In
te
r
n
ation
a
l Jou
rn
al
o
f E
v
al
u
a
t
i
on
a
n
d
R
e
se
arc
h
in
Ed
u
c
ation
(
IJERE
)
V
o
l.7,
N
o.1,
M
a
r
ch
2018,
pp.
77~
8
6
ISSN
: 2252-
88
22,
D
O
I
:
10.11
59
1
/ijer
e
.
v
7
.
i
1
.11
6
8
2
77
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
ERE
The Impact of Different Missin
g Data Handli
n
g Methods on
DINA M
odel
Se
ç
i
l
Ö
m
ür
S
ün
b
ü
l
D
e
partm
e
n
t
o
f M
easu
r
emen
t an
d
Eval
ua
t
i
on i
n
E
du
catio
n
,
M
ersin
U
niv
e
rsi
t
y,
Tu
r
key
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
ce
i
v
e
d
Jan
2
4, 201
8
Re
vise
d F
e
b 20,
201
8
A
c
c
e
pte
d
F
eb 28,
2
0
1
8
In
t
h
i
s
stu
dy,
it
was
aim
e
d
t
o
i
nvest
ig
a
t
e
th
e
im
p
act
o
f
d
i
ff
er
en
t
m
i
s
s
i
ng
dat
a
han
d
l
i
ng
m
e
t
hods
o
n
DINA
mod
e
l
param
e
ter
est
i
m
a
ti
on
a
n
d
c
las
s
if
icati
on
accur
acy
.
In
t
h
e
s
tu
dy,
s
im
ul
a
t
ed
d
ata
w
e
r
e
u
sed
and
t
h
e
d
a
ta
w
e
r
e
ge
ne
ra
te
d
by
m
an
ip
u
l
at
in
g
th
e
n
u
m
b
er
o
f
item
s
a
nd
s
am
p
l
e
s
i
ze.
I
n
t
h
e
gen
erat
ed
d
at
a,
tw
o
diff
eren
t
m
i
ss
ing
d
a
ta
m
ech
anisms
(
missing
complet
e
ly
a
t
ra
ndo
m
and
m
i
s
s
i
ng
at
r
an
dom
)
w
e
re
c
re
ated
a
c
c
o
r
di
ng
t
o
th
ree
diff
eren
t
am
ou
nt
s
of
m
i
s
s
i
ng
dat
a
.
Th
e
gen
e
rated
mi
ss
in
g
d
a
ta
w
as
c
o
m
p
l
e
t
ed
b
y
u
s
i
n
g
m
etho
ds
of
t
reat
in
g
miss
i
n
g
d
a
ta
a
s
i
n
co
rrect
,
pers
on
m
ean
i
m
putati
o
n
,
tw
o-
way
im
p
u
t
a
tio
n
,
an
d
exp
ectati
o
n
-
m
a
x
i
mi
zati
on
al
gorith
m
i
m
p
u
t
ati
on.
As
a
r
esult
,
it
w
a
s
ob
serv
e
d
t
hat
b
o
t
h
s
a
nd
g
p
aram
eter
e
s
tim
ati
ons
a
n
d
c
la
ssificati
o
n
accur
acies
w
ere
ef
f
e
ct
ed
f
ro
m,
m
i
ssin
g
d
ata
rat
e
s,
m
issin
g
d
ata
h
an
dli
ng
metho
d
s
and
missin
g
data
m
echa
n
isms.
K
eyw
ord
:
Cla
s
s
i
fica
ti
o
n
acc
urac
y
D
I
NA
M
ode
l
Ha
n
d
l
i
ng
Mi
ssing data
Pa
ra
m
e
te
r e
s
tim
ation
Co
pyri
gh
t © 2
018 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
Scien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
S
e
çil Ö
m
ür S
ünb
ü
l
,
D
e
pa
rtme
nt
o
f
M
e
as
ure
m
e
n
t
and E
v
a
l
ua
tio
n
in
E
d
u
cat
i
on,
Mersi
n
U
ni
ver
s
i
t
y,
Mersin,
Turkey.
Em
ail:
se
ci
lom
u
r@
me
rsi
n
.
e
d
u
.
t
r
1.
I
N
TR
OD
U
C
TI
O
N
C
o
g
n
i
t
i
v
e
di
a
g
nosis
a
sse
s
sm
e
n
t
s
(
CDAs)
are
i
n
cre
a
si
n
g
ly
b
ecom
i
n
g
a
pop
ul
ar
r
ese
a
r
c
h
a
re
a
i
n
t
he
fie
l
ds
o
f
m
easure
m
e
n
t
an
d
p
s
yc
ho
log
y
.
Le
igh
t
on
a
nd
G
i
e
r
l
[1],
p
o
i
n
t
e
d
t
ha
t
CD
A
“
i
s
des
i
gne
d
t
o
m
ea
sure
spec
ific
k
now
l
e
dge
s
t
r
uc
ture
s
a
nd
pro
c
ess
i
ng
s
k
il
ls
i
n
st
ude
n
t
s
s
o
a
s
t
o
pro
v
i
d
e
in
fo
rma
t
i
o
n
ab
ou
t
the
i
r
cog
n
i
t
i
ve
s
tre
n
gths
a
nd
w
e
ak
nesses”
.
Cog
n
i
tive
D
i
a
g
n
o
s
tic
M
o
d
e
l
s
(CD
M
s)
a
re
p
syc
h
ome
t
r
i
c
mode
ls
w
hic
h
w
e
r
e
d
e
v
el
o
p
e
d
t
o
i
d
e
n
t
i
fy
t
he
e
xam
i
ne
es’
abi
l
i
t
y
to
m
a
s
te
r
fin
e
-
gra
i
ne
d
sk
i
lls.
CD
Ms
p
ro
vide
a
p
rof
ile
o
f
w
h
et
her
t
h
e
i
n
div
i
d
u
a
l
h
as
p
r
e
-de
t
e
r
m
i
ne
d
s
k
i
l
l
s
.
B
y
t
his
w
a
y,
richer,
m
o
re
m
eaningful
a
n
d
m
o
re
i
nform
a
tive
in
form
ation
ab
ou
t t
h
e
ind
i
vi
d
u
al c
an be
pr
ov
ide
d
.
Th
e
c
ogn
iti
v
e
d
i
a
gn
osti
c
mod
e
ls
(
C
D
M
s
)
co
nn
ect
t
h
e
l
at
en
t
ski
l
l
s
w
i
t
h
obs
er
ved
be
h
a
vi
o
r
s
(task
s
)
which
were
r
equired
by
a
Q
-m
atri
x
[
2
]
.
T
h
e
Q
-
m
a
t
r
i
x
i
s
a
f
o
r
m
a
t
f
or
s
pec
i
fyi
ng
t
h
e
un
derly
i
ng
c
o
gn
iti
ve
attr
ib
u
t
e
s
m
easure
d
b
y
t
h
e
t
e
st
item
s
.
C
r
eati
ng
a
Q
m
a
trix
i
s
o
ne
o
f
t
h
e
most
i
m
por
t
a
n
t
s
t
e
ps
o
f
t
h
e
CD
Ms
a
p
p
l
i
c
a
t
i
o
n
s
.
I
n
a
Q
-
m
a
tr
ix
i
te
m
s
(J)
y
i
e
l
d
s
i
n
t
h
e
r
o
w
s
a
n
d
a
t
t
r
i
b
u
t
e
s
(K)
y
i
e
lds
i
n
t
he
c
ol
um
n
s
w
i
t
h
t
h
e
elem
en
ts
o
f
qj
k.
T
h
e
e
l
e
m
e
n
t
s
qj
k
o
f
Q
m
a
t
r
ix
g
e
t
v
a
l
ues
1
or
0
.
1
in
di
cate
s
t
ha
t
m
a
st
er
y
of
a
tt
ribute
k
i
s
requ
ire
d
b
y
i
t
em
j
.
Contrary,
0
indicates
th
a
t
m
a
s
t
e
r
y
o
f
a
t
t
r
i
b
u
t
e
k
i
s
n
ot
r
eq
ui
re
d
by
i
t
e
m
j
[
3
]
.
B
e
f
o
r
e
run
n
i
n
g a
CD
M
to
t
est da
ta
, the
Q
-m
atrix
must t
o be
alre
a
dy
de
t
erm
i
ne
d.
The
l
itera
t
u
r
e
r
eview
sh
ows
t
h
at,
CD
Ms
w
e
r
e
class
i
fie
d
i
nto
var
ious
w
ays
[
4
],[5]
and
se
veral
CD
M
s
h
a
v
e
b
een
d
eve
l
op
ed
t
o
eva
l
u
a
t
e
e
x
a
min
e
e
s
'
st
at
u
s
r
el
ati
v
e
to
m
astery
o
r
no
n-ma
st
e
r
y
o
n
e
ac
h
of
a
s
et
o
f
attr
ibut
es
[
6]--[10].
O
ne
o
f
the
f
r
equentl
y
u
sed
CD
M
s
i
s
the
det
e
rm
i
n
is
ti
c
,
inpu
ts,
no
isy
“an
d
” g
a
te
(DI
N
A)
[1
0]
m
ode
l
.
Th
i
s st
ud
y is l
imi
t
e
d
w
i
t
h
t
he
D
IN
A
Model.
A
br
i
e
f
de
scrip
t
io
n
of
D
IN
A
mo
de
l
is
g
ive
n
bel
ow
:
The
D
I
N
A
mode
l
(H
a
e
rte
l
,
[8
])
is
a
n
onc
om
pen
s
at
ory
m
o
d
e
l
a
n
d
i
t
h
a
s
c
o
n
jec
tiv
e
c
o
n
d
e
n
sa
tio
n
ru
le
[1
1].
It
i
s
easy t
o
e
s
tima
t
e
D
I
N
A
m
odel pa
r
a
m
e
ter
s
for
the
item
r
esponse
fu
nc
tio
n
w
h
ic
h
is gi
v
en
b
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2252-
8822
IJERE
V
ol
.
7,
N
o.
1,
Ma
r
ch 201
8
: 77
– 86
78
1
1
(1)
wher
e
Xij
de
no
tes
the
r
esp
o
n
s
e
o
f
t
h
e
i
t
h
e
xa
m
i
ne
e
to
item
j,
w
ith
1
r
epre
se
nti
n
g
a
c
o
rr
ect
a
nd
0
r
epre
se
nti
ng
i
n
co
rrec
t
r
espo
n
s
e
[
1
2
]
.
gj
a
n
d
sj
r
epre
se
n
t
the
gues
s
an
d
s
li
p
par
am
eters
f
or
the
j
th
i
te
m
,
r
espec
tive
l
y.
T
h
e
slip para
m
e
t
e
r
i
s in
te
rprete
d
a
s
th
e
pr
oba
bil
it
y
t
ha
t st
u
d
en
ts
w
ho pos
se
ss
al
l the
re
q
u
i
r
e
d
a
tt
r
i
b
u
tes for an
i
te
m
answ
e
r
it
i
n
c
o
r
r
ec
tly,
w
h
e
r
ea
s
the g
u
ess
pa
ram
eter
is
t
he
p
r
oba
b
i
l
i
ty
t
h
a
t
s
tu
de
nt
s
w
ho la
ck
a
t l
e
as
t
o
n
e
of
the
requ
ire
d
a
ttrib
ute
s
for a
n ite
m
to ans
w
e
r
i
t
correctly [
12]
. η
ij
i
s
t
he
la
t
e
n
t
r
esponse a
n
d i
t
is g
i
ve
n
by
∏
(
2)
η
ij
a
s
s
u
m
e
s
a
v
a
l
u
e
o
f
1
o
r
0
.
I
f
η
ij
= 1, it i
n
di
c
a
tes tha
t stu
d
e
n
t
i
pos
sesse
s al
l
t
h
e a
t
t
r
ibu
t
es req
u
i
re
d
for
it
em
,
and
η
ij
=
0,
it
i
ndic
a
tes
t
ha
t
s
t
ude
n
t
i
lac
k
s
at
lea
st
o
ne
o
f
t
h
e
attr
ib
ute
s
r
e
q
uire
d
for
item
j
[
1
2
]
.
qjk
r
e
f
e
r
s
t
o
the e
n
t
r
y i
n
t
he
j
th
r
ow
,
k
th c
o
l
um
n o
f
t
he
Q
m
atrix [12].
I
n
t
hi
s
s
t
ud
y,
t
he
ef
f
ec
t
of
t
h
e
m
issi
n
g
d
ata
o
n
t
he
p
ar
am
eter
est
i
m
at
i
o
n
and
cla
ssi
fica
ti
on
a
ccur
ac
y
of
the
CDM’s
DINA
model
was
investigated.
The
following
section
briefly
provided
information
for
the
missing data
.
M
i
ssin
g
d
ata
a
n
d
m
i
ss
i
n
g
da
t
a
h
a
ndl
in
g
me
tho
d
s
ar
e
imp
o
rta
n
t
t
o
p
i
cs
i
n
m
any
re
se
arc
h
f
ie
l
d
.
Ma
ny
educ
a
t
i
o
na
l
a
n
d psy
c
h
o
lo
gi
ca
l
data
f
r
e
q
u
e
n
t
l
y
have
m
issin
g
va
lu
es
b
ecaus
e
o
f
several
rea
s
ons.
S
i
n
ce,
m
o
s
t
o
f
the
sta
t
is
t
ica
l
a
ppr
oa
ches
r
e
q
uire
f
u
ll
da
ta,
m
issi
ng
va
l
u
e
s
th
re
a
t
en
s
th
e
d
a
t
a
a
n
a
l
y
si
s
process.
M
issing
d
ata
han
d
li
ng
m
eth
ods
ar
e
u
se
d
t
o
d
eal
w
i
t
h
m
i
ss
in
g
da
t
a
.
H
o
w
eve
r
th
es
e
me
tho
d
s
m
a
y
h
a
v
e
b
i
ased
e
st
i
m
a
te
s
l
ik
e
as
o
t
h
er
s
ta
tis
ti
c
a
l
p
roc
e
ss.
S
ever
al
m
iss
i
n
g
d
ata
ha
nd
li
ng
m
et
h
ods
h
a
v
e
bee
n
d
ev
elo
p
e
d
t
o
ove
rcom
e
t
h
i
s
p
r
obl
em
.
The
firs
t
s
tep
o
f
m
i
ssi
n
g
da
t
a
a
na
lys
i
s
i
s
d
e
term
i
nin
g
t
h
e
r
e
as
ons
f
or
the
m
iss
i
n
g
d
ata
a
n
d
t
h
e
am
oun
t
o
f
m
i
s
si
ng
da
t
a
.
Mis
s
i
ng
da
ta
p
a
tte
r
n
s
and
m
i
ss
in
g
da
t
a
me
ch
a
n
i
s
ms
a
re
t
h
e
r
ea
son
s
f
o
r
d
eci
si
on
s
a
b
out
w
h
e
t
h
er
o
r
not
m
i
s
si
ng
d
at
a
wil
l
b
e
n
e
g
l
e
c
t
e
d
.
T
he
m
i
ssin
g
d
a
t
a
p
a
t
t
e
r
n
d
e
s
c
r
i
b
e
s
t
h
e
p
a
t
t
e
r
n
s
o
f
missi
ng
da
ta
o
cc
urre
n
c
e
o
f
o
bse
r
ve
d
da
ta
i
n
a
da
ta
s
e
t
an
d
the
m
iss
i
ng
da
t
a
m
ec
ha
n
ism
s
de
scribe
p
ossib
le
rela
tio
ns
hips
b
etw
ee
n
t
he
m
e
asured
varia
b
le
s
and
the
proba
bi
l
it
y
of
mi
ssi
ng
d
a
t
a
.
V
a
rious
m
issi
ng
da
ta
h
a
n
d
l
i
n
g
m
et
h
o
d
s
and
ana
l
ysis
w
ere
deve
lo
p
e
d
f
or
t
he
m
issi
ng
da
ta
mec
h
an
i
s
ms,
wi
th
di
f
f
e
re
nt
a
ssu
mpt
i
on
s
a
b
out
mi
ssing
da
t
a
.
Acc
o
rd
in
g
t
o
R
ubi
n
[13
]
, t
h
e
re ar
e
t
hree t
ypes
o
f
mi
ssin
g
d
at
a
mec
h
a
n
isms
:
m
i
ssing
co
mple
t
e
l
y
a
t
rand
om
(
M
C
A
R
)
,
m
i
ss
in
g a
t
r
a
nd
om
(
M
A
R
)
a
n
d
missing
no
t at ra
nd
om
(MNAR)
[
13],
[
1
4
].
Miss
in
g
com
p
le
te
ly
a
t
r
an
dom
(
M
CA
R)
arises
w
hen
a
s
u
b
j
e
c
t
w
ith
inc
o
m
p
le
t
e
obs
er
vat
ions
a
r
e
a
r
and
o
m
subse
t
o
f
the
c
o
mple
te
s
a
m
ple
of
s
u
b
j
e
c
t
s
[
1
3].
M
C
A
R
i
s
def
i
ne
d
a
s
i
f
t
h
e
p
r
o
b
a
bi
li
t
y
t
h
a
t
th
e
d
a
t
a
a
re
m
i
s
sin
g
d
oes
not
d
e
p
end
on
a
n
y
var
iab
les,
e
i
the
r obse
r
ved
or
u
n
obs
e
r
ved
[1
4].
M
A
R
oc
c
u
rs
w
he
n
the
pro
b
a
b
il
ity
o
f
missin
g
d
ata
on
a
v
ari
a
b
l
e
i
s
u
n
r
e
l
a
t
e
d
w
i
t
h
t
h
e
v
a
l
u
e
o
f
t
h
a
t
varia
b
l
e
h
ow
e
v
e
r
it ma
y
be
r
e
l
a
te
d
w
it
h ot
h
e
r
va
riab
les in t
he
d
a
t
a
s
e
t.
N
MA
R
oc
c
urs w
hen t
he
pr
oba
bil
i
t
y o
f
missi
ng data
o
n a
va
riab
le i
s
a func
t
i
on o
f
the
va
l
ue
of tha
t
v
ar
i
a
b
l
e
[1
3],[1
5
]
. If t
h
e
m
issi
ng da
t
a
m
ec
h
ani
sms
are
MC
A
R
o
r
MA
R
the
n
it
is
n
o
t
n
e
cessa
ry
t
o
m
o
de
l
the
p
r
oc
ess
t
ha
t
ge
n
era
tes
the
miss
in
g
d
a
ta
i
n
ord
er
to
ac
com
m
oda
te
the
m
iss
i
ng
da
ta.
MCA
R
a
n
d
MA
R
me
chan
ism
t
h
a
t
p
r
o
d
u
c
e
s
t
h
e
m
i
s
s
i
n
g
d
a
t
a
a
r
e
i
gn
o
r
a
b
l
e
.
H
o
w
eve
r
MN
A
R
m
e
cha
n
i
s
m
i
s
no
n
-
ig
no
ra
ble.
I
t
is
n
e
cessa
ry
t
o
mo
d
e
l
this
m
ech
a
n
ism
to
d
eal
w
it
h
t
h
e
missi
ng da
ta
i
n
a
valid m
an
ne
r
.
Mi
ssi
ng
d
a
t
a
i
n
t
r
o
du
c
e
an
e
l
e
men
t
o
f
a
m
bi
g
uit
y
i
nt
o
d
at
a
an
al
y
s
i
s
a
n
d
t
h
e
y
c
a
n
a
f
f
e
c
t
p
r
o
p
e
r
t
i
e
s
o
f
st
a
t
i
s
t
i
ca
l
e
s
ti
m
ators.
V
ar
i
ou
s
m
etho
d
s
ha
ve
b
e
en
de
v
el
o
p
e
d
t
o
so
l
v
e
t
h
e
prob
lem
of
m
issing
da
ta
a
nd
t
h
ey
ca
n
ha
ve
p
rofou
n
d
l
y
d
iffer
ent
effec
t
s
o
n
e
st
i
m
ati
o
n.
T
he
p
r
o
b
l
e
ms
of
an
a
ly
z
i
ng
d
a
t
a
w
i
th
mi
ssi
ng
v
a
lues
have
b
e
en
re
v
i
e
w
ed
e
xt
e
n
s
i
v
e
l
y
i
n
the
li
t
e
r
ature
[
14],
[
1
6
]
-[18
]
.
S
o
me
fre
que
n
tly
u
sed
m
issi
ng
data
h
a
n
d
lin
g
met
h
od
s
a
r
e;
d
el
e
t
i
o
n
met
h
ods
(
p
a
i
r
wi
s
e
a
nd
c
a
s
e
w
i
s
e
d
e
le
t
i
on
)
a
n
d
i
m
pu
t
a
ti
on
m
e
t
hods
(
me
an
i
mp
u
ta
t
ion
,
regr
ession
i
m
p
u
ta
t
ion,
E
M
i
m
puta
tio
n,
m
u
lt
iple
i
m
p
u
tat
i
o
n
[14],
[1
6].
In
th
is
st
ud
y
;
trea
tin
g
m
issi
ng
d
a
t
a
a
s
incorrect
(
IN),
p
erson
m
e
an
i
mput
at
i
o
n
(P
M),
tw
o-w
a
y
impu
ta
t
i
o
n
(
TW),
a
n
d
e
xp
ect
at
io
n–
ma
xi
mi
za
ti
on
(EM)
alg
ori
thm
i
m
puta
t
io
n
m
etho
d
s
w
e
re
i
n
v
e
s
t
i
ga
ted
for
D
I
NA
m
o
del
a
n
a
l
ysis.
In
CD
M
a
pp
l
i
ca
ti
o
n
s,
trea
tin
g miss
i
n
g da
ta as inc
o
r
r
ec
t
is
w
ide
l
y use
d
. In t
his
m
eth
o
d
, m
i
ssin
g
r
espo
nse
s
a
re score
d
a
s
i
ncorre
ct. In
perso
n
m
e
an
im
puta
t
i
o
n
me
t
hod,
a
t
first
t
h
e
ave
r
age
of
th
e
obs
e
r
v
ed
item
sc
ores
i
s
com
p
u
t
e
d
f
o
r
e
a
c
h
respo
nde
n
t t
he
n
c
o
mpu
te
d
av
er
age is imp
u
te
d
for t
he i
tem
sc
ores
tha
t
ar
e missing
for t
h
a
t
re
sp
onde
n
t
.
I
n
tw
o
-
w
ay
imp
u
ta
t
io
n
[
19]
m
e
t
hod,
the
imp
ute
d
v
a
lue
is
c
a
lc
u
la
t
ed
b
y
a
d
d
i
ng
t
h
e
pers
on
me
a
n
t
o
the
i
t
e
m
m
e
an
and
s
u
b
t
r
act
s
the
overa
ll
m
ea
n
o
f
t
he
d
a
t
a
from
t
ha
t
s
c
ore.
E
xp
e
ct
at
i
o
n
–
ma
xi
m
i
zat
io
n
(EM)
al
g
ori
t
hm
impu
ta
t
io
n
m
eth
o
d
is
a
t
w
o-
ste
p
m
et
ho
d
b
a
se
d
on
t
h
e
c
omple
t
io
n
o
f
m
issi
ng
d
a
ta
u
s
in
g
the
m
a
x
im
u
m
like
l
i
h
oo
d
e
s
t
i
m
a
t
e
s
.
In
t
he
E
-step,
t
he
m
i
s
sing
da
ta
i
s
c
o
m
p
l
e
te
d
b
y
the
ex
p
e
cte
d
va
l
u
e
s
an
d
in
the
M
s
t
e
p
,
para
me
ter
estim
atio
n is d
o
n
e
us
i
n
g
the
va
lue
s
e
stima
t
e
d
i
n t
h
e
f
i
rs
t step
[
20].
Li
ter
a
t
u
re revi
e
w
show
s n
u
m
e
rous mis
sin
g
d
ata
an
d m
i
ssi
ng da
ta
ha
n
d
li
ng m
e
th
o
d
s in
ves
ti
g
a
tio
ns i
n
term
s
of
c
om
bi
n
a
tio
ns
o
f
fa
ctors
l
i
ke,
sa
m
p
le
s
ize
,
p
ro
por
tio
n
of
m
is
si
ng
da
ta,
me
tho
d
o
f
a
n
a
l
ys
is,
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
IJERE
I
S
S
N
:
2252-
88
22
T
h
e Im
pac
t of
D
i
f
f
ere
n
t
M
i
ssi
ng D
a
ta
H
a
n
d
l
i
n
g
Me
t
hods
o
n
D
I
NA M
ode
l (Se
ç
i
l
Ö
m
ü
r Sü
nb
ü
l
)
79
missing
data
h
andling
met
h
od
[
1
7],[21]-[26
]
.
Al
so
t
her
e
a
re
m
an
y
in
ves
t
i
g
a
tio
ns
i
n
cog
n
iti
ve
d
i
a
gn
ost
i
c
models
w
hich us
e
D
I
NA
m
o
del
[1],
[
3
]-[12],
[
27
]
-
[
3
3].
H
o
w
e
ver
the
r
e
a
re
l
imite
d p
r
ac
tica
l
re
s
ear
ch
o
n CD
M
s
w
h
er
e m
i
ssin
g
respo
n
ses w
e
re
p
re
se
nt
[
32],
[
3
4
],
[35].
In
C
DMs,
p
a
r
amet
er
e
st
i
m
at
es
m
i
g
h
t
b
e
t
h
re
a
t
en
ed
b
y
mi
s
s
i
n
g
d
a
t
a
,
t
oo
.
W
h
il
e
t
r
y
i
ng
t
o
p
r
ov
ide
mor
e
d
e
t
a
ile
d
i
n
for
m
a
t
i
o
n
a
b
out
t
he
i
nd
i
v
idua
l
s
b
y
us
i
n
g
CD
Ms,
b
i
a
s
e
d
e
s
t
i
m
a
t
e
s
c
a
n
b
e
m
a
d
e
w
i
t
h
t
h
e
prese
n
ce
o
f
the
m
i
ssi
n
g
da
t
a
. In
th
is st
udy,
it is a
i
m
ed
t
o de
t
er
mine t
he pe
rform
a
n
c
e
s of di
f
fere
nt mis
sin
g
da
t
a
han
d
l
i
ng
me
th
ods
f
or
C
D
M
e
st
im
atio
ns.
F
o
r
thi
s
p
urp
o
se
s
eve
r
al
d
a
t
a
s
e
t
s
wit
h
m
i
s
si
ng
d
at
a
we
re
a
nal
y
zed
by
u
sin
g
C
D
M
i
n
order
to
d
e
t
erm
i
ne
e
ffe
cti
v
e
fa
c
t
ors
w
h
ic
h
c
a
u
s
e
b
i
ase
d
e
s
t
i
m
ati
ons.
L
i
tera
t
u
re
r
eview
show
s
very
l
i
m
ited
st
u
dy
fo
r
missi
n
g
d
a
t
a
in
C
D
M
a
p
p
l
ic
a
tio
ns.
Thi
s
s
tu
dy
w
il
l
cont
ri
b
u
t
e
t
hi
s
g
a
p
wi
th
i
t
s
di
ffe
re
nt m
ani
p
u
l
a
tio
n
fac
t
or
s and
its
l
e
v
e
l
s.
2.
RESEARCH
M
ETH
O
D
2.1.
Simu
la
t
i
on
D
esign
2.
1.1.
S
i
mu
la
t
i
on
C
on
d
i
tion
s
M
ode
l:
Th
e
DINA
mo
d
e
l
i
s
u
se
d
t
o
g
e
n
era
t
e
d
a
t
a
,
to
e
sti
m
a
t
e
pa
ra
me
t
e
rs
a
nd
t
o
ca
l
c
ul
a
t
e
t
h
e
class
i
fica
t
i
o
n
a
c
c
ura
c
y.
D
I
N
A
mode
l
is
p
re
fer
r
ed
b
ec
a
u
se
i
t
i
s
w
i
del
y
u
s
e
d
w
i
th
in
t
he
C
D
M
s
t
u
dies
a
nd
i
t
i
s
ea
sie
r
to e
s
tim
ate
the p
a
ram
e
ter
s
.
Sam
ple S
i
ze
(N)
:
Li
t
e
ra
tu
re
r
ev
i
e
w
sho
w
s
t
h
at
s
a
m
pl
e
si
ze
i
s
an
i
mpo
r
t
a
nt
f
a
c
t
o
r
a
ffec
t
i
n
g
p
ara
m
e
t
er
est
i
ma
t
i
o
n
.
de
l
a
Torre
,
H
ong
a
n
d
D
e
ng
[3
0]
u
se
d
1
0
00,
2
0
0
0
a
n
d
5
00
0
sam
p
le
s
i
z
e
s
,
de
l
a
Tor
r
e
and
Do
ug
l
a
s
[29
]
u
sed
10
00
s
ampl
e
si
z
e
,
a
n
d
d
e
l
a
To
rre
a
n
d
Do
ugl
a
s
[
6]
u
sed
2
0
00
sam
p
l
e
s
ize
in
t
he
i
r
s
t
u
d
i
es.
In th
i
s st
ud
y t
h
ree
differe
n
t
sa
mple
sizes
(
10
00,
200
0
and
300
0
)
w
e
re
u
s
e
d
f
o
r
e
a
c
h
c
o
n
d
it
ion
.
Nu
mb
e
r
of
it
em
(N
I)
a
n
d
nu
mb
e
r
of
att
r
ib
ut
e
s
(K):
L
it
e
r
ature
rev
i
ew
s
how
s
tha
t
t
h
e
n
umbe
r
o
f
attr
ib
u
t
e
s
v
ari
e
d
be
tw
e
e
n
3
–
8
ranges
[3],[5],[6],[29
]
.
In
t
hi
s
st
u
dy,
n
um
b
e
r
of
a
t
t
ribu
te
s
w
a
s
fixe
d
as
4
a
n
d
numbe
r of i
te
m
s
f
or
4
a
t
t
rib
u
te
s m
a
nip
u
l
at
ed
a
s 15
an
d 3
0
.
s
an
d g P
a
r
a
m
e
t
e
r L
eve
l
s
:
H
e
nso
n
a
nd D
o
ug
las [3] use
d
s a
n
d
g ≈
U
(
.
05 - .40); Ru
p
p
an
d
Tem
plin
[5]
used
s
≈
U
(
.
0
-
.
25)
a
n
d
g
≈
U
(
.0
-
.
15).
In
t
h
i
s
s
t
u
dy
t
h
e
par
a
m
e
ter
d
i
stri
bu
tio
n
a
n
d
ra
nge
w
er
e
pre
f
err
e
d
as
s a
nd g
U
(
.10 - .
30).
M
i
ss
i
ng
da
t
a
m
e
cha
n
i
s
m
s
a
nd M
i
ss
i
ng R
a
te
(MR)
:
I
n
t
h
i
s
stu
d
y
t
hree
l
eve
l
s
of
m
iss
i
ng
ra
t
e
(
5%,
10
%, 15%) a
n
d tw
o miss
ing
data m
ech
a
n
is
m
s
(MCA
R
a
n
d
M
A
R
) w
e
r
e
i
nve
st
i
g
ate
d
.
In the l
i
t
e
ra
t
u
re
, rat
es
o
f
missi
ng da
ta
r
a
n
g
e
d from
2% to
5
0
%
h
o
w
e
v
e
r most of
t
h
e
m
yield b
e
t
ween
5
% - 3
0
%
.
M
i
ss
i
ng da
t
a
im
p
u
ta
ti
o
n
m
e
th
o
d
s:
In
t
his
stu
dy,
fo
ur
m
i
ssi
ng
da
ta
h
an
d
l
i
n
g
m
e
th
ods
(
trea
t
i
n
g
missi
ng
da
ta
a
s
i
n
corr
ect
(IN
)
,
p
erson
me
an
i
m
p
u
t
a
tio
n
(P
M
)
,
t
w
o-w
a
y
impu
ta
t
i
o
n
(
T
W
),
a
nd
E
x
p
e
c
t
a
t
i
on
Ma
ximiz
a
t
i
o
n
(EM) im
puta
t
ion
w
e
re
used
missi
ng da
ta
h
and
l
ing.
Tab
l
e
1.
S
imula
t
i
o
n D
e
si
g
n
F
a
c
tors a
n
d
Lev
e
l
s
Fa
ct
o
r
s
Nu
m
b
er
o
f
L
e
v
e
ls
V
al
u
e
s
o
f
L
ev
e
l
s
Sa
m
p
l
e
S
i
z
e
3
1000,
20
00,
300
0
Nu
m
b
er o
f
Item
2
1
5
, 3
0
Missin
g
M
ech
a
n
ism
2
MC
A
R
,
MA
R
M
i
ssing
R
a
t
e
3
5
%,
10%
,
15%
M
i
ssing
Im
put
a
tion
4
I
N
,
P
M
,
T
W,
E
M
2.
1.2.
Da
ta
G
enera
t
i
o
n
The
da
ta
w
ere
ge
ne
rate
d
acc
ord
i
n
g
t
o
t
h
e
D
I
NA
m
ode
l
.
T
he
p
ara
m
e
te
r
v
a
lu
e
s
o
f
s
a
n
d
g
w
e
r
e
range
d be
tw
e
e
n
0
.
1
a
nd 0.3 (s a
nd g
U
(
.
10 -
.
3
0)
), the n
um
ber
of a
ttribut
e
s
were f
ixed
a
s
4.
Th
e
n
u
m
ber of
i
t
e
m
s
w
e
r
e
s
e
t
t
o
1
5
a
n
d
3
0
,
a
n
d
t
h
e
s
a
m
p
l
e
s
i
z
e
s
w
e
r
e
p
r
e
f
e
r
r
e
d
as
1
00
0
,
200
0
and
3
000
.
1
0
0
re
pli
c
a
tio
ns
w
e
r
e
c
on
duc
t
e
d
for
eac
h
cr
ossin
g
c
o
n
d
iti
o
n
.
R
3
.
0
w
a
s
use
d
f
or
da
ta
g
ene
r
at
io
n
a
n
d
da
ta
ma
nage
me
nt
p
roce
dur
es.
D
a
ta
d
e
l
e
t
i
o
n
w
a
s
pe
rform
e
d
ac
cord
in
g
to
M
CA
R
a
n
d
MA
R
for
ea
ch
e
xper
i
m
e
nta
l
c
e
ll
o
f
c
on
d
i
t
i
on
crossi
n
g
s.
I
n
o
r
de
r
to
a
c
h
ieve
a
m
issi
n
g
c
o
m
plete
l
y
a
t
r
and
o
m
c
o
ndi
t
i
o
n
,
the
pro
b
a
b
i
l
ity
o
f
m
i
ssi
n
g
of
a
n
y
data
i
s
e
qua
l
t
o
t
he
p
ro
ba
b
i
l
i
t
y
o
f
m
i
ss
in
g
of
d
a
t
a
i
n
a
n
o
t
he
r
ce
l
l
,
a
n
d
t
h
es
e
prob
a
b
ili
t
i
e
s
m
ust
b
e
i
nd
epe
nde
n
t
from
eac
h
o
t
h
e
r.
F
or
t
hi
s
pu
r
pose
,
f
irst
l
y
t
he
n
um
ber
o
f
c
e
l
l
s
to
b
e
de
l
e
ted
in
t
he
d
a
t
a
se
t
w
a
s
de
te
rm
ined
ac
cord
in
g
t
o
t
he
a
mo
un
t
of
m
issi
ng
d
a
t
a.
A
fte
r
t
ha
t,
t
he
d
a
t
a
o
f
the
de
t
e
rm
i
n
e
d
num
ber
o
f
c
e
lls
i
s
dele
te
d
from
t
he
d
a
t
a
set
ra
n
dom
ly
w
i
t
h
t
h
e
w
r
i
t
ten
pro
g
r
a
m
.
I
n
or
de
r
t
o
ach
ieve
a
m
i
s
s
i
n
g
at
r
an
dom
(
MAR)
c
o
ndi
ti
o
n
,
t
h
e
p
rob
a
bil
i
ty
o
f
mi
ssin
g
o
f
a
ny
d
a
t
a
s
ho
ul
d
be
r
e
l
ate
d
t
o
an
ot
her
var
i
a
b
le
w
ith
a
c
omp
l
e
t
e
e
rror,
and
t
h
e
co
n
d
i
t
i
ona
l
prob
ab
i
l
i
tie
s
for
thi
s
v
ar
iab
l
e
m
u
s
t
b
e
e
q
u
a
l
.
F
o
r
t
h
is
pur
pose,
f
ir
st
ly
t
he
e
xam
i
nees
w
er
e
sorte
d
i
n asce
n
d
in
g by
t
h
e
i
r
t
o
t
a
l
tes
t
s
c
o
res
.
T
he 80
%
d
e
l
e
t
i
o
n
w
as
p
e
rfor
m
e
d
f
or
e
xa
m
i
ne
es
'
r
e
sp
o
n
se
s
w
h
o
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2252-
8822
IJERE
V
ol
.
7,
N
o.
1,
Ma
r
ch 201
8
: 77
– 86
80
we
re
i
n
t
h
e
fi
rst
q
u
a
nt
il
e
and
20
%
d
e
l
e
ti
on
w
a
s
p
e
r
f
o
rme
d
f
o
r
e
xam
i
nee
s
'
r
e
s
p
o
n
se
s
w
h
o
w
e
r
e
i
n
the
four
th
qua
n
t
i
l
e
re
gard
in
g
t
o
t
he
a
m
oun
t
o
f
m
issi
n
g
da
t
a
.
F
i
nal
l
y,
t
he
gene
ra
ted
missi
n
g
d
ata
w
a
s
c
o
mple
ted
usin
g
fo
ur
m
issing
d
a
t
a
h
a
n
dl
i
ng
me
tho
d
s
(
t
r
eat
in
g
m
i
ssi
n
g
d
a
t
a
as
i
n
correct
(IN)
,
p
erson
m
e
an
i
mputation
(P
M
)
,
tw
o-w
a
y
imp
u
t
a
ti
o
n
(TW),
a
n
d
E
x
p
ecta
t
io
n Ma
xim
i
z
a
t
io
n (EM))
.
2.
1.3.
A
n
alys
is of
Data
To
a
n
a
l
y
z
e
t
he
d
a
t
a,
t
h
e
r
esu
l
t
s
o
f
t
h
e
it
e
m
p
a
r
amet
ers
an
d
a
t
t
ribut
e
p
rofiles
obtained
f
r
o
m
the
com
p
le
te
d
da
t
a
w
ere
com
p
a
r
ed
w
i
t
h
e
s
t
i
m
a
t
e
s
wh
ich
wer
e
o
b
t
ai
ne
d
from
ea
ch
m
i
s
s
i
n
g
d
a
t
a
h
a
nd
lin
g
me
tho
d
s.
T
he
r
oo
t
me
an
s
qu
are
error
(RMS
EA
)
w
a
s
c
o
mpute
d
f
or
t
h
e
c
o
nsiste
nc
y
of
t
he
item
pa
ra
me
t
e
r
est
i
ma
t
e
s
an
d
the
pa
tter
n
-
w
i
s
e
class
i
fica
ti
o
n
acc
urac
ies
w
e
r
e
c
om
pu
ted
for
t
h
e
c
l
ass
i
f
i
c
a
ti
o
n
acc
urac
y
for
ea
ch e
xper
i
m
e
nta
l
c
el
l.
3.
RESULT
S
3.1.
Resu
l
t
s
for s P
a
rameter
E
s
timat
i
on
Th
e
ef
fe
ct
s
o
f
d
i
f
f
e
ren
t
m
i
s
si
n
g
d
at
a
mec
h
an
isms,
s
a
mp
l
e
s
i
z
es,
n
umbe
r
of
i
tem
s
,
and
m
i
ssi
ng
r
ates
on
t
he
a
ve
rage
R
M
S
EA
o
f
s
para
me
t
e
r
est
i
m
a
tio
n
w
e
re
g
ive
n
i
n
Ta
b
l
e
2
a
n
d
t
h
e
r
e
s
u
lts
o
f
t
h
e
in
t
e
rac
tio
n
effec
t
s
w
e
re
g
i
v
en
i
n
F
i
g
u
re
1
a
n
d
F
i
gure
2
.
W
hen
Ta
b
l
e
2
is
e
x
am
ine
d
,
i
t
w
as
s
ee
n
t
h
at
a
vera
ge
R
M
S
EA
val
u
es
o
b
t
a
i
ne
d
in
b
o
t
h
M
C
A
R
a
nd
M
A
R
c
o
ndi
t
i
o
n
s
w
e
re
l
ow
.
It
w
a
s
a
l
so
s
ee
n
t
h
at
bot
h
i
n
M
CA
R
and
MA
R
c
o
n
d
i
t
i
o
ns,
the
a
v
era
g
e
RM
S
E
A
val
u
es
o
b
t
a
i
ne
d
fro
m
missing
ha
n
d
li
ng
s
m
e
th
ods
i
n
d
i
ffe
ren
t
s
am
ple
si
z
e
s
an
d
n
u
m
b
ers
of
item
d
i
d
no
t
c
h
a
n
ge
m
uch.
S
a
m
ple
si
z
e
a
nd
n
u
m
b
er
o
f
ite
m
m
a
ni
p
u
la
t
i
on
w
a
s
no
t
aff
e
c
t
ive
for
the
s
param
e
te
r
es
t
i
m
a
t
i
o
n
s
.
H
o
w
e
v
e
r
,
i
n
b
o
t
h
M
C
A
R
and
M
A
R
co
nd
i
tio
ns,
the
a
v
era
g
e
RMS
E
A va
l
u
e
s
t
en
ded
to
i
ncre
ase
as m
issi
n
g
r
ates w
ere in
cre
a
sed
.
Tab
l
e
2. A
verage R
MS
EA
o
f s
P
a
ram
e
ter for
S
i
m
u
lati
o
n
C
ond
i
t
i
ons
M
CAR
M
A
R
E
M
IN
P
M
TW
E
M
IN
P
M
T
W
S
a
m
p
l
e
S
i
z
e
1000
0
.
0198
0
.
0
807
0
.
0176
0
.
0194
0
.
0056
0
.
0167
0
.
0048
0
.
0049
2000
0
.
0167
0
.
0
796
0
.
0146
0
.
0175
0
.
0041
0
.
0159
0
.
0037
0
.
0039
3000
0
.
0154
0
.
0
789
0
.
0138
0
.
0170
0
.
0035
0
.
0156
0
.
0034
0
.
0035
Nu
m
b
e
r
o
f Item
15
0
.
0190
0
.
0
792
0
.
0186
0
.
0215
0
.
0048
0
.
0172
0
.
0043
0
.
0045
30
0
.
0155
0
.
0
802
0
.
0121
0
.
0144
0
.
0040
0
.
0149
0
.
0037
0
.
0037
M
i
s
s
i
n
g
R
a
t
e
0.
05
0
.
0101
0
.
0
407
0
.
0086
0
.
0097
0
.
0030
0
.
0085
0
.
0026
0
.
0026
0.
10
0
.
0172
0
.
0
798
0
.
0151
0
.
0178
0
.
0045
0
.
0160
0
.
0040
0
.
0042
0.
15
0
.
0246
0
.
1
187
0
.
0223
0
.
0264
0
.
0057
0
.
0236
0
.
0053
0
.
0055
A
ll
me
t
h
o
d
s,
e
xc
ep
t
t
h
e
IN
m
e
t
ho
d,
p
e
r
for
m
e
d
s
imilar
l
y
u
nder
t
h
e
a
l
l
m
i
ssi
n
g
r
a
t
e
con
d
it
io
ns.
Espec
i
a
l
l
y
,
i
t
h
as
b
e
e
n
o
bser
ved
tha
t
t
he
R
MS
EA
v
a
l
ue
s
ob
ta
ine
d
fro
m
t
h
e
IN
m
e
t
hod
a
t
t
h
e
1
5
%
m
i
s
si
ng
rate
c
o
n
d
i
t
i
o
n
go
t
the
ma
x
i
m
u
m
val
u
es.
R
M
S
E
A
val
u
es
o
b
t
a
i
ne
d
fr
om
t
he
m
et
h
ods
w
it
h
di
ffe
ren
t
m
iss
i
n
g
rate
s
see
m
t
o
be
h
ig
he
r fo
r
M
C
A
R
t
ha
n MA
R.
Wh
en
t
h
e
f
ac
to
r
int
e
rac
t
i
o
n
ef
f
ect
g
ra
ph
f
or
t
h
e
s
i
s
ex
a
m
i
n
ed
,
i
t
w
a
s
o
b
s
er
ved
t
h
at
i
n
bot
h
M
C
A
R
and
MA
R
c
o
n
d
it
io
ns,
di
ffe
re
nt
s
am
p
l
e
siz
e
s
a
n
d
n
umbe
r
of
i
tem
d
i
d
n
o
t
c
h
a
ng
e
t
h
e
ave
r
ag
e
R
M
SEA
v
a
lu
e
s
to
o m
u
ch.
H
o
w
e
ve
r it is a
lso
obse
r
ve
d
th
a
t
R
M
S
EA
va
l
u
e
s w
e
re
i
n
c
r
ea
sed w
i
t
h
the
i
ncr
e
ase
of m
issin
g
r
ates.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJERE
I
S
S
N
:
2252-
88
22
T
h
e Im
pac
t of
D
i
f
f
ere
n
t
M
i
ssi
ng D
a
ta
H
a
n
d
l
i
n
g
Me
t
hods
o
n
D
I
NA M
ode
l (Se
ç
i
l
Ö
m
ü
r Sü
nb
ü
l
)
81
Figure
1.
MCA
R
Avera
g
e R
M
SEA
Values
o
f the
Inter
act
i
o
n
Effect
(
s param
e
ter
)
F
i
gure
2.
MA
R
A
ver
a
ge
R
MS
EA
V
a
l
ues of
t
he I
nt
e
r
ac
ti
on
E
ffe
c
t
(s
P
ar
am
e
t
e
r
)
3.2.
Resu
l
t
s
for g
Par
a
met
er
E
s
timat
i
on
Th
e
ef
fe
ct
s
o
f
d
i
f
f
e
ren
t
m
i
s
si
n
g
d
at
a
mec
h
an
isms,
s
a
mp
l
e
s
i
z
es,
n
umbe
r
of
i
tem
s
,
and
m
i
ssi
ng
r
ates
on
t
he
a
ver
a
ge
R
MS
EA
o
f
g
pa
ram
e
te
r
e
s
ti
m
a
tion
w
e
r
e
g
ive
n
i
n
Ta
b
l
e
3
a
n
d
t
h
e
res
u
lts
o
f
t
h
e
in
t
e
r
a
c
tio
n
effec
t
s were
g
i
v
en
i
n
Fi
g
u
re
3
a
n
d
F
i
gure 4. Whe
n Tab
l
e 3 is
e
x
a
m
i
n
ed
,
si
mi
l
a
r
t
o
th
e
s
pa
r
amet
er
e
st
i
m
a
t
ion
,
it
w
as
o
bserve
d
t
h
at
a
ver
a
ge
R
MS
EA
v
a
l
ue
s
ob
tai
n
e
d
f
or
b
o
t
h
M
C
A
R
an
d
M
A
R
c
ondit
i
on
s
we
re
l
o
w
.
It
w
a
s
als
o
s
e
e
n t
h
at bo
t
h i
n
MCA
R
and MA
R
c
o
n
d
it
io
ns, the
ave
r
age
R
M
S
EA
v
alues
whi
c
h
obtained f
rom
m
i
ssing
han
d
l
i
ngs
m
et
ho
ds
f
or
d
i
f
fer
e
nt
s
am
ple
siz
e
s
a
n
d
numbe
r
s
o
f
ite
ms
d
i
dn’
t
c
h
an
ge
m
u
c
h.
F
or
M
CA
R
a
n
d
MA
R
w
i
t
h
t
he
i
ncr
ease
of
m
i
s
s
i
n
g
r
ate
s
,
it
w
a
s
observe
d
t
h
a
t
t
h
e
r
e
s
u
l
t
s
o
f
t
h
e
a
v
e
r
a
g
e
R
M
S
E
A
v
a
l
u
e
s
wer
e
increas
ed.
F
o
r
M
C
A
R
,
t
h
e
EM
m
et
ho
d
pe
rfor
me
d
be
t
t
e
r
t
ha
n
the
o
t
h
e
r
me
t
h
o
d
s
i
n
a
ll
m
i
ssi
ng
r
at
e
c
o
nd
it
io
n
s
;
wher
eas
t
he
R
MS
EA
v
a
l
ue
s
o
b
ta
i
n
ed
f
r
o
m
t
h
e
IN
m
etho
d
was
h
i
g
h
e
r
t
ha
n
the
o
t
her
me
t
h
od
s.
A
vera
ge
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2252-
8822
IJERE
V
ol
.
7,
N
o.
1,
Ma
r
ch 201
8
: 77
– 86
82
R
M
S
E
A
v
a
l
u
e
s
w
h
i
c
h
w
e
r
e
o
b
ta
in
e
d
f
r
o
m
t
h
e
m
e
th
o
d
s
w
i
t
h
d
if
fe
r
e
n
t
mi
ssi
ng
r
a
t
es
s
ee
m
t
o
b
e
h
i
gher
f
o
r
M
C
A
R
t
ha
n
M
A
R.
Ta
b
l
e
3.
A
ver
a
ge
R
MS
EA
of g P
a
ram
e
ter
for S
i
m
u
l
a
ti
on
C
o
n
d
iti
on
s
MC
A
R
M
A
R
EM
I
N
PM
T
W
EM
I
N
PM
T
W
Sample
Siz
e
1000
0
.
0144
0
.
0232
0
.
0169
0
.
0180
0
.
0056
0
.
0071
0
.
0055
0
.
0054
2000
0
.
0115
0
.
0223
0
.
0156
0
.
0164
0
.
0045
0
.
0065
0
.
0048
0
.
0048
3000
0
.
0104
0
.
0220
0
.
0150
0
.
0156
0
.
0041
0
.
0065
0
.
0045
0
.
0044
Nu
mb
er
o
f
I
t
e
m
15
0
.
0131
0
.
0228
0
.
0174
0
.
0176
0
.
0053
0
.
0066
0
.
0048
0
.
0047
30
0
.
0110
0
.
0220
0
.
0142
0
.
0157
0
.
0042
0
.
0066
0
.
0049
0
.
0050
Mis
s
ing Rat
e
0.
05
0
.
0075
0
.
0120
0
.
0084
0
.
0091
0
.
0031
0
.
0036
0
.
0028
0
.
0028
0.
10
0
.
0121
0
.
0225
0
.
0156
0
.
0166
0
.
0048
0
.
0066
0
.
0049
0
.
0048
0.
15
0
.
0165
0
.
0329
0
.
0234
0
.
0243
0
.
0064
0
.
0097
0
.
0070
0
.
0069
Whe
n
t
he
i
n
t
era
c
ti
o
n
e
ffec
t
g
ra
ph
for
t
h
e
fa
c
t
ors
is
e
xam
i
ned,
i
t
w
a
s
a
ls
o
see
n
t
ha
t
in
b
o
t
h
M
C
A
R
and
MA
R
co
n
d
i
t
i
o
n
s,
d
iffere
nt
s
am
ple
siz
e
s
and
num
ber
s
o
f
i
t
em
s
d
i
d
n’t
c
h
an
ge
t
he
a
v
e
rage
R
MS
EA
v
al
ue
s
w
h
ic
h
w
e
re
o
b
t
ai
ne
d
fr
om
m
issi
ng
h
a
n
d
l
i
n
g
s
m
etho
ds
t
oo
m
u
ch.
H
o
w
e
ver
w
ith
t
he
i
n
c
re
ase
of
m
issi
ng
ra
t
e
s,
the a
v
era
g
e R
M
S
E
A
value
s
t
e
nde
d t
o
inc
rea
s
e
.
F
i
gur
e 3.
MCA
R
Avera
g
e
RM
SEA Va
l
u
e
s
o
f
t
h
e
Inter
act
i
o
n
Effec
t
(
g
Par
a
m
e
ter)
Evaluation Warning : The document was created with Spire.PDF for Python.
IJERE
I
S
S
N
:
2252-
88
22
T
h
e Im
pac
t of
D
i
f
f
ere
n
t
M
i
ssi
ng D
a
ta
H
a
n
d
l
i
n
g
Me
t
hods
o
n
D
I
NA M
ode
l (Se
ç
i
l
Ö
m
ü
r Sü
nb
ü
l
)
83
F
i
gure
4.
M
A
R
A
vera
ge
R
MS
E
A
V
a
l
ue
s
of
t
he
Inte
r
ac
ti
on
Effec
t
(
g
pa
r
am
ete
r
)
3.3.
Resu
l
t
s for
Classif
i
c
a
tion A
ccu
racy
Th
e
ef
fe
ct
s
o
f
d
i
f
f
e
ren
t
m
i
s
si
n
g
d
at
a
mec
h
an
isms,
s
a
mp
l
e
s
i
z
es,
n
umbe
r
of
i
tem
s
,
and
m
i
ssi
ng
r
ates
on
t
h
e
c
l
a
ssi
fic
a
tio
n
acc
urac
y
w
e
r
e
g
i
v
en
i
n
Ta
b
l
e
4
a
n
d
the
re
s
u
lts
o
f
the
i
n
t
e
rac
tio
n
e
ffe
c
t
s
w
e
r
e
g
i
v
en
i
n
F
i
gure
5
a
n
d
F
i
gure
6.
W
he
n
Ta
b
l
e
4
i
s
e
x
a
mine
d,
i
t
w
a
s
seen
t
h
a
t
a
ve
rage
c
lass
i
f
ic
ati
o
n
acc
urac
y
rates
w
h
ic
h
w
e
re
obt
a
i
ne
d
from
M
CA
R
an
d
MA
R
c
o
n
d
i
t
i
o
n
s
w
e
re
h
i
g
h.
I
t
was
also
s
een
that
i
n
MC
AR
con
d
i
t
i
on
s,
t
he
a
ve
rage
c
l
a
ssi
fic
a
t
i
o
n
ac
cura
cy
r
ates
w
hic
h
w
er
e
obta
i
ne
d
fr
om
m
i
ssin
g
h
a
n
d
lin
gs
m
et
h
ods
i
n
di
ffe
re
nt
s
am
p
l
e
si
z
e
d
i
d
n’t
c
h
an
ge
m
uc
h.
H
ow
e
v
er,
w
i
t
h
t
he
i
nc
r
ease
o
f
n
umbe
r
of
i
te
m
s
,
the
c
l
a
ssifi
ca
tio
n
ac
cura
cy
r
a
t
es
t
en
de
d
to
i
ncre
ase.
T
he
c
la
ss
ifica
t
i
o
n
a
c
c
u
r
a
c
y
r
ate
s
d
ecr
ease
d
w
it
h
t
h
e
i
n
cr
ease
o
f
m
is
sin
g
rate
.
I
n
M
A
R
c
on
di
t
i
on,
t
h
e
a
ver
a
ge
c
la
ssifica
t
i
o
n
a
c
c
u
ra
cy
r
at
es
w
hi
c
h
w
er
e
o
b
t
a
ine
d
f
rom
m
i
ss
i
n
g
han
d
l
i
ngs
m
et
ho
ds
i
n
d
i
ffe
r
ent
sam
p
le
s
ize
s
a
nd
n
u
m
b
er
o
f
i
t
em
di
dn’
t
chan
ge
m
uc
h.
F
or
M
CA
R
a
n
d
MA
R
w
ith
t
he
i
ncre
ase
of
m
issin
g
r
a
tes,
i
t
w
a
s
obs
er
ved
tha
t
t
he
r
e
su
l
t
s
o
f
c
l
a
ssific
a
tio
n
acc
urac
y
ra
t
e
s
w
e
r
e
dec
r
ea
se
d.
A
ll
m
e
tho
d
s
e
x
ce
p
t
t
he
I
N
m
e
tho
d
p
er
form
ed
s
i
m
ilar
l
y
u
n
d
e
r
t
h
e
m
i
s
s
i
n
g
r
a
t
e
c
o
n
d
i
t
i
o
n
s
.
I
t
w
a
s
seen
t
ha
t
c
l
a
ssi
fic
a
t
i
o
n
a
c
c
u
r
acy
r
ates
w
h
i
c
h
w
er
e
obta
i
ned
fr
o
m
m
e
tho
d
s
w
ith
d
iffere
n
t
m
issi
ng
ra
t
i
os
w
er
e
lower
f
o
r
MCAR than
M
A
R
.
Tab
l
e
4. A
verage C
lass
ifica
t
i
on Ac
cura
cy R
ates
o
f g
Pa
ram
e
ter
f
or
S
i
m
ulat
i
on
Con
d
i
t
ions
MCA
R
MAR
E
M
I
N
PM
T
W
EM
I
N
PM
T
W
Sampl
e
Siz
e
1000
0
.
8275
0
.
8155
0
.
8498
0
.
8378
0
.
9465
0
.
9563
0
.
9745
0
.
9745
2000
0
.
8242
0
.
8260
0
.
8445
0
.
8270
0
.
9548
0
.
9502
0
.
9735
0
.
9735
3000
0
.
8315
0
.
7950
0
.
8236
0
.
8328
0
.
9487
0
.
9396
0
.
9617
0
.
9617
Nu
mb
er
o
f
I
t
e
m
15
0
.
7978
0
.
7893
0
.
8196
0
.
8095
0
.
9409
0
.
9438
0
.
9672
0
.
9672
30
0
.
8576
0
.
8350
0
.
8591
0
.
8556
0
.
9591
0
.
9536
0
.
9723
0
.
9723
Mi
ssing R
a
te
0.
05
0
.
8982
0
.
8833
0
.
9152
0
.
9158
0
.
9665
0
.
9685
0
.
9823
0
.
9823
0.
10
0
.
8296
0
.
8028
0
.
8326
0
.
8268
0
.
9488
0
.
9465
0
.
9673
0
.
9673
0.
15
0
.
7554
0
.
7504
0
.
7702
0
.
7550
0
.
9347
0
.
9310
0
.
9596
0
.
9596
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2252-
8822
IJERE
V
ol
.
7,
N
o.
1,
Ma
r
ch 201
8
: 77
– 86
84
Figure
5.
MCA
R
C
la
ssi
fica
ti
on Ac
cura
cy
R
a
t
e
s
of
the
Inte
r
acti
o
n Ef
fec
t
F
i
gur
e 6.
MA
R
Class
i
f
i
c
a
t
ion
A
c
c
u
rac
y
Rat
e
s
of the
In
tera
ctio
n
Ef
f
ect
4.
DISC
USSION
In
t
h
i
s
s
t
ud
y
,
i
t
w
a
s
o
b
serve
d
t
ha
t,
t
he
i
ncre
ase
o
f
m
iss
i
ng
r
a
te,
ave
r
age
RMS
E
A
va
lue
s
t
en
de
d
t
o
incre
a
se
a
nd
r
a
tes
o
f
c
las
s
i
f
i
cati
o
n
acc
urac
i
e
s
w
e
re
t
e
nde
d
to
dec
r
ea
se.
I
t
i
s
co
ns
iste
nt
w
i
t
h
t
he
r
esul
t
s
o
f
D
a
i
[34]
.
D
e
spi
t
e
t
h
e
low
m
i
ssi
ng
ra
tes,
a
vera
ge
R
M
S
EA
v
al
ues
t
e
n
de
d
to
i
ncr
e
a
s
e
w
ith
t
he
i
nc
rea
s
e
of
missi
ng
r
a
tes.
S
a
m
ple
size
m
ani
p
ula
t
ion
w
a
s
no
t
a
ffe
c
t
ive
for
t
h
e
p
a
r
amet
er
e
st
i
m
a
tions
a
n
d
cl
a
s
s
i
fi
cat
i
o
n
ac
cura
cies.
Nu
m
b
er
o
f
i
t
e
m
s
we
re
not
a
f
f
ec
tive
for
para
me
ter
e
s
ti
ma
t
i
o
n
wh
ere
a
s
i
t
w
as
a
f
f
ect
i
v
e
fo
r
rat
e
o
f
class
i
fica
t
i
o
n
a
ccur
acy.
The
i
n
cre
a
se
o
f
num
ber
of
i
t
e
ms,
in
cre
ased
t
h
e
r
at
e of c
l
a
ssific
a
tion
acc
urac
y.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJERE
I
S
S
N
:
2252-
88
22
T
h
e Im
pac
t of
D
i
f
f
ere
n
t
M
i
ssi
ng D
a
ta
H
a
n
d
l
i
n
g
Me
t
hods
o
n
D
I
NA M
ode
l (Se
ç
i
l
Ö
m
ü
r Sü
nb
ü
l
)
85
It
w
as
o
bse
r
ve
d
t
h
at
a
vera
ge
R
MS
E
A
v
a
l
ue
s
w
h
ic
h
w
e
r
e
obt
a
i
ne
d
f
or
M
A
R
w
ere
l
o
w
e
r
and
rates
of
class
i
fica
t
i
o
n
a
ccur
acie
s
w
er
e
h
i
g
h
er
t
h
a
n
the
aver
ag
e
RMSEA
va
lues
w
hi
c
h
w
er
e
ob
ta
ine
d
f
or
M
CAR.
These
resu
lts
a
re
a
lso
c
o
ns
i
s
t
e
nt
w
i
t
h
t
he
l
it
er
ature.
I
n
a
ddit
i
on
t
o
t
ha
t,
f
o
r
m
any
c
o
n
d
it
i
ons
it
w
a
s
o
b
s
e
rved
t
h
at
,
a
v
era
g
e
RM
SEA
v
a
lu
e
s
w
h
i
ch
w
e
r
e
o
b
t
a
i
n
e
d
f
ro
m
mis
s
in
g
d
a
t
a
ha
n
d
l
i
ng
m
e
t
h
od
s
w
e
re
l
ow
a
nd
r
a
te
o
f
class
i
fica
t
i
o
n
a
ccur
acie
s
w
ere
hi
gh.
A
mon
g
t
he
m
issi
n
g
d
ata
ha
n
d
l
in
g
me
t
h
od
s,
h
i
g
h
e
r
av
erag
e
RM
SEA
val
u
es
a
nd
low
e
r
ra
t
e
o
f
c
l
as
s
i
f
i
c
a
t
i
on
a
ccur
a
cies
w
er
e
obse
r
ve
d
fo
r
IN
m
et
hod
.
Th
e
re
su
lt
s
o
f
o
t
h
er
m
et
h
o
d
s
w
e
r
e
se
e
m
e
d to
b
e c
l
ose
r
to
eac
h ot
her.
This
re
sul
t
i
s
als
o
con
s
i
s
t
e
n
t w
i
th t
he
l
i
t
era
t
ure
[2
1],[23],[3
6
].
5.
CONCL
U
S
ION
A
s
a
r
esul
t,
m
i
ssi
ng
r
a
tes
a
f
fe
cte
d
s
a
nd
g
pa
ra
me
t
e
r
esti
m
a
t
i
o
n
s
a
n
d
c
l
a
ssi
fi
cat
ion
ac
cu
ra
c
i
es
f
o
r
a
l
l
me
tho
d
s.
A
ls
o, the r
es
ul
t
s
o
f t
h
e stu
d
y
show
e
d
t
ha
t perfor
m
a
n
ce
of me
th
ods va
r
ie
d acc
ord
i
ng
to m
an
i
p
u
l
a
tio
n
fa
ct
ors
f
o
r
di
ffere
nt
m
issi
n
g
da
t
a
m
ec
ha
n
i
sms.
I
n
th
i
s
s
t
u
d
y
,
i
t
w
a
s
a
i
me
d
t
o
i
n
v
es
t
i
ga
te
t
h
e
i
m
p
a
c
t
o
f
di
ffe
re
nt m
issi
ng da
ta ha
n
dli
ng m
e
t
h
ods o
n
D
I
NA
mode
l
par
a
m
e
ter
esti
m
a
t
io
n a
nd c
l
a
s
sific
a
t
i
o
n c
o
n
s
iste
n
c
y.
Fu
rt
h
e
r
st
u
d
i
e
s
wi
ll
b
e
co
nduc
t
e
d
f
o
r
oth
e
r
c
o
gni
t
i
v
e
d
i
a
gn
o
s
ti
c
mode
l
s
i
n
v
es
t
i
ga
tio
ns
w
ith
d
iffe
ren
t
num
ber
of
a
t
t
r
i
bu
tes,
miss
i
n
g
r
ates a
n
d
m
issi
ng da
t
a
m
ec
hani
sm
s.
REFE
RENCES
[1]
J.
P
.
Lei
ghton
a
n
d
M
.
J
.
G
ierl,
“W
hy
c
og
n
i
tive
d
iag
nos
ti
c
ass
e
s
sm
ent,”
C
o
g
n
itiv
e
Dia
g
n
o
s
t
i
c
As
se
s
s
m
e
n
t fo
r
Ed
uca
t
io
n: T
h
eo
r
y
an
d
A
p
p
l
i
c
ation
s
,
pp.
3
–
18,
200
7.
[2]
K.
K
.
T
a
ts
uok
a,
“
Rul
e
s
p
ace:
A
n
ap
pro
a
c
h
f
or
d
eali
n
g
wit
h
m
isco
ncep
tio
ns
b
as
ed
o
n
i
t
em
r
esp
o
n
s
e
t
h
eo
ry,”
Jou
r
n
a
l o
f
Ed
ucat
io
nal
M
e
as
u
r
em
ent
,
v
o
l/is
su
e
:
2
0(4
)
,
p
p
.
3
45
–354,
1
9
8
3
.
[3]
R.
H
enson
and
J.
D
ouglas,
“T
es
t
construct
i
on
f
o
r
cognitive
di
ag
no
si
s,”
Ap
p
l
ied
Ps
ycho
l
ogica
l
M
e
as
ur
ement
,
vo
l/issue:
2
9(4),
pp
.
2
6
2
-2
77
,
2005
.
[4]
L.
V
.
D
i
B
e
llo,
et al.
,
“
R
evi
e
w
of
c
o
gniti
vel
y
d
i
a
gn
ostic
a
s
s
essm
ent
an
d
a
sum
m
ary
o
f
p
s
y
c
h
o
m
etri
c
m
o
dels,”
Ha
nd
boo
k of S
t
a
t
is
ti
cs
Psych
omet
r
i
cs
,
vol.
2
6
,
pp.
9
7
9
–
1
0
3
0
,
2
0
07.
[5]
A.
A
.
Ru
pp
and
J
.
L
.
Tem
p
lin
,
“The
e
ff
ects
of
Q
-m
at
rix
missp
eci
fi
catio
n
on
p
a
ram
e
t
e
r
es
tim
a
tes
and
cl
ass
i
ficat
ion
accur
acy
i
n
th
e DINA
m
od
el,
”
Ed
ucat
io
nal
a
nd Ps
ycho
l
og
ical M
e
as
urem
ent
,
v
o
l/is
su
e
:
6
8(1
)
,
pp.
7
8-9
6
,
2
00
8.
[6]
J.
d
e
la
T
orre
a
n
d
J
.
A.
D
ou
gl
as,
“Hig
her-o
rd
er
l
aten
t
t
r
ait
m
o
dels
f
or
c
ognitive
diagnosi
s,
”
P
s
ycho
m
et
rika
,
vo
l/issue:
6
9(3),
p
p
.
3
3
3
-3
53
,
2004
.
[7]
L.
V
.
DiBello,
et al.
,
“
U
nif
i
e
d
c
o
g
n
i
ti
ve/
p
s
y
ch
om
etri
c
d
i
agno
stic
a
s
s
es
s
m
en
t
li
ke
l
i
h
ood
-based
c
l
a
ss
ificat
io
n
tech
niq
u
es
,” i
n P.
D
. Nich
o
l
s
,
et
a
l
.
,
C
og
n
itivel
y Di
ag
nosti
c
Asses
s
m
e
nt,
pp
.
3
6
1
–
3
8
9,
1
9
95.
[8]
E.
H
.
Haerte
l
,
“
U
s
in
g
res
t
ri
cted
l
at
ent
c
l
as
s
m
odel
s
t
o
m
a
p
th
e
s
k
i
l
l
s
t
r
u
c
t
u
r
e
o
f
a
c
h
i
e
v
e
m
e
n
t
i
t
e
m
s
,
”
Jo
ur
nal
of
Ed
uca
t
io
na
l M
e
as
ur
e
m
ent
,
v
o
l
. 26
,
p
p.
333
-35
2
,
198
9.
[9]
S
.
M
.
C.
H
art
z
,
“
A
B
ayesian
f
r
a
m
e
w
ork
f
o
r
the
un
if
ied
m
o
d
e
l
for
a
ssessing
c
og
nitive
abil
i
t
i
e
s
:
B
lending
theor
y
with
p
racti
cality
,
”
(Unp
ub
li
she
d
d
o
c
to
ra
l
d
i
ssertati
o
n
)
,
Univ
er
s
i
t
y
o
f
Il
li
nois
at
U
rb
ana-Cham
p
a
ign
,
U
rb
ana-
Ch
a
m
p
a
ig
n,
IL,
2
00
2.
[10]
B.
W
.
Junker
a
nd
K
.
S
ijtsma
,
“Cog
ni
ti
ve
a
ss
essment
model
s
w
ith
f
e
w
as
su
m
p
ti
on
s,
a
n
d
c
on
nect
io
ns
w
it
h
no
np
ara
m
et
ric item
res
pon
se theo
r
y,”
Appli
e
d
Psych
ol
ogi
cal
M
e
asu
r
emen
t
,
vol/is
sue:
25(3),
pp. 258–272
, 2001.
[11]
A.
A
.
Ru
pp,
et
a
l
.
,
“
D
i
a
gno
stic
m
easurem
en
t:
T
h
e
ory
,
M
e
t
ho
d
s
,
an
d
App
l
i
cations
,
”
New
York
:
Guilf
o
rd
P
ress,
20
10
.
[12]
J
.
d
e
l
a
T
o
r
r
e
a
n
d
Y
.
S
.
L
e
e
,
“
A
n
o
t
e
o
n
t
h
e
i
n
v
a
r
i
a
n
c
e
o
f
t
h
e
DIN
A
m
od
e
l
p
aramet
ers,”
Jo
ur
nal
of
Ed
ucat
io
n
a
l
Me
asu
r
e
m
e
n
t
,
v
o
l
/
i
s
s
u
e:
4
7
(
1),
pp.
1
1
5–1
27
,
2
010.
[13]
Ru
bin
D.
B
.
,
“
In
fe
re
nc
e
a
n
d miss
in
d d
a
ta
,
”
Bi
om
et
ri
ka,
vol/
i
ss
ue: 63
(3),
p
p
.
5
8
1
–
5
9
2
,
1
97
6.
[14]
R.
J
.
A.
L
it
tl
e
an
d
D.
B
.
Ru
b
i
n
,
“
Statis
t
i
cal
A
nalys
i
s
wit
h
M
is
sing
D
a
ta,
”
2
nd
e
d
.
,
N
e
w
Y
o
r
k
,
J
o
h
n
W
i
l
e
y
&
S
o
n
s
,
20
02
.
[15]
P.
D
.
A
l
l
i
son
, “M
i
s
s
ing
Da
ta,” T
h
o
u
s
a
n
d Oa
ks
,
CA,
Sa
ge
P
u
b
lic
a
t
io
ns,
2
0
01.
[16]
R.
J
.
A
.
L
i
ttl
e,
“
Regres
sion
w
i
t
h
missing
X
's:
A
revi
ew,”
Jou
r
n
a
l
o
f
t
h
e
Am
e
r
ican
St
atisti
cal A
ssocia
t
i
o
n
,
vol.
87,
pp
.
1
227
-12
3
7
, 1
992
.
[17]
D.
B
.
R
ubin,
“
Mul
t
i
p
l
e
I
m
putatio
n
f
o
r
Non
r
esp
onse
i
n
S
u
r
veys
,
”
N
e
w
Y
o
rk,
J
o
hn Wi
ley
&
S
o
n
s
,
198
7.
[18]
J. L.
S
c
ha
f
e
r,
“
A
n
alysis o
f In
comp
l
e
t
e
Mu
lti
v
a
r
i
at
e Data,” New
Yo
rk, Ch
a
pman
&
Hal
l
,
1
99
7.
[19]
C.
A
.
Bernaards
a
nd
K
.
S
ijtsma,
“Influence
of
i
mpu
t
at
i
on
and
EM
m
e
t
h
ods
o
n
f
act
or
a
nal
y
sis
w
h
en
ite
m
no
nres
pon
se
i
n
q
u
est
i
o
n
n
a
ire
dat
a
i
s
no
n
i
g
n
o
r
abl
e
,
”
Mu
lti
variate
Beh
a
vi
or
al Resea
r
ch
,
vol/is
sue:
3
5(3),
pp.
321–
36
4,
200
0.
[20]
C
.
K
.
E
n
d
e
r
s
,
“
A
p
r
i
m
e
r
o
n
m
a
x
i
m
u
m
l
i
k
e
l
i
h
o
o
d
a
l
g
o
r
i
t
h
m
s
a
v
a
i
l
a
b
l
e
f
o
r
use
wit
h
m
issin
g
d
ata,”
Struc
t
u
r
al
Equ
a
t
i
on
Mo
de
lin
g
,
vol.
8
,
pp
.
128-1
4
1
,
2
0
0
1
.
[21]
R
.
J
.
D
e
A
y
a
l
a
,
et al
.
,
“
T
h
e
impact
o
f
omitted
response
s
on
t
h
e
a
cc
uracy
of
a
bili
ty
e
s
t
i
ma
t
i
on
i
n
i
t
e
m
r
e
s
po
ns
e
theory,”
Jou
r
n
a
l of
Ed
uca
t
io
nal
M
e
as
urem
ent
, v
o
l/issue:
38
(
3), p
p. 21
3
–
2
3
4
, 2
00
1.
[22]
Y.
D
on
g
an
d
C.
Y
.
J.
P
en
g,
“
P
r
i
n
ci
p
l
ed
m
is
si
ng
data
m
et
ho
ds
f
o
r
r
esear
chers
,
”
Sp
ri
ng
e
r
Pl
u
s
,
v
o
l/issue:
2
(1),
p
p.
22
2,
201
3.
[23]
H.
F
in
ch,
“
E
stim
atio
n
of
i
t
e
m
resp
on
se
t
h
e
ory
p
a
ram
e
ters
i
n
th
e
p
res
e
nce
of
m
issin
g
d
at
a
,
”
Jo
urn
a
l
o
f
Ed
uca
t
io
nal
Me
asu
r
e
m
e
n
t
,
v
o
l
.
45
,
p
p.
2
25
–2
45
, 20
0
8
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2252-
8822
IJERE
V
ol
.
7,
N
o.
1,
Ma
r
ch 201
8
: 77
– 86
86
[24]
J
.
R
.
V
.
G
i
n
k
e
l
,
et al.
,
“
T
w
o
-
w
a
y
i
m
p
u
t
a
t
i
o
n
:
A
B
a
y
e
s
i
a
n
m
e
t
h
o
d
f
o
r
e
s
t
i
m
a
t
i
n
g
m
i
s
s
i
n
g
s
cores
in
t
est
s
a
n
d
qu
est
i
on
na
i
r
es, and an
a
c
c
u
r
ate
a
p
pro
x
im
a
t
io
n
,
”
Co
mp
ut
a
t
i
o
n
a
l
Statisti
cs
&
Dat
a
An
alysis
,
vo
l.
5
1
,
p
p
.
4
01
3–
40
2
7
,
20
07
.
[25]
C
.
Y
.
J
.
P
e
n
g
,
et
a
l
.
,
“
A
d
v
ances
i
n
mi
ssing
d
ata
m
e
t
hod
s
and
im
p
l
icatio
ns
f
or
e
ducat
io
nal
research,
”
Real D
a
ta
Anal
y
s
is
,
p
p
.
31–78
,
2
00
6.
[26]
J.
L
.
Pe
ug
h
a
n
d
C.
K
.
En
de
rs
,
“M
issin
g
d
a
t
a
in
e
du
c
a
t
io
na
l
re
se
ar
ch:
A
rev
i
ew
o
f
repo
rting
p
r
actices
a
n
d
su
gg
esti
on
s
f
o
r imp
r
ov
em
e
n
t,
”
Revi
ew
of
Ed
ucatio
na
l R
e
sea
r
ch
,
v
o
l.
7
4
, p
p.
52
5
−5
56
,
2
00
4
.
[27]
L.
T
.
DeCarlo,
“
O
n
t
he
a
nal
y
sis
of
fract
io
n
sub
t
ract
ion
d
a
ta:
T
h
e
D
IN
A
mo
del
,
c
lass
ifi
c
at
io
n
,
l
at
e
n
t
clas
s
sizes
,
and
the Q-
mat
r
ix,
”
Ap
pl
ied Psych
ol
o
g
ical
M
e
a
s
urement
,
vol.
35
,
pp
. 8
-26
,
2
0
1
1
.
[28]
J.
d
e
la
T
orre,
“
A
n
e
m
pi
ricall
y
b
ased
m
et
ho
d
o
f
Q
-m
a
t
ri
x
v
a
lid
a
t
i
o
n
f
o
r
t
h
e
D
I
N
A
m
o
d
e
l
:
D
e
v
e
l
o
p
m
e
n
t
a
n
d
app
l
i
c
at
io
n
s
,”
Jo
u
r
n
a
l of Ed
ucation
a
l M
e
as
ur
eme
n
t
,
v
o
l/i
s
s
u
e
:
45(4
)
,
p
p.
343
-36
2
,
20
08.
[29]
J.
d
e
la
T
o
r
re
a
nd
J.
A
.
Do
ug
l
a
s,
“
M
o
de
l
ev
aluatio
n
and
m
u
ltip
l
e
st
ra
teg
i
es
i
n
co
g
n
i
t
i
v
e
d
i
agn
o
sis:
A
n
an
alysis
o
f
f
r
actio
n
subtract
io
n d
a
ta,”
P
s
ych
omet
ri
ka,
vol/iss
u
e:
7
3
(
4),
pp.
5
9
5
-6
24,
2
0
0
8
.
[30]
J
.
d
e
l
a
T
o
r
r
e
,
et al.
,
“
F
acto
r
s
aff
e
ct
in
g
th
e
i
t
e
m
p
aram
eter
e
s
t
i
m
a
tio
n
and
cl
ass
i
fi
catio
n
accur
acy
o
f
th
e
DIN
A
mo
de
l,”
A
ppli
e
d
P
s
ycho
l
o
g
i
c
a
l
Mea
s
ur
emen
t,
v
o
l.
4
7,
p
p
.
2
2
7
-2
49
,
20
10
.
[31]
R.
A
.
Hens
on
,
et
a
l
.
,
“Defi
n
i
n
g
a
f
a
m
ily
o
f
cog
n
i
t
i
v
e
d
i
ag
n
o
sis
m
o
del
s
u
s
i
ng
l
og-l
i
n
ear
m
o
d
els
wit
h
l
ate
n
t
vari
ables
,
”
P
s
ycho
m
et
ri
ka,
vo
l
.
7
4
, pp
. 1
91
-21
0
, 2
00
9.
[32]
Y.
S
.
L
ee,
et
a
l
.
,
“A
c
ogn
itive
d
i
agnos
tic
m
odel
ing
of
a
t
t
ribu
t
e
m
astery
i
n
Mass
achu
s
et
ts
,
Minneso
ta,
an
d
th
e
U
S
nat
i
o
n
al
s
am
p
l
e us
in
g
t
h
e T
I
MSS
20
07
,”
In
t
e
rna
t
iona
l Journal of Tes
t
ing
,
vo
l/issu
e:
11(2),
pp. 144
–177, 2011.
[33]
Y.
L
i
u
,
et al.
,
“Tes
ti
ng pers
on
fit
i
n
c
o
g
n
i
ti
ve d
i
a
g
n
o
s
i
s
,
”
Appli
e
d Psych
ol
ogi
ca
l
M
e
a
s
u
r
em
ent,
vol/issue:
3
3(8)
,
pp.
57
9-5
98,
2
0
0
9
.
[34]
S
.
D
ai,
“
I
n
v
estigati
on
o
f
miss
in
g
res
p
o
n
s
e
s
i
n
i
m
p
l
e
men
t
atio
n
o
f
cognitive
di
agnosti
c
m
odel
s,”
(Unpubl
i
shed
do
cto
r
a
l
d
iss
e
rtat
io
n),
I
n
d
i
a
na
U
ni
versity
,
2
017
.
[35]
X.
X
u
and
M
.
v
on
Davier,
“C
ognitive
diagnosis
f
o
r
NAEP
profi
c
ie
nc
y
da
ta
,”
ET
S
Res
e
ar
ch R
e
po
rt
Series
,
vo
l/issue:
2
006
(1),
pp.
i–
2
5
,
2
00
6
.
[36]
K.
S
i
jtsma
a
nd
L
.
Va
n
d
e
r
Ark
,
“
A.
I
nv
e
s
t
i
ga
tio
n
a
n
d
tre
a
t
me
nt
of
m
issi
ng
it
e
m
s
cores
in
t
es
t
an
d
q
u
es
tio
nn
aire
dat
a
,
”
Mul
t
ivar
iate Beha
viora
l
Resear
ch
,
v
o
l
/issu
e:
3
8(4
)
,
p
p
. 5
05
–5
28
, 20
0
3
.
B
I
OG
RAP
HY
O
F
A
U
T
H
O
R
S
ecil
Omu
r
S
u
n
bu
l
is
a
n
A
s
s
i
st
ant
P
r
o
f
ess
o
r
in
M
ers
i
n
Univ
ersty
i
n
t
h
e
D
e
partm
e
n
t
o
f
M
easu
r
em
ent
an
d
Ev
aluat
i
o
n
i
n
Edu
cati
on.
S
h
e
r
eci
ved
h
e
r
BC
s
d
e
gree
(
20
04)
i
n
Ank
a
ra
a
t
H
acettep
e
U
n
i
versi
t
y
,
F
acul
t
y
of
E
d
u
cati
on
and
M
S
c
an
d
P
h
D
degr
ee
f
r
o
m
D
epartm
en
t
of
M
easu
r
em
ent
and
E
v
alu
a
ti
on
i
n
Edu
cati
o
n
,
M
ersi
n
Un
iversit
y
.
Her
m
a
i
n
interests
ar
e
E
ducat
io
nal
Meas
urem
ent
,
I
tem
Res
pon
se
T
heory
,
C
og
niti
ve
D
iagn
o
stic
M
ode
l
s
and
Statis
tica
l
Program
m
ing.
Evaluation Warning : The document was created with Spire.PDF for Python.