Datapipeline using ALSPAC data

1
Data-pipelineusing ALSPAC data
2
Contents

• Introduction to ALSPAC
• Description of the measures
• Preparing my data for the pipeline
• The pipeline (in stata)
• Summarize / Codebook
• Polychoric correlations
• Polychoric PCA
• Loevingers H
• Mokken Scale Procedure
• Options for SPSS users

3
Day 2 Contents

• Introduction to Psychometrics
• Item Response Theory in Stata
• Non-parametric procedures
• Mokken,Description of the measures
• Parametric models
• Singe parameter logistic model (Rasch)
• Two parameter logistic (Lord-Birnbaum)
• An R 2 Detour (a detour to R)
• Running psychometric analyses from Stata
• From Data to PAPER
• Automated IRT analyses that yield publication
  quality graphics
• Connections from Stata

4
Contents

• Introduction to ALSPAC
• Description of the measures
• Preparing my data for the pipeline
• The pipeline (in stata)
• Summarize / Codebook
• Polychoric correlations
• Polychoric PCA
• Loevingers H
• Mokken Scale Procedure
• Options for SPSS users

5
What is ALSPAC?

• Avon Longitudinal Study of Parents and Children
  AKA Children of the Nineties
• Cohort study of 14,000 children and their
  parents, based in south-west England
• Eligibility criteria Mothers had to be resident
  in Avon and have an expected date of delivery
  between April 1st 1991 and December 31st 1992
• Population based prospective cohort study

6
Wheres Avon to, my luvver? trans Where is Avon?
7
The county of Avon

• 1) A nice short name
• 2) Known for its ladies
• 3) Replaced in 1996 with
• Bristol
• North Somerset
• Bath and North East Somerset
• South Gloucestershire
• Collectively known as CUBA
• (Counties which Used to Be Avon)

8
What data does ALSPAC have?

• Self completion questionnaires
• Mothers, Partners, Children, Teachers
• Hands on assessments
• 10 sample tested regularly since birth
• Yearly clinics for all since age 7
• Data from external sources
• SATS from LEA, Child Health database
• Biological samples
• DNA / cell lines

9
Contents

• Introduction to ALSPAC
• Description of the measures
• Preparing my data for the pipeline
• The pipeline (in stata)
• Summarize / Codebook
• Polychoric correlations
• Polychoric PCA
• Loevingers H
• Mokken Scale Procedure
• Options for SPSS users

10
Todays Measures 1 - MFQ

• Moods and Feelings Questionnaire
• Angold and Costello (1987).
• Mood and feelings questionnaire (MFQ). Durham
  Duke University, Developmental Epidemiology
  Program.
• Short version, 13 items
• Parental response at 13 years Questionnaire
• Child response at 14 years Clinic, computer

11
(No Transcript)
12
Todays Measures 2 - EAS

• EAS Temperament Survey (Parental Ratings)
• Buss and Plomin, (1984).
• A temperament theory of personality development.
  New York John Wiley.
• 20 questions
• 4 subscales
• Emotionality, Activity, Shyness Sociability
• Parental response at 4 years Questionnaire

13
(No Transcript)
14
(No Transcript)
15
Contents

• Introduction to ALSPAC
• Description of the measures
• Preparing my data for the pipeline
• The pipeline (in stata)
• Summarize / Codebook
• Polychoric correlations
• Polychoric PCA
• Loevingers H
• Mokken Scale Procedure
• Options for SPSS users

16
Rename variables for clarity and consistency
gen mum01_012 ta5020 gen mum02_012 ta5021 gen
mum03_012 ta5022 gen mum04_012 ta5023 gen
mum05_012 ta5024 gen mum06_012 ta5025 gen
mum07_012 ta5026 gen mum08_012 ta5027 gen
mum09_012 ta5028 gen mum10_012 ta5029 gen
mum11_012 ta5030 gen mum12_012 ta5031 gen
mum13_012 ta5032
gen kid01_012 fg6410 gen kid02_012 fg6412
gen kid03_012 fg6413 gen kid04_012 fg6414
gen kid05_012 fg6415 gen kid06_012 fg6416
gen kid07_012 fg6418 gen kid08_012 fg6419
gen kid09_012 fg6421 gen kid10_012 fg6422
gen kid11_012 fg6423 gen kid12_012 fg6424
gen kid13_012 fg6425
ta5020 fg6410 or ta5027 fg6419???
? mum01_012 kid01_012 and mum08_012
kid08_012 ?
17
Derive binary variables
recode _012 (30)(21)(12) foreach x in
"mum01" "mum02" "mum03" "mum04" "mum05" "mum06"
/// "mum07" "mum08" "mum09" "mum10" "mum11"
"mum12" "mum13" /// "kid01" "kid02" "kid03"
"kid04" "kid05" "kid06" "kid07" "kid08" ///
"kid09" "kid10" "kid11" "kid12" "kid13" gen
x'_001 x'_012 recode x'_001
(00)(10)(21) gen x'_011 x'_012 recode
x'_011 (00)(11)(21) mum01_012 mum0
1_001 mum01_011
18
Variable labels
foreach var of varlist 01_ label variable
var' "Felt miserable/unhappy var'" foreach
var of varlist 02_ label variable var'
"Didnt enjoy anything at all var'" foreach
var of varlist 03_ label variable var'
"Felt so tired they just sat around did nothing
var'" foreach var of varlist 04_
label variable var' "Was restless
var'" Etc.
19
Value Labels
foreach var of varlist _012 label define
var'_lab 0 "Not true" 1 "Sometimes true" 2
"True" label values var' var'_lab foreach
var of varlist _011 label define var'_lab 0
"Not true" 1 "Sometimes true / True" label
values var' var'_lab foreach var of
varlist _001 label define var'_lab 0
"Sometimes true / not true" 1 "True" label
values var' var'_lab
20
Contents

• Introduction to ALSPAC
• Description of the measures
• Preparing my data for the pipeline
• The pipeline (in Stata)
• Summarize / Codebook
• Polychoric correlations
• Polychoric PCA
• Loevingers H
• Mokken Scale Procedure
• Options for SPSS users

21
Typical data-pipeline syntax
log using "mfq_dataprep.log", replace foreach x
in "mum" "kid" su x'_012 codebook x'_012
loevH x'_012 polychoric x'_012 polychoricp
ca x'_012 msp x'_012 log close Repeat
with _011 and _001
22
summarize / codebook
23
su emo__01234

• Variable Obs Mean Std. Dev.
  Min Max
• -------------------------------------------------
  ------------------
• emo_l_02_04 9467 1.564276 .806012
  0 4
• emo_l_06_04 9445 1.7081 .8448107
  0 4
• emo_l_11_04 9448 1.274238 .8241389
  0 4
• emo_l_15_04 9431 1.613933 .8029195
  0 4
• emo_l_19_04 9342 1.594198 1.008401
  0 4

24
codebook emo__01234

• --------------------------------------------------
  ---------------------------------------------
• emo_l_02_01234
  Child cries easily emo_l_02_01234
• --------------------------------------------------
  ---------------------------------------------
• type numeric (float)
• label emo_l_02_01234_lab
• range 0,4
  units 1
• unique values 5
  missing . 5196/14663
• tabulation Freq. Numeric Label
• 761 0 E-Like
• 3620 1 Q-like
• 4202 2 S-like
• 751 3 NM-Like
• 133 4
  NAA-Like
• 5196 .
• --------------------------------------------------
  ---------------------------------------------
• emo_l_06_01234 Child
  tends to be somewhat emotional emo_l_06_01234
• --------------------------------------------------
  ---------------------------------------------
• type numeric (float)
• label emo_l_06_01234_lab

25
codebook emo__01234

• --------------------------------------------------
  ---------------------------------------------
• emo_l_11_01234
  Child often fusses and cries emo_l_11_01234
• --------------------------------------------------
  ---------------------------------------------
• type numeric (float)
• label emo_l_11_01234_lab
• range 0,4
  units 1
• unique values 5
  missing . 5215/14663
• tabulation Freq. Numeric Label
• 1538 0 E-Like
• 4420 1 Q-like
• 2942 2 S-like
• 457 3 NM-Like
• 91 4
  NAA-Like
• 5215 .
• --------------------------------------------------
  ---------------------------------------------
• emo_l_15_01234
  Child gets upset easily emo_l_15_01234
• --------------------------------------------------
  ---------------------------------------------
• type numeric (float)
• label emo_l_15_01234_lab

26
codebook emo__01234

• --------------------------------------------------
  ---------------------------------------------
• emo_l_19_01234
  Child reacts intensely when upset
  emo_l_19_01234
• --------------------------------------------------
  ---------------------------------------------
• type numeric (float)
• label emo_l_19_01234_lab
• range 0,4
  units 1
• unique values 5
  missing . 5321/14663
• tabulation Freq. Numeric Label
• 1329 0 E-Like
• 3038 1 Q-like
• 3459 2 S-like
• 1127 3 NM-Like
• 389 4
  NAA-Like
• 5321 .

27
Multihist

• pause on
• foreach x in "01" "02" "03" "04" "05" "06" "07"
  "08" "09" "10" "11" "12" "13"
• multihist x'_012
• pause
• pause off
• Compare response to same questions at different
  times
• Big differences would suggest an error in
  previous code
• - reversal of responses
• - change to order of questions asked
• - change to response options (aargh!)

28
Multihist for first item of MFQ (6 repeat
measures)
29
Polychoric Correlations
30
Correlation -v- regression coefficient
Correlation coefficient The interdependence
between pairs of variables i.e. the extent to
which values of the variable change together
The strength and direction of the linear
relationship A fatter ellipse will result in a
greater degree of scatter for a regression line
of a given gradient, and a lower correlation
31
Polychoric Correlation - Assumptions

• A binary or categorical variable is the observed
  (or manifest) part of an underlying (or latent)
  continuous variable
• Here well also assume that latent variables are
  normally distributed
• THRESHOLD relates the manifest to the latent
  variable
• Uebersax link http//ourworld.compuserve.com/home
  pages/jsuebersax/tetra.htm

32
Thresholds
Figure from Uebersax webpage
33
2 binary variables

• . tab mum01_001 mum04_001
• Felt Was restless
• miserable/unhappy mum04_001
• mum01_001 ST / NT True
  Total
• ------------------------------------------------
  ------
• ST / NT 6,343 78
  6,421
• True 234 54
  288
• ------------------------------------------------
  ------
• Total 6,577 132
  6,709
• This is all we see, however .

34
this is what we assume is going on
Figure from Uebersax webpage
35

• What we are really interested in is the
  correlation (r) between the continuous latent
  variables
• Computer algorithm used to search for a
  correlation r and thresholds t1 and t2 which best
  reproduce the cell counts of the 2x2 table

36
Poly / tetra

• Tetrachoric
• Special case where both variables are binary
• Polychoric
• More general (any categorical variable)
• Bi/Polyserial
• One continuous and one categorical variable

37
Poly versus standard correlations
foreach x in "emo_l_02" "emo_l_06" "emo_l_11"
"emo_l_15" "emo_l_19" gen x'_00001
x'_01234 recode x'_00001 (00)(10)(20)(30)(
41) gen x'_00011 x'_01234 recode
x'_00011 (00)(10)(20)(31)(41) gen
x'_00111 x'_01234 recode x'_00111
(00)(10)(21)(31)(41) gen x'_01111
x'_01234 recode x'_01111 (00)(11)(21)(31)(
41) gen x'_01122 x'_01234 recode
x'_01122 (00)(11)(21)(32)(42) gen
x'_00123 x'_01234 recode x'_00123
(00)(10)(21)(32)(43)
38
log using "eas_dataprep_poly_corr.log",
replace foreach x in "emo__00001" "emo__00011
" "emo__00111 " /// "emo__01111" "emo__01122
" "emo__00123 " "emo__01234" corr
x' polychoric x' log close
39
Polychoric Correlation Matrix (01234)
Standard Correlation Matrix (01234)
40
(No Transcript)
41
Poly versus standard correlations

• Polychoric correlations always higher than
  Pearson correlations
• Polychoric correlations more robust to changes in
  the number of categories
• For polychoric in Stata, if categories gt 10,
  variable treated as if continuous, so the
  correlation of two variables that have 10
  categories each would be simply the usual Pearson
  moment correlation found through correlate.

42
Polychoric PCA
43
Polychoric PCA

• Performs PCA on the polychoric correlation matrix
• Produces eigenvectors, eigenvalues, and the
  correlation matrix as with standard PCA

44
PCA v PolychoricPCA, mum MFQ
45
(No Transcript)
46
PCA v PolychoricPCA, EAS
47
(No Transcript)
48
Assumptions of PCA/FA

• Items can be regarded as parallel (same frequency
  distribution)
• PCA/FA not always appropriate when items differ
  in their frequency distribution such as when
  items have differing levels of difficulty
• Alternative methods may be more appropriate.
  find out tomorrow

49
Loevingers H

• Coefficient of Homogeneity

50
Item Response Function
Increasing probability of endorsing item
Increasing level of latent trait
51
Non-parametric

• No fixed form on function of the relationship
  between trait and probability of positive
  response to each item
• Unlike polychoric, no assumption made about the
  distribution of the latent trait

52
Bit about scaling
53
(Guttman) Error Cells

• . tab mum01_001 mum04_001
• Felt Was restless
• miserable/unhappy mum04_001
• mum01_001 ST / NT True
  Total
• ------------------------------------------------
  ------
• ST / NT 6,343 78
  6,421
• True 234 54
  288
• ------------------------------------------------
  ------
• Total 6,577 132
  6,709
• mum04_001 is more difficult than mum01_001
• If mum01_001 and mum04_001 formed a hierarchy,
  there would be a zero count in the top right cell

54
EAS, Emotionality 00011
55
EAS, Emotionality 00011
S 655
56
EAS, Emotionality 00011
57
EAS, Emotionality 00011
S 3130
58
Expected Guttman Errors

• CH often
• fusses and
• cries Child cries easily
• emo_l_11_ emo_l_02_00011
• 00011 0 1 Total
• -------------------------------------------
• 0 8,248 503 8,751
• 1 180 363 543
• -------------------------------------------
• Total 8,428 866 9,294
• Under perfect Guttman scaling, cell count 0
• Under marginal independence,
• cell count (8428/9294)(543/9294)9294
  492.4

59
Expected Guttman Errors

• Total observed Guttman errors for emo_l_11
• 180141166178
• 655
• Total expected Guttman errors for emo_l_11
• 492.4 487.26 468.74 454.84
• 1903.25
• Loevinger H coefficient for emo_l_11 (H11)
• 1 S(observed) / S(expected)
• 1 (655/1903.25)
• 0.651

60
loevH emo__00011
Hi
61
loevH emo__00011
Loevinger H for scale
62
Acceptable values of Hi, H

• Acceptable Scale
• Hi all gt 0.3
• this then implies H gt 0.3
• Weak scale 0.3 H lt 0.4
• Medium scale 0.5 H lt 0.5
• Strong scale 0.5 H

Mokken Scale
63
loevH mum_012

• Observed
  Expected
  Number
• Difficulty Guttman
  Guttman Loevinger H0 Hjlt0 of
  NS
• Item Obs P(Xj0) errors
  errors H coeff z-stat. p-value
  Hjk
• --------------------------------------------------
  -------------------------------------------------
• mum01_012 6623 0.5886 4663
  11129.80 0.58103 102.2589 0.00000
  0
• mum02_012 6623 0.8629 5001
  9567.51 0.47729 103.0832 0.00000
  0
• mum03_012 6623 0.7315 7720
  11642.62 0.33692 68.7850 0.00000
  0
• mum04_012 6623 0.7331 6742
  11163.54 0.39607 79.9763 0.00000
  0
• mum05_012 6623 0.9050 3560
  8243.22 0.56813 117.8687 0.00000
  0
• mum06_012 6623 0.9244 3889
  7076.82 0.45046 88.9681 0.00000
  0
• mum07_012 6623 0.7944 6135
  11147.15 0.44964 95.7725 0.00000
  0
• mum08_012 6623 0.9349 2601
  6340.91 0.58981 112.2358 0.00000
  0
• mum09_012 6623 0.9500 2246
  5144.76 0.56344 99.9250 0.00000
  0
• mum10_012 6623 0.8474 5238
  9951.33 0.47364 102.4057 0.00000
  0
• mum11_012 6623 0.9064 3847
  8124.81 0.52651 108.8859 0.00000
  0
• mum12_012 6623 0.8655 5069
  9987.87 0.49248 106.8244 0.00000
  0
• mum13_012 6623 0.8209 4927
  10431.72 0.52769 113.1608 0.00000
  0
• --------------------------------------------------
  -------------------------------------------------

64
loevH kid_012

• Observed
  Expected
  Number
• Difficulty Guttman
  Guttman Loevinger H0 Hjlt0 of
  NS
• Item Obs P(Xj0) errors
  errors H coeff z-stat. p-value
  Hjk
• --------------------------------------------------
  -------------------------------------------------
• kid01_012 5703 0.3730 8579
  16440.13 0.47817 88.0802 0.00000
  0
• kid02_012 5703 0.7998 9763
  14118.52 0.30850 64.2818 0.00000
  0
• kid03_012 5703 0.4780 12234
  17415.56 0.29752 57.5953 0.00000
  0
• kid04_012 5703 0.4638 13379
  18379.14 0.27206 53.4953 0.00000
  0
• kid05_012 5703 0.7891 8096
  16659.66 0.51404 109.7532 0.00000
  0
• kid06_012 5703 0.8048 9308
  15947.63 0.41634 88.8534 0.00000
  0
• kid07_012 5703 0.4277 10736
  18173.50 0.40925 79.3781 0.00000
  0
• kid08_012 5703 0.8197 7914
  16091.78 0.50820 107.3113 0.00000
  0
• kid09_012 5703 0.8040 9132
  15004.31 0.39137 82.7063 0.00000
  0
• kid10_012 5703 0.6846 8939
  18013.31 0.50376 103.7182 0.00000
  0
• kid11_012 5703 0.8313 7740
  15178.88 0.49008 101.7086 0.00000
  0
• kid12_012 5703 0.7315 9445
  17874.94 0.47161 98.9656 0.00000
  0
• kid13_012 5703 0.8101 7959
  15065.70 0.47171 99.6037 0.00000
  0
• --------------------------------------------------
  -------------------------------------------------
• Scale 5703 61612
  1.1e05 0.42516 219.7088 0.00000

65
loevH kid_012

• Observed
  Expected
  Number
• Difficulty Guttman
  Guttman Loevinger H0 Hjlt0 of
  NS
• Item Obs P(Xj0) errors
  errors H coeff z-stat. p-value
  Hjk
• --------------------------------------------------
  -------------------------------------------------
• kid01_012 5703 0.3730 8579
  16440.13 0.47817 88.0802 0.00000
  0
• kid02_012 5703 0.7998 9763
  14118.52 0.30850 64.2818 0.00000
  0
• kid03_012 5703 0.4780 12234
  17415.56 0.29752 57.5953 0.00000
  0
• kid04_012 5703 0.4638 13379
  18379.14 0.27206 53.4953 0.00000
  0
• kid05_012 5703 0.7891 8096
  16659.66 0.51404 109.7532 0.00000
  0
• kid06_012 5703 0.8048 9308
  15947.63 0.41634 88.8534 0.00000
  0
• kid07_012 5703 0.4277 10736
  18173.50 0.40925 79.3781 0.00000
  0
• kid08_012 5703 0.8197 7914
  16091.78 0.50820 107.3113 0.00000
  0
• kid09_012 5703 0.8040 9132
  15004.31 0.39137 82.7063 0.00000
  0
• kid10_012 5703 0.6846 8939
  18013.31 0.50376 103.7182 0.00000
  0
• kid11_012 5703 0.8313 7740
  15178.88 0.49008 101.7086 0.00000
  0
• kid12_012 5703 0.7315 9445
  17874.94 0.47161 98.9656 0.00000
  0
• kid13_012 5703 0.8101 7959
  15065.70 0.47171 99.6037 0.00000
  0
• --------------------------------------------------
  -------------------------------------------------
• Scale 5703 61612
  1.1e05 0.42516 219.7088 0.00000

Need a procedure to derive a Mokken scale by
selecting a subset of the above items
66
MSP

• Mokken Scaling Procedure

67
Mokken Scaling Procedure

• Bottom-up, hierarchical clustering procedure
• Contrast to top-down procedures such as PCA/FA

68
Employs Hij

• CH often
• fusses and
• cries Child cries easily
• emo_l_11_ emo_l_02_00011
• 00011 0 1 Total
• -------------------------------------------
• 0 8,248 503 8,751
• 1 180 363 543
• -------------------------------------------
• Total 8,428 866 9,294
• Observed Guttman errors 180
• Expected Guttman errors 492.4
• Hij 1 ( observed / expected) 0.634

Under marginal independence
69
Procedure

• Derive Hij for all pairs of items and select the
  pair with the highest value (gt 0.3). Favour more
  difficult items if two pairs give the same Hij
• Find the next best item in the scale
• If item k is a new item not already in the scale
  then calculate
• Hik for all items i in the scale, and also
• Hk between item k and the current scale as a
  whole, and
• H for each new scale (items i plus k)
• again, favouring more difficult items and those
  with higher Hk in
• the event of a tied H value and ensuring all H/
  Hik/ Hk gt 0.3

70
Worked example using emo__00011
Observed
Expected
71
Stage 1. derive Hij
72
Select highest Hij
73
Stage 2. Find next best item

• Items 11 and 15 were selected
• Calculate H for each new scale and Hk between
  each item not in scale, and the current scale

• Select the new item with highest H and Hk
  provided all H gt 0.3
• Repeat step offering emo_l_06 and emo_l_19 to
  this new scale

74
msp emo__00011

• Scale 1
• ----------
• Significance level 0.005000
• The two first items selected in the scale 1 are
  emo_l_11_00011 and emo_l_15_00011 (Hjk0.7106)
• Significance level 0.003846
• The item emo_l_02_00011 is selected in the scale
  1Hj0.6243 H0.6482
• Significance level 0.003333
• The item emo_l_06_00011 is selected in the scale
  1Hj0.5799 H0.6115
• Significance level 0.003125
• The item emo_l_19_00011 is selected in the scale
  1Hj0.4563 H0.5424
• Significance level 0.003125
• There is no more items remaining.

75
msp kid_012

• Scale 1
• ----------
• Significance level 0.000641
• The two first items selected in the scale 1 are
  kid10_012 and kid11_012 (Hjk0.7083)
• Significance level 0.000562
• The item kid01_012 is selected in the scale 1
  Hj0.6145 H0.6467
• Significance level 0.000505
• The item kid05_012 is selected in the scale 1
  Hj0.6254 H0.6358
• Significance level 0.000463
• The item kid08_012 is selected in the scale 1
  Hj0.6373 H0.6364
• Significance level 0.000431
• The item kid12_012 is selected in the scale 1
  Hj0.5845 H0.6175
• Significance level 0.000407
• The item kid13_012 is selected in the scale 1
  Hj0.5642 H0.6032
• Significance level 0.000388
• The item kid06_012 is selected in the scale 1
  Hj0.4978 H0.5769
• Significance level 0.000373
• The item kid07_012 is selected in the scale 1
  Hj0.4437 H0.5463
• Significance level 0.000362

76
Item kid04_012 has been dropped and 12 item scale
now is acceptable
77
msp _01234 (EAS)

• Scale 1
• ----------
• Significance level 0.000263
• The two first items selected in the scale 1 are
  emo_l_11_01234 and emo_l_15_01234 (Hjk0.7457)
• The following items are excluded at this step
  soc_l_03_01234 act_l_04_01234 act_l_07_01234
  act_l_09_01234 soc_l_10_01234 a
• gt ct_l_13_01234 soc_l_16_01234 act_l_17_01234
• Significance level 0.000250
• The item emo_l_02_01234 is selected in the scale
  1Hj0.7093 H0.7208
• Significance level 0.000239
• The item emo_l_06_01234 is selected in the scale
  1Hj0.6106 H0.6644
• Significance level 0.000230
• The item emo_l_19_01234 is selected in the scale
  1Hj0.4860 H0.5826
• The following items are excluded at this step
  shy_l_20_01234
• Significance level 0.000224
• None new item can be selected in the scale 1
  because all the Hj are lesser than .3
• or none new item had all the related Hjk
  coefficients significantely greater than 0.
• Observed
  Expected
  Number
• Difficulty Guttman
  Guttman Loevinger H0 Hjlt0 of
  NS

78
Scale 2 ---------- Significance level
0.000476 The two first items selected in the
scale 2 are act_l_09_01234 and act_l_13_01234
(Hjk0.6861) The following items are excluded at
this step shy_l_01_01234 shy_l_08_01234
shy_l_12_01234 shy_l_14_01234 soc_l_18_01234 s gt
hy_l_20_01234 Significance level 0.000446 The
item act_l_04_01234 is selected in the scale
2Hj0.6439 H0.6585 Significance level
0.000424 The item act_l_17_01234 is selected in
the scale 2Hj0.4013 H0.5339 Significance
level 0.000407 The item act_l_07_01234 is
selected in the scale 2Hj0.3528
H0.4674 Significance level 0.000394 None new
item can be selected in the scale 2 because all
the Hj are lesser than .3 or none new item had
all the related Hjk coefficients significantely
greater than 0.
Observed Expected
Number
Difficulty Guttman Guttman Loevinger
H0 Hjlt0 of NS Item Obs
P(Xj0) errors errors H coeff
z-stat. p-value Hjk --------------------
--------------------------------------------------
----------------------------- act_l_07_01234
8928 0.0060 12055 18626.72
0.35281 58.5754 0.00000
0 act_l_17_01234 8928 0.0030 11927
19687.06 0.39417 61.8768 0.00000
0 act_l_04_01234 8928 0.0016 9516
19832.30 0.52018 87.5901 0.00000
0 act_l_09_01234 8928 0.0087 12018
23677.34 0.49243 82.3819 0.00000
0 act_l_13_01234 8928 0.0010 8508
19606.32 0.56606 95.2809 0.00000
0 --------------------------------------------
--------------------------------------------------
----- Scale 8928
27012 50714.87 0.46738 121.7656
0.00000
79
Scale 3 ---------- Significance level
0.001111 The two first items selected in the
scale 3 are shy_l_08_01234 and shy_l_12_01234
(Hjk0.6433) The following items are excluded at
this step soc_l_03_01234 soc_l_05_01234
soc_l_10_01234 soc_l_16_01234 Significance level
0.001020 The item shy_l_01_01234 is selected in
the scale 3Hj0.4853 H0.5448 Significance
level 0.000962 The item shy_l_14_01234 is
selected in the scale 3Hj0.5151
H0.5294 Significance level 0.000926 The item
shy_l_20_01234 is selected in the scale
3Hj0.4863 H0.5098 The following items are
excluded at this step soc_l_18_01234 Significance
level 0.000926 There is no more items
remaining.
Observed Expected
Number Difficulty
Guttman Guttman Loevinger
H0 Hjlt0 of NS Item Obs P(Xj0)
errors errors H coeff z-stat.
p-value Hjk --------------------------------
--------------------------------------------------
----------------- shy_l_20_01234 8928
0.0736 13559 26393.66 0.48628
78.0926 0.00000 0 shy_l_14_01234 8928
0.0719 10629 23587.87 0.54939
91.0884 0.00000 0 shy_l_01_01234 8928
0.1221 10559 21603.72 0.51124
82.3020 0.00000 0 shy_l_08_01234 8928
0.3863 12010 22334.00 0.46225
75.4764 0.00000 0 shy_l_12_01234
8928 0.3985 10079 22018.14
0.54224 88.5938 0.00000
0 ------------------------------------------------
--------------------------------------------------
- Scale 8928 28418
57968.70 0.50977 130.7685 0.00000
80
Scale 4 ---------- Significance level
0.005000 The two first items selected in the
scale 4 are soc_l_03_01234 and soc_l_10_01234
(Hjk0.4400) Significance level 0.003846 The
item soc_l_05_01234 is selected in the scale
4Hj0.3941 H0.4082 Significance level
0.003333 The item soc_l_16_01234 is selected in
the scale 4Hj0.3693 H0.3889 The following
items are excluded at this step
soc_l_18_01234 Significance level 0.003333 There
is no more items remaining.
Observed Expected
Number
Difficulty Guttman Guttman Loevinger
H0 Hjlt0 of NS Item
Obs P(Xj0) errors errors H
coeff z-stat. p-value
Hjk ----------------------------------------------
--------------------------------------------------
--- soc_l_16_01234 8928 0.0043 8974
14228.65 0.36930 50.2618 0.00000
0 soc_l_05_01234 8928 0.0040 8936
14840.68 0.39787 55.7348 0.00000
0 soc_l_03_01234 8928 0.0010
7252 12405.87 0.41544 58.1266
0.00000 0 soc_l_10_01234 8928 0.0077
9878 15864.61 0.37736 54.2418
0.00000 0 ----------------------------------
--------------------------------------------------
--------------- Scale 8928
17520 28669.91 0.38891 76.7622
0.00000 There is only one item remaining
(soc_l_18_01234). Relate this back to PCA results
81
MSP Simpler example

• msp mum_011on a sample of 20 children

82
Scale 1 ---------- Significance level
0.000641 The two first items selected in the
scale 1 are fg05_011 and fg10_011
(Hjk1.0000) Significance level 0.000562 The
item fg03_011 is selected in the scale 1
Hj1.0000 H1.0000 Significance level
0.000505 The item fg13_011 is selected in the
scale 1 Hj1.0000 H1.0000 Significance
level 0.000463 The item fg02_011 is selected in
the scale 1 Hj0.8261 H0.9205 Significan
ce level 0.000431 The item fg11_011 is selected
in the scale 1 Hj0.7059
H0.8452 Significance level 0.000407 The item
fg09_011 is selected in the scale 1 Hj0.5506
H0.7697 Significance level 0.000388 The
item fg01_011 is selected in the scale 1
Hj0.6324 H0.7412 Significance level
0.000373 The item fg08_011 is selected in the
scale 1 Hj0.6635 H0.7225 Significance
level 0.000362 The item fg06_011 is selected in
the scale 1 Hj0.6078 H0.6964 Significan
ce level 0.000355 The item fg12_011 is selected
in the scale 1 Hj0.4872 H0.6531 The
following items are excluded at this step
fg04_011 Significance level 0.000352 The item
fg07_011 is selected in the scale 1 Hj0.3929
H0.6100 Significance level 0.000352 There
is no more items remaining.
83
MSP output (reordered by difficulty and H)
84
Original dataset
85
Mokken set of variables reordered
86
Guttman scale

• Will produce a perfect scale pattern
• It will be possible to sort the cases and
  variables in such a way to produce a triangular
  pattern with a clear delineation between the
  zeros and ones

87
Cases sorted to create triangular 0/1 split
88
Violations highlighted in yellow
89
66
90
Each yellow square contributed at least one
Guttman error to the scale
91
Monotone Homogeneity and Double Monotonicity
92
Monotone Homogenity
93
Double Monotonicity

• Lead in to the next slides which demonstrate the
  P(1,1) matrix

94
P(1,1) Matrix for sample of 20 cases
95
(No Transcript)
96
P(1,1) for full sample
97
(No Transcript)