La en a iable modeling RANCH
Ru h Koole
29-04-2020
We ha e impo ed he da a o RANCH om he SAS ile.
Da a con ains 3207 ows and 949 a iables.
In he RANCH s udy men al heal h was measu ed using he pa en - a ed e sion o he S eng hs and
Di icul ies Ques ionnai e (SDQ). The SDQ is a 25 i em beha iou al sc eening ques ionnai e consis ing o
i e subscales (emo ional symp oms, conduc p oblems, hype ac i i y/ina en ion, pee ela ionship p oblems
and p osocial beha iou ). A o al SDQ sco e can be compu ed using 20 o hese a iables.
## E o in p y ::whe e(obj_name) : leng h(name) == 1 is no TRUE
Da a p epa a ion o analysis
The 20 SDQ a iables ha a e used o he compu a ion o he o al SDQ sco e a e showed in he able
below.
a iable_name a iable_label
p_20_7neg Obedien
p_20_11neg F iendly
p_20_14neg Liked
p_20_21neg Thinke
p_20_25neg Good a en ion
p_20_2pos Res less
p_20_3pos Headaches
p_20_5pos Tempe s
p_20_6pos Soli a y
p_20_8pos Wo ie
p_20_10pos Fidge
p_20_12pos Figh s
p_20_13pos Unhappy
p_20_15pos Lacks concen a ion
p_20_16pos Ne ous
p_20_18pos Lies_chea s
p_20_19pos Picked on
p_20_22pos S eals
p_20_23pos P e e s adul s
p_20_24pos Fea ul
1
Table 1: Gene al s a is ics on SDQ sco e
alue
Mean 9.785
S d.De 5.693
Min 0.000
Q1 6.000
Median 9.000
Q3 13.000
Max 34.000
MAD 5.930
IQR 7.000
CV 0.582
Skewness 0.652
SE.Skewness 0.052
Ku osis 0.134
N.Valid 2237.000
Pc .Valid 69.754
Based on he guide o he GGD, he SDQ subscales can only be compu ed in case 3 o mo e ques ions
ega ding ha subscale ha e been comple ed. The o al SDQ sco e can only be compu ed i all subscales
ha e been compu ed. Since he o SDQ sco es ha e al eady been compu ed, we will emo e all ows o
which he o al SDQ sco e is a missing alue.
The cleaned da a hen con ains 2237 ows and 949 a iables.
Fo applying he la en a iable modeling, we make a subse o he da a con aining he 20 a iables ha a e
used o compu e he o al SDQ sco e.
Fac o analysis
Be o e we apply ac o analysis, all missing alues in his da ase a e eplaced wi h he mean o he column
o all i ems.
Be o e applying ac o analysis, we compu e he co ela ion ma ix.
2
Table 2: Co ela ion ma ix o SDQ a iables
Obedien F iendly Liked Thinke Good a en ion Res less Headaches Tempe s Soli a y Wo ie Fidge Figh s Unhappy Lacks concen a ion Ne ous Lies_chea s Picked on S eals P e e s adul s Fea ul
Obedien 1.00 0.12 0.23 0.29 0.25 0.26 0.03 0.30 -0.03 0.10 0.22 0.24 0.13 0.24 0.10 0.29 0.15 0.13 0.07 0.07
F iendly 0.12 1.00 0.33 0.12 0.14 0.05 0.04 0.06 0.16 0.10 0.09 0.15 0.14 0.07 0.09 0.09 0.18 0.13 0.13 0.05
Liked 0.23 0.33 1.00 0.20 0.23 0.09 0.08 0.16 0.15 0.19 0.13 0.23 0.16 0.17 0.13 0.15 0.32 0.16 0.19 0.11
Thinke 0.29 0.12 0.20 1.00 0.44 0.26 0.02 0.21 0.05 0.06 0.25 0.14 0.10 0.38 0.12 0.25 0.16 0.11 0.03 0.07
Good a en ion 0.25 0.14 0.23 0.44 1.00 0.25 0.05 0.17 0.07 0.12 0.24 0.16 0.12 0.57 0.20 0.25 0.19 0.12 0.10 0.12
Res less 0.26 0.05 0.09 0.26 0.25 1.00 0.06 0.33 -0.02 0.15 0.62 0.22 0.14 0.39 0.13 0.26 0.15 0.13 0.12 0.16
Headaches 0.03 0.04 0.08 0.02 0.05 0.06 1.00 0.18 0.07 0.27 0.07 0.06 0.24 0.10 0.17 0.06 0.13 0.01 0.12 0.14
Tempe s 0.30 0.06 0.16 0.21 0.17 0.33 0.18 1.00 0.04 0.21 0.28 0.29 0.26 0.24 0.17 0.28 0.21 0.12 0.13 0.18
Soli a y -0.03 0.16 0.15 0.05 0.07 -0.02 0.07 0.04 1.00 0.20 0.04 0.05 0.18 0.06 0.14 0.01 0.19 0.03 0.19 0.15
Wo ie 0.10 0.10 0.19 0.06 0.12 0.15 0.27 0.21 0.20 1.00 0.19 0.19 0.39 0.19 0.32 0.09 0.23 0.08 0.16 0.34
Fidge 0.22 0.09 0.13 0.25 0.24 0.62 0.07 0.28 0.04 0.19 1.00 0.22 0.16 0.39 0.17 0.23 0.15 0.12 0.07 0.13
Figh s 0.24 0.15 0.23 0.14 0.16 0.22 0.06 0.29 0.05 0.19 0.22 1.00 0.17 0.23 0.13 0.33 0.20 0.21 0.12 0.11
Unhappy 0.13 0.14 0.16 0.10 0.12 0.14 0.24 0.26 0.18 0.39 0.16 0.17 1.00 0.16 0.27 0.18 0.31 0.07 0.19 0.29
Lacks concen a ion 0.24 0.07 0.17 0.38 0.57 0.39 0.10 0.24 0.06 0.19 0.39 0.23 0.16 1.00 0.26 0.28 0.23 0.13 0.14 0.16
Ne ous 0.10 0.09 0.13 0.12 0.20 0.13 0.17 0.17 0.14 0.32 0.17 0.13 0.27 0.26 1.00 0.12 0.17 0.06 0.10 0.35
Lies_chea s 0.29 0.09 0.15 0.25 0.25 0.26 0.06 0.28 0.01 0.09 0.23 0.33 0.18 0.28 0.12 1.00 0.21 0.29 0.10 0.09
Picked on 0.15 0.18 0.32 0.16 0.19 0.15 0.13 0.21 0.19 0.23 0.15 0.20 0.31 0.23 0.17 0.21 1.00 0.12 0.23 0.23
S eals 0.13 0.13 0.16 0.11 0.12 0.13 0.01 0.12 0.03 0.08 0.12 0.21 0.07 0.13 0.06 0.29 0.12 1.00 0.09 0.02
P e e s adul s 0.07 0.13 0.19 0.03 0.10 0.12 0.12 0.13 0.19 0.16 0.07 0.12 0.19 0.14 0.10 0.10 0.23 0.09 1.00 0.18
Fea ul 0.07 0.05 0.11 0.07 0.12 0.16 0.14 0.18 0.15 0.34 0.13 0.11 0.29 0.16 0.35 0.09 0.23 0.02 0.18 1.00
3
We will apply wo some es s o see i he da ase is sui able o ac o analysis.
## # Is he da a sui able o Fac o Analysis?
##
## - KMO: The Kaise , Meye , Olkin (KMO) measu e o sampling adequacy sugges s
ha da a seems app op ia e o ac o analysis (KMO = 0.83).
## - Sphe ici y: Ba le 's es o sphe ici y sugges s ha he e is
su icien signi ican co ela ion in he da a o ac o analaysis (Chisq(210)
= 8705.01, p < .001).
We will use ac o analysis using he ac anal unc ion in R.
1 ac o
##
## Call:
## ac anal(x = subse ( anch_MH_ o _FA, selec = -s udno), ac o s = 1, sco es
= " eg ession", o a ion = " a imax")
##
## Uniquenesses:
## Obedien F iendly Liked Thinke
## 0.806 0.939 0.846 0.781
## Good a en ion Res less Headaches Tempe s
## 0.711 0.697 0.954 0.753
## Soli a y Wo ie Fidge Figh s
## 0.971 0.841 0.703 0.809
## Unhappy Lacks concen a ion Ne ous Lies_chea s
## 0.830 0.613 0.852 0.777
## Picked on S eals P e e s adul s Fea ul
## 0.808 0.928 0.926 0.884
##
## Loadings:
## Fac o 1
## Obedien 0.440
## F iendly 0.247
## Liked 0.392
## Thinke 0.468
## Good a en ion 0.538
## Res less 0.551
## Headaches 0.214
## Tempe s 0.497
## Soli a y 0.170
## Wo ie 0.399
## Fidge 0.545
## Figh s 0.437
## Unhappy 0.413
## Lacks concen a ion 0.622
## Ne ous 0.385
## Lies_chea s 0.472
## Picked on 0.438
## S eals 0.267
## P e e s adul s 0.273
## Fea ul 0.341
4
##
## Fac o 1
## SS loadings 3.573
## P opo ion Va 0.179
##
## Tes o he hypo hesis ha 1 ac o is su icien .
## The chi squa e s a is ic is 3305.25 on 170 deg ees o eedom.
## The p- alue is 0
2 ac o s
##
## Call:
## ac anal(x = subse ( anch_MH_ o _FA, selec = -s udno), ac o s = 2, sco es
= " eg ession", o a ion = "none")
##
## Uniquenesses:
## Obedien F iendly Liked Thinke
## 0.787 0.931 0.840 0.701
## Good a en ion Res less Headaches Tempe s
## 0.643 0.633 0.872 0.759
## Soli a y Wo ie Fidge Figh s
## 0.886 0.619 0.656 0.819
## Unhappy Lacks concen a ion Ne ous Lies_chea s
## 0.636 0.541 0.776 0.768
## Picked on S eals P e e s adul s Fea ul
## 0.753 0.931 0.881 0.750
##
## Loadings:
## Fac o 1 Fac o 2
## Obedien 0.428 -0.174
## F iendly 0.243 0.102
## Liked 0.387 0.102
## Thinke 0.466 -0.287
## Good a en ion 0.541 -0.254
## Res less 0.549 -0.255
## Headaches 0.229 0.275
## Tempe s 0.490
## Soli a y 0.182 0.285
## Wo ie 0.436 0.437
## Fidge 0.544 -0.218
## Figh s 0.426
## Unhappy 0.444 0.409
## Lacks concen a ion 0.630 -0.249
## Ne ous 0.404 0.247
## Lies_chea s 0.458 -0.147
## Picked on 0.445 0.221
## S eals 0.257
## P e e s adul s 0.277 0.205
## Fea ul 0.365 0.342
##
## Fac o 1 Fac o 2
## SS loadings 3.637 1.180
5
## P opo ion Va 0.182 0.059
## Cumula i e Va 0.182 0.241
##
## Tes o he hypo hesis ha 2 ac o s a e su icien .
## The chi squa e s a is ic is 2030.43 on 151 deg ees o eedom.
## The p- alue is 0
0.2 0.3 0.4 0.5 0.6
−0.2 0.0 0.2 0.4
Fac o 1
Fac o 2
Obedien
F iendly Liked
Thinke
Good a en ion
Res less
Headaches
Tempe s
Soli a y
Wo ie
Fidge
Figh s
Unhappy
Lacks concen a ion
Ne ous
Lies_chea s
Picked on
S eals
P e e s adul s
Fea ul
−1 0 1 2 3
−2 −1 0 1 2 3
Fac o 1
Fac o 2
3 ac o s
##
## Call:
## ac anal(x = subse ( anch_MH_ o _FA, selec = -s udno), ac o s = 3, sco es
= " eg ession", o a ion = "none")
##
## Uniquenesses:
## Obedien F iendly Liked Thinke
## 0.814 0.909 0.800 0.662
## Good a en ion Res less Headaches Tempe s
## 0.410 0.296 0.874 0.753
## Soli a y Wo ie Fidge Figh s
## 0.880 0.627 0.467 0.832
## Unhappy Lacks concen a ion Ne ous Lies_chea s
## 0.634 0.492 0.781 0.800
## Picked on S eals P e e s adul s Fea ul
## 0.741 0.939 0.880 0.759
##
## Loadings:
## Fac o 1 Fac o 2 Fac o 3
## Obedien 0.420
## F iendly 0.207 0.211
## Liked 0.338 0.273 -0.105
## Thinke 0.477 -0.329
6
## Good a en ion 0.571 -0.513
## Res less 0.687 -0.402 0.265
## Headaches 0.186 0.259 0.156
## Tempe s 0.473 0.135
## Soli a y 0.132 0.316
## Wo ie 0.369 0.414 0.255
## Fidge 0.636 -0.291 0.208
## Figh s 0.396
## Unhappy 0.372 0.422 0.222
## Lacks concen a ion 0.655 -0.279
## Ne ous 0.356 0.296
## Lies_chea s 0.441
## Picked on 0.388 0.327
## S eals 0.239
## P e e s adul s 0.242 0.233
## Fea ul 0.319 0.315 0.199
##
## Fac o 1 Fac o 2 Fac o 3
## SS loadings 3.589 1.252 0.808
## P opo ion Va 0.179 0.063 0.040
## Cumula i e Va 0.179 0.242 0.282
##
## Tes o he hypo hesis ha 3 ac o s a e su icien .
## The chi squa e s a is ic is 1237.02 on 133 deg ees o eedom.
## The p- alue is 2.76e-178
7
0.2 0.3 0.4 0.5 0.6 0.7
−0.4 −0.2 0.0 0.2 0.4
Fac o 1
Fac o 2
Obedien
F iendly
Liked
Thinke
Good a en ion
Res less
Headaches
Tempe s
Soli a y
Wo ie
Fidge
Figh s
Unhappy
Lacks concen a ion
Ne ous
Lies_chea s
Picked on
S eals
P e e s adul s
Fea ul
−1 0 1 2 3
−2 −1 0 1 2 3
Fac o 1
Fac o 2
0.2 0.3 0.4 0.5 0.6 0.7
−0.4 −0.2 0.0 0.2
Fac o 1
Fac o 3
Obedien
F iendly Liked
Thinke
Good a en ion
Res less
Headaches Tempe s
Soli a y
Wo ie Fidge
Figh s
Unhappy
Lacks concen a ion
Ne ous
Lies_chea s
Picked on
S eals
P e e s adul s
Fea ul
−1 0 1 2 3
−2 −1 0 1 2 3
Fac o 1
Fac o 3
−0.4 −0.2 0.0 0.2 0.4
−0.4 −0.2 0.0 0.2
Fac o 2
Fac o 3
Obedien F iendly
Liked
Thinke
Good a en ion
Res less
Headaches
Tempe s
Soli a y
Wo ie
Fidge
Figh s
Unhappy
Lacks concen a ion
Ne ous
Lies_chea s
Picked on
S eals
P e e s adul s
Fea ul
−2 −1 0 1 2 3
−2 −1 0 1 2 3
Fac o 2
Fac o 3
8
4 ac o
##
## Call:
## ac anal(x = subse ( anch_MH_ o _FA, selec = -s udno), ac o s = 4, sco es
= " eg ession", o a ion = " a imax")
##
## Uniquenesses:
## Obedien F iendly Liked Thinke
## 0.748 0.854 0.718 0.677
## Good a en ion Res less Headaches Tempe s
## 0.314 0.320 0.866 0.725
## Soli a y Wo ie Fidge Figh s
## 0.880 0.595 0.458 0.730
## Unhappy Lacks concen a ion Ne ous Lies_chea s
## 0.644 0.456 0.725 0.704
## Picked on S eals P e e s adul s Fea ul
## 0.725 0.854 0.879 0.705
##
## Loadings:
## Fac o 1 Fac o 2 Fac o 3 Fac o 4
## Obedien 0.409 0.210 0.199
## F iendly 0.142 0.343
## Liked 0.214 0.462 0.147
## Thinke 0.275 0.166 0.469
## Good a en ion 0.108 0.197 0.794
## Res less 0.155 0.784 0.185
## Headaches 0.361
## Tempe s 0.234 0.342 0.314
## Soli a y 0.320
## Wo ie 0.618 0.101 0.111
## Fidge 0.128 0.148 0.682 0.195
## Figh s 0.147 0.457 0.189
## Unhappy 0.553 0.207
## Lacks concen a ion 0.191 0.157 0.312 0.621
## Ne ous 0.481 0.184
## Lies_chea s 0.465 0.213 0.179
## Picked on 0.371 0.352 0.106
## S eals 0.370
## P e e s adul s 0.282 0.196
## Fea ul 0.526 0.116
##
## Fac o 1 Fac o 2 Fac o 3 Fac o 4
## SS loadings 1.863 1.589 1.501 1.469
## P opo ion Va 0.093 0.079 0.075 0.073
## Cumula i e Va 0.093 0.173 0.248 0.321
##
## Tes o he hypo hesis ha 4 ac o s a e su icien .
## The chi squa e s a is ic is 663.69 on 116 deg ees o eedom.
## The p- alue is 1.12e-77
9
−4 −2 0 2 4
0.0 0.6
I em Response Ca ego y Cha ac e is ic Cu es
I em: Soli a y
La en a iable
P obabili y
No ue
Pa ly ue Ce ainly ue
−4 −2 0 2 4
0.0 0.6
I em Response Ca ego y Cha ac e is ic Cu es
I em: Wo ie
La en a iable
P obabili y
No ue
Pa ly ue Ce ainly ue
−4 −2 0 2 4
0.0 0.6
I em Response Ca ego y Cha ac e is ic Cu es
I em: Fidge
La en a iable
P obabili y
No ue
Pa ly ue
Ce ainly ue
−4 −2 0 2 4
0.0 0.6
I em Response Ca ego y Cha ac e is ic Cu es
I em: Figh s
La en a iable
P obabili y
No ue
Pa ly ue
Ce ainly ue
16
−4 −2 0 2 4
0.0 0.6
I em Response Ca ego y Cha ac e is ic Cu es
I em: Unhappy
La en a iable
P obabili y
No ue
Pa ly ue
Ce ainly ue
−4 −2 0 2 4
0.0 0.6
I em Response Ca ego y Cha ac e is ic Cu es
I em: Lacks concen a ion
La en a iable
P obabili y
No ue
Pa ly ue
Ce ainly ue
−4 −2 0 2 4
0.0 0.6
I em Response Ca ego y Cha ac e is ic Cu es
I em: Ne ous
La en a iable
P obabili y
No ue
Pa ly ue Ce ainly ue
−4 −2 0 2 4
0.0 0.6
I em Response Ca ego y Cha ac e is ic Cu es
I em: Lies_chea s
La en a iable
P obabili y
No ue
Pa ly ue
Ce ainly ue
17
−4 −2 0 2 4
0.0 0.6
I em Response Ca ego y Cha ac e is ic Cu es
I em: Picked on
La en a iable
P obabili y
No ue
Pa ly ue
Ce ainly ue
−4 −2 0 2 4
0.0 0.6
I em Response Ca ego y Cha ac e is ic Cu es
I em: S eals
La en a iable
P obabili y
No ue
Pa ly ue
Ce ainly ue
−4 −2 0 2 4
0.0 0.6
I em Response Ca ego y Cha ac e is ic Cu es
I em: P e e s adul s
La en a iable
P obabili y
No ue
Pa ly ue Ce ainly ue
−4 −2 0 2 4
0.0 0.6
I em Response Ca ego y Cha ac e is ic Cu es
I em: Fea ul
La en a iable
P obabili y
No ue
Pa ly ue Ce ainly ue
In I em Response Theo y (IRT) he concep o in o ma ion is used o e lec how p ecisely an i em can
measu e he unde lying ai . G ea e in o ma ion is associa ed wi h g ea e measu emen p ecision. The
in o ma ion is in e sely ela ed o he s anda d e o o he es ima e.
O e he ange o he unde lying ai , an in o ma ion unc ion cu e can be de i ed o each i em o e eal
how measu emen p ecision can a y ac oss di e en le els o he ai .
18
19
−4 −2 0 2 4
123456
Tes In o ma ion Func ion
Abili y
In o ma ion
To al in o ma ion in ( −4 , 4 ): 34.96 ( 85.34 %)
To al in o ma ion in ( 0 , 4 ): 34.96 ( 61.07 %)
Based on he i ed model, we can compu e ac o sco es o each undi idual.
Dis ibu ion la en a iable
La en ai
F equency
−2 −1 0 1 2 3
0 100 200 300 400
20
−2 −1 0 1 2 3
Boxplo la en a iable
21
