Tim Croudace

1
Latent Goldberg

• Tim Croudace
• tjc39_at_cam.ac.uk
• University of Cambridge

• Department of Health Career Scientist (Public
  Health)
• Senior Lecturer (Psychometric Epidemiology)

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With thanks to

• Post-docs
• Rosemary A Abbott
• George B Ploubidis
• Collaborators
• Felicia A Huppert
• Peter Jones
• NSHD
• Mike Wadsworth
• Di Kuh
• Marcus Richards
• And data managers

• Funding
• Leverhulme-Project grants
• NHS NCCRCD Pers. award

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Psychiatric Epidemiology

• Measures are error-laden
• Psychological / psychopathological measurements
  are fallible (not false just not as precise as
  we think they are)
• Psychometric epidemiology is the quantitative
  discipline that articulates these ideas as
  statistical models
• Major focus on reliability and validity
  assessment
• Exploits multiple quantitative measurements as
  well as discrete psychiatric diagnoses

• A field in which there is a fruitful interplay
  between the ideas typical of the medical model
  of disease
• And those coming from a psychometric tradition of
  educational, personality or behavioural research
• Psychometric tradition captures
  quantitative modelling with latent variables
  (factor analysis, latent classes and traits, and
  structural equation models

Psychometric Epidemiology
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Contemporary Psychometrics
Multivariate Analysis
Test (Item Theory Response)
Factor (Binary, Analysis Ordinal)
Psychometric Epidemiology
Structural (SEM) Regressions
Mixture (Latent Components Classes)
Multilevel (Further Models Dependence)
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Multi-dimensional (scaled) GHQ-28
Latent Goldberg
Publication
Goldberg and Hillier (1989) Psych Med
A Factor 1
Somatic
OHP General Specific Factor Model Second Order
Factor Model
B Factor 2
Scaled GHQ-28
Anxiety / insomnia
C Factor 3
Social dysfunction
(Goldberg and Hillier, 1979) Psych Med
D Factor 4
Severe Depression
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GHQ-28 in the NSHDLife course associations
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Latent Goldberg

• Psychometric statistics
• and the General Health Questionnaire(s)

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GHQ ABC
Latent Goldberg
General Health Questionnaire
Full name
No. It is not about general health
Really? Is it?
Emotional Disturbance Psychological Distress Psy
chosocial dysfunction
What is it?
Screening questionnaire
GHQ
Detects?
Minor Psychiatric Morbidity non-psychotic
No-identifies risk only Clinical interview
required for diagnosis
Diagnoses?
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GHQ Psychometrics
Instruments in family
Publisher
nferNelson Publishing Co Ltd
GHQ-60
Original instrument
Goldbergs General Health Questionnaires
GHQ-30
Omitting somatic items
GHQ-28
Scaled/multi- dimensional4 factors
281234
GHQ-12
Shortest version for Screening applicns
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Psychiatric Morbidity and the GHQ
Latent Goldberg
GHQ-12
6 negative items
02 Lost much sleep over worry 03
Felt constantly Under strain 06 Felt you
couldnt overcome yours
difficulties 09 Been feeling unhappy and
depressed 10 Been losing
confidence in yourself 11 Been thinking
of yourself as a worthless person
Negative
GHQ 02,05,06,09,10,11
GHQ-28 Scale D
GHQ - vely Worded items
Severe Depression
Interval GHQ items 22 feeling unhappy and
depressed 23 been llosing confidence in
yourself 24 thinking of yourself as a worthless
person 25 felt life is entirely hopeless 29
Felt life isnt worth living 30 Found couldnt
do anything cos nerves were so bad
GHQ-30
Interval GHQ Surtees Miller (1990)
Surtees, P and Miller, (1990) The interval GHQ,
BJP, 157.
Items from GHQ-30 22,23,24,25, 29,30 See OHP for
HALS results
Interval GHQ
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Item scores options alternatives
GHQ scoring methods
Traditional scoring
1-2-3-4 0-0-1-1
Screening applications
Alternative to traditional
Likert scoring
Consecutive integers 1-2-3-4
Verbal anchors for response categories
Corrected scoring
Captures Prevalent cases
1-2-3-4 0-0-1-1 Neg 1-2-3-4 0-1-1-1 Pos
Positive Likert
1-2-3-4 2-1-0-0 Pos
Huppert
Ploubidis et al (2007) LatentClass
Binary positive
1-2-3-4 1-0-0-0
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Standard (!) models
Latent Goldberg GHQ
Scores
PCA Lewis (1992) PM Traditional LFA (many)
PCA Linear FA
1-2-3-4
Latent Trait Analysis
Duncan-Jones et al (1989) Psych Med
0-0-1-1
Ordinal Rasch Model
GHQ Psychometrics
Andrich Van Schoubroek (1989) PM.
0-1-2-3
Graded Response
Croudace et al (under Review) Jrnl of Clin Epi
0-0-1-2
Latent Classes
Ploubidis,GP et al (2007) Pers
Indiv. Differences (online)
1-0-0-0 Positive
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More novel analyses /scenarios
GHQ Psychometrics
Multiple instruments
GHQ-12 SF-36 GHQ-12 Malaise
BHPS 58/70 BCs
Mixed scoring methods
On latent, multi- dimensionality
P 1-0-0-0 N 0-0-1-1
Analysis Scenarios methods
Interval metrics
Rasch subsets among GHQ-12,28,30,34 items
IRT
Standard applied Psychometrics (FIML)
Adolescent cohort study Mum Dad both complete
GHQ-12
Clustered data
Multivariate Multilevel
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Positively worded items (1)
Item characteristics GHQ
GHQ-12
6 positive 6 negative
01 Able to concentrate 03 Playing
a useful part in things 04 Capable of
making decisions 07 Able to enjoy
normal activities 08 Able to face up to
problems 12 Feeling reasonably happy
Positive
ve 01,03,04,07,08,12 -ve 02,05,06,09,10,11
Lewis (1992)
GHQ vely Worded items
2nd PCA bipolar factor Pos Neg MH at each end
Hu Y, Stewart-Brown S, Twigg L and Weich, S
(2007) Can the 12 item GHQ be used to measure
positive Mental health. Psych Med online.
EFA
Often factors defined by valence of items /-
Hu Y, Stewart-Brown S, Twigg L and Weich, S
(2007) Can the 12 item GHQ be used to measure
positive Mental health. Psych Med online.
Two factor CFA (no 3!) Positive
factor Wellbeing-PosMenHlth?
Hu et al (2007)
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Positively worded items (2)
Item characteristics GHQ
GHQ-28
Doing things well Satisfied with tasks Taking
longer over things Keeping self
occupied Playing a useful part in
things Capable of making decisions Enjoying
daily activities NB GHQ-30 contains more
positive items
8 positive (1,10-15,17) 20 negative
Been feeling perfectly well and in good health
Scale A 1/7 items
Scale C 7/7 items
GHQ vely Worded items
Social dysfunction 10-15 17 are ve)
Mod. Likert scoring
Factor loads 0-0-1-2 See OHP for full model
Stand 0012 0011 10 0.87 0.80 11
0.81 0.81 12 0.84 0.95 13 0.93 0.92 14 0.91
0.87 15 0.75 0.86 17 0.95 0.89
Preferred scoring for morbidity assessment 0011
or 0012 (-ve items)
Morbidity scoring
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Positively worded items (3)
Item characteristics GHQ
GHQ-30
15 positive 15 negative
GHQ-30 contains more positively worded items than
the GHQ-28 Same 6 as GHQ-12 (see previous
slide) All but one of the 7 GHQ-28 ve items are
also in GHQ-30. In addition GHQ30 has Getting
out of the house as much as usual Managing as
well as most people would Able to feel warmth
and affection for those near Finding it easy to
get on with other people Spent much time
chatting with people Been feeling hopeful about
future
Huppert Whittington Whittington Huppert
Huppert, FA
Scoring
GHQ vely Worded items
A priori 1-2-3-4 to 2-1-0-0
Modified Likert
2-1-0-0 is 0-0-1-2 No psychometric evid.
For latent constructs scored from
items currently very weak
Construct validity
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Software considerations (1)
Latent Goldberg GHQ
Scores
PCA
1-2-3-4
Traditional FA
1-2-3-4
Modelling estimation method(s)
Rasch Analysis
Random effects Logistic regression
0-0-1-1
Response functions Full information estimation
Graded Response
0-0-1-2
Underlying variables Limited information estimatio
n
Normal ogive IRT
0-1-2-3
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Software considerations (2)
Latent Goldberg GHQ
Scientific Software Int.
SSI
BILOG MULTILOG PARSCALETESTFACT
IRT suite
SSI IRT (commercial Psychometric suite)
BILOG / BILOG-MG
Binary outcomes
MULTILOG and PARSCALE
Ordinal (both) Nominal (PARSCALE)
FIML (Binary outcomes) Multidimensional
TESTFACT
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Software considerations (3)
Latent Goldberg GHQ
NPMLE? No No Yes Yes Yes
Random effects Logistic regression
Multilevel
ltm
R
Marginal Maximum Likelihood estimation of the
Rasch model
Stata
raschest gllamm
Mplus
Samejimas Graded Response Model
Discretized latent trait approach (Heinen thesis)
Latent Gold
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Software considerations (4)
Latent Goldberg GHQ
Limited inform only
Test Theory (1999) McDonald. LEA.
NOHARM
Normal ogive Item response models
Stata
Full inform only
gllamm
Categorical Data Factor Analysis
Mplus
Both
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Psychometrics in Stata (1)
Latent Goldberg
pca and factor
tetrachoric
polychoricpca
Stata procedures
pca on polychoric, tetrachorics
msp
Mokken scaling procedure
raschtext
See Stata Journal article by Hardouin, J.
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Psychometrics in Stata (2)
Latent Goldberg
Same as xtlogit
rasch
Same as Mplus (logistic) Probit is different
Logistic/probit IRT
NPMLE
gllamm procedures
Non-normal Latent distributions
Multilevel IRT
Clustered data Extensions of IRT A further level
or more
See gllamm manual Skrondal RabeHesketh Book
(Generalised LVM)
Much much more!
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Psychometrics in Mplus 4.2
Latent Goldberg
F by GHQ011 GHQ02-GHQ12 (1)
Rasch
F by GHQ01-GH12
2-param.logistic IRT
Logistic Graded Resp.
Mplus FIML estimatorML
F by GHQ01-GH12
NPML discrete distn
Point masses (LCs) for latent trait distn
Multilevel extension
CLUSTER FAMILY TYPE IS TWOLEVEL
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Rasch model Mplus then Stata
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multihist plot GHQ-30 HALS
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GHQ-30 Graded response model item
callibrationPARSCALE ITEM PARAMETERS assuming
unidimensional

• item slope (se) location
  (se) cutpoints
• ----------------------------------------------
  -------------------------
• 1 ghq1 0.654 (0.009) 0.811
  (0.029) 4.025 -0.825 -3.200
• 2 ghq2 0.811 (0.013) 1.464
  (0.019) 1.756 -0.105 -1.651
• 3 ghq3 0.167 (0.002) 3.710
  (0.084) 6.552 -1.518 -5.034
• 4 ghq4 0.267 (0.004) 3.441
  (0.058) 6.290 -1.453 -4.837
• 5 ghq5 0.359 (0.005) 1.687
  (0.043) 4.575 -1.078 -3.498
• 6 ghq6 0.461 (0.007) 2.773
  (0.038) 4.784 -1.352 -3.432
• 7 ghq7 0.666 (0.009) 1.585
  (0.025) 3.339 -0.554 -2.786
• 8 ghq8 0.617 (0.008) 1.697
  (0.028) 3.697 -0.650 -3.047
• 9 ghq9 0.313 (0.004) 3.541
  (0.053) 6.241 -1.383 -4.858
• 10 ghq10 0.487 (0.007) 2.388
  (0.041) 5.237 -1.301 -3.937
• 11 ghq11 0.299 (0.004) 2.823
  (0.053) 5.814 -1.207 -4.607
• 12 ghq12 0.528 (0.007) 1.378
  (0.030) 3.609 -0.726 -2.883
• 13 ghq13 0.304 (0.004) 2.269
  (0.056) 6.616 -1.374 -5.242
• 14 ghq14 1.089 (0.016) 0.897
  (0.014) 1.605 -0.047 -1.558
• 15 ghq15 1.237 (0.020) 1.330
  (0.013) 1.577 -0.177 -1.400
• 16 ghq16 0.474 (0.007) 1.734
  (0.030) 2.863 -0.497 -2.366
• 17 ghq17 0.264 (0.003) 1.835
  (0.065) 7.603 -1.733 -5.870

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Effective measurement range of the GHQ-30
(consecutive integer scores 1234graded response
IRT model)
Scatter plot of posterior means (x-axis) versus
posterior Std Dev.

• Histogram of posterior means

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(No Transcript)
29
More novel analyses /scenarios
GHQ Psychometrics
Multiple instruments
GHQ-12 SF-36 GHQ-12 Malaise
BHPS 58/70 BCs
Mixed scoring methods
On latent, multi- dimensionality
P 1-0-0-0 N 0-0-1-1
Analysis Scenarios methods
Interval metrics
Rasch subsets among GHQ-12,28,30,34 items
IRT
Standard applied Psychometrics (FIML)
Adolescent cohort study Mum Dad both complete
GHQ-12
Clustered data
Multivariate Multilevel
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Clustered / multilevel data children in
classes, patients in general practices, workers
in teams

• Number of patterns 11 Number of
  clusters 88
• Size (s) Cluster ID with Size s
• 1 22 80
• 2 28 72 79 16
  81 82
• 3 39 36 74 75
  83 88
• 4 37
• 5 2 87 18
• 6 40 41 71 8
  38 84 7 76
• 7 19 34 15
• 8 10 78 35 46
  60 69 20 21
• 17 3
• 9 33 86 57 45
• 10 44 9 4 73
  47 13 59 77
• 42
• 11 51 52 1 32
  14 24 70 50
• 12 49 66 12

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Test of model fit (with clustering)

• Loglikelihood
• H0 Value
  -2513.807
• H0 Scaling Correction Factor
  1.320
• for MLR
• Information Criteria
• Number of Free Parameters
  7
• Akaike (AIC)
  5041.613 (40 pts lower)
• Bayesian (BIC)
  5075.041 (35 pts lower)
• Sample-Size Adjusted BIC
  5052.811 (40 pts lower)
• Akaike (AIC) 5083.187
• Bayesian (BIC)
  5111.840
• Sample-Size Adjusted BIC
  5092.785

Test of model fit (without clustering)
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Software considerations (5)
Latent Goldberg GHQ
Latent class and Discrete lat trait models
Heinen PhD Thesis
Thousand Oaks, Sage
Published
Discretized latent Trait models
Stata
gllamm NPMLE
Mplus
Examples
Latent Gold
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The data 0000 1000 0001 0010 1001 1010 0011 1011
0100 1100 0101 0110 1101 1110 0111 1111 n1729
n 477 63 12 150 7 32 11 4 231 94 13 378 12 169 45
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logit phi ah 0 ah 1zi
ah0 a10
a21
ah1
Cancer Knowledge zi
z i 0
ah0 a40
h item i individual
Sources of knowledge q1 radio q2 newspapers
q3 reading q4 lectures A single latent
dimension Z Normal (mean 0 std dev 1 ) so Var
1 too!
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• Tests of Model Fit
• Pearson Chi-Square Value
  18.300
• Degrees of Freedom
  7
• P-Value
  0.0107
• Likelihood Ratio Chi-Square Value
  16.770
• Degrees of Freedom
  7
• P-Value
  0.0189
• Estimates S.E. Est/SE Std
  StdYX
• Z by Q1 0.721 0.093 7.765
  0.721 0.369
• Z by Q2 3.358 1.035 3.244
  3.358 0.880
• Z by Q3 1.344 0.167 8.025
  1.344 0.595
• Z by Q4 0.769 0.145 5.307
  0.769 0.391
• Q11 Threshold 1.287 0.068 18.852
  1.287 0.660
• Q21 Threshold -0.593 0.185 -3.198
  -0.593 -0.155
• Q31 Threshold 0.140 0.065 2.140
  0.140 0.062
• Q41 Threshold 2.708 0.127 21.340
  2.708 1.374

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• Mplus version 4.1 ML Estimate S.E.
• Z by Q1 alpha h 1 0.721 0.093
• Z by Q2 alpha h 2 3.358 1.035
• Z by Q3 alpha h 3 1.344 0.167
• Z by Q4 alpha h 4 0.769 0.145
• Variances Z 1
• Compare with Bartholomew (1987) p160
• 0.72 (0.09)
• 3.40 (1.14)
• 1.34 (0.17)
• 0.77 (0.15)

Tests of Model Fit Pearson Chi-Square Value
18.300 Degrees of Freedom
7 P-Value 0.0107 Likelihood Ratio
Chi-Square Value
16.770 Degrees of Freedom 7 P-Value
0.0189
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Item information functions- shown alongside
their ICCs
3.0 0.14
0.14 0.40
beware y axis scaling not all the same