 0.2457 0.8789
## 457  457    2 0.9442 0.0574 0.0169
## 458  458    2 0.7454 0.5484 0.2951
## 459  459    2 0.4778 0.6696 0.5849
## 460  460    2 0.0000 0.0000 0.0341
## 461  461    2 0.0608 0.0407 0.0893
## 462  462    2 0.1022 0.2031 0.4721
## 463  463    2 0.4678 0.7394 0.7818
## 464  464    2 0.8959 0.5430 0.2725
## 465  465    2 0.2782 0.3377 0.3184
## 466  466    2 0.0151 0.0428 0.5271
## 467  467    2 0.2540 0.4811 0.6867
## 468  468    2 0.2151 0.0244 0.0152
## 469  469    2 0.8160 0.6523 0.3710
## 470  470    2 0.1365 0.3097 0.7210
## 471  471    2 0.9864 0.1457 0.0497
## 472  472    2 0.4063 0.0280 0.0110
## 473  473    2 0.0681 0.0625 0.1364
## 474  474    2 0.0397 0.0298 0.0946
## 475  475    2 0.9568 0.9799 0.8462
## 476  476    2 0.2046 0.2540 0.2874
## 477  477    2 0.3030 0.5583 0.7460
## 478  478    2 0.7591 0.0893 0.0295

plot(dif)

A lot o items were flagged, but given the relatively small values of the difference between initial and pure variables I’m not overly concerned.

#dif2 <- lordif(Vocab_short2, 
#              Vocab_with_predictors$college_grad,
#              criterion="Chisqr", 
#              alpha = .01)
#saveRDS(dif2, "vocab_output/dif2.rds")
dif2  <- readRDS("vocab_output/dif2.rds")

plot(dif2)

Psychometric modeling of the Syntactic Vocabulary of the CDI