Using latent class analysis in survey research
Dr. Anja Neundorf
(University of Nottingham, School of Politics & IR)
Nottingham-Warwick-Birmingham Advanced Quantitative Methods
Nottingham, 8th March 2013
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
1 / 58
Outline
1
Surveys and measurement models in general
2
What is latent class analysis?
3
Example I: Role conflict
4
Example II: Religiosity
5
Summary: What is this all good for?
6
Practical issues
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
2 / 58
Surveys and measurement models in general
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
3 / 58
Using surveys
The purpose of survey research
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
4 / 58
Using surveys
The purpose of survey research
I
Collect information about respondents / consumers
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
4 / 58
Using surveys
The purpose of survey research
I
Collect information about respondents / consumers
I
Some information is straight-forward and not questionable (age,
gender, race...)
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
4 / 58
Using surveys
The purpose of survey research
I
Collect information about respondents / consumers
I
Some information is straight-forward and not questionable (age,
gender, race...)
I
Most information – esp. attitudes – is not straight-forward at all
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
4 / 58
Using surveys
The purpose of survey research
I
Collect information about respondents / consumers
I
Some information is straight-forward and not questionable (age,
gender, race...)
I
Most information – esp. attitudes – is not straight-forward at all
I
Examples: Racial prejudice, religious beliefs, partisan affiliations,
consumer loyalty....
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
4 / 58
Using surveys
The purpose of survey research
I
Collect information about respondents / consumers
I
Some information is straight-forward and not questionable (age,
gender, race...)
I
Most information – esp. attitudes – is not straight-forward at all
I
Examples: Racial prejudice, religious beliefs, partisan affiliations,
consumer loyalty....
→ Measurement models needed!
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
4 / 58
From concepts to measurements
An example:
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
5 / 58
From concepts to measurements
An example:
I
Concept: Religious commitment
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
5 / 58
From concepts to measurements
An example:
I
Concept: Religious commitment
I
Measurement: Church attendance, denomination, praying, believe in
God, importance of religion in one’s life...
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
5 / 58
From concepts to measurements
An example:
I
Concept: Religious commitment
I
Measurement: Church attendance, denomination, praying, believe in
God, importance of religion in one’s life...
→ These are highly correlated
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
5 / 58
Measurement Model: Religious commitment
Religious
Pray
Belong
Church
є1
є2
є3
Anja Neundorf (Nottingham)
Importance God
є4
є5
Using latent class analysis in survey research
6 / 58
Measurement Model: Religious commitment
Religious
Pray
Belong
Church
є1
є2
є3
Importance God
є4
є5
Assumption: Observed co-variation between observed variables is due to
unobserved, true variable
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
6 / 58
Measurement Model: General
η
y1
y2
y3
y4
y5
є1
є2
є3
є4
є5
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
7 / 58
Contrasting different measurement models
Latent
Concept: η
Manifest measure: yi
Categorical
Continuous
Categorical
Latent Class
Latent Profile
Continues
Latent Trait/
IRT
Factor Analysis
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
8 / 58
Contrasting different measurement models
Latent
Concept: η
Manifest measure: yi
Categorical
Continuous
Categorical
Latent Class
Latent Profile
Continues
Latent Trait/
IRT
Factor Analysis
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
9 / 58
Contrasting different measurement models
Factor Analysis (FA)
I
Latent Variable: continues → normal distribution
I
People differ quantitatively along one or more continua
Latent Class Analysis (LCA)
I
Latent Variable: categorical → multinominal distribution
I
Qualitative differences exist between groups or people
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
10 / 58
What is latent class analysis?
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
11 / 58
What is latent class analysis?
1
Measurement instrument
I
I
2
Confirmatory or exploratory
Non-causal
Using latent variable in causal model
I
Can be used as dependent or independent variable
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
12 / 58
Latent Class Analysis (LCA): A measurement instrument
Overview: Aim of LCA
I
Identify clusters of similar "types" of individuals from multivariate
categorical data → Typology-formation!
I
Estimating the characteristics of these latent groups
I
Estimating the probability that each observation belongs to each
group
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
13 / 58
Latent Class Analysis (LCA): A measurement instrument
Overview: Aim of LCA
I
Identify clusters of similar "types" of individuals from multivariate
categorical data → Typology-formation!
I
Estimating the characteristics of these latent groups
I
Estimating the probability that each observation belongs to each
group
I
Investigating sources of confounding and non-independence among
a set of categorical variables
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
13 / 58
Latent Class Analysis (LCA): An illustration
Observed relationship
Eval. of economy
bad
good
Approval
Cameron
negative
positive
95
70
55
80
165
135
150
150
→ Significant relationship (chi2 = 8.42, p<.01)
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
14 / 58
Latent Class Analysis (LCA): An illustration
The confounder: Vote
Vote in last election
Labour
Conservatives
Approval
Cameron
negative
positive
Eval. of economy
bad
good
Eval. of economy
bad
good
80
40
15
30
20
10
35
70
→ Non-Significant relationship between Econ. and Cameron, conditional
on vote (chi2 = 0.00)
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
15 / 58
Latent Class Analysis (LCA): An illustration
The confounder: Vote
Vote in last election
Labour
Conservatives
Approval
Cameron
negative
positive
Eval. of economy
bad
good
Eval. of economy
bad
good
80
40
15
30
20
10
35
70
→ Non-Significant relationship between Econ. and Cameron, conditional
on vote (chi2 = 0.00)
→ Items are locally independent
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
15 / 58
Measurement Model: General
η
y1
y2
y3
y4
y5
є1
є2
є3
є4
є5
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
16 / 58
Latent Class Analysis (LCA)
Aim of LCA
I
Identify the unobserved / latent variable that explains systematic
relationship between observed variables
I
What is the "vote" variables in your model?
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
17 / 58
Example I
Stouffer and Toby (1951) “Role conflict and personality”.
American Journal of Sociolog y. 56: 395-406.
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
18 / 58
Stouffer and Toby (1951)
I
Four set of situations “involving conflict between obligations to a
friend and more general social obligations” (p. 396).
I
Example item: “You are riding in a car that your close friend is
driving, and he hits a pedestrian. You know that he was going at
least 35 miles an hour in a 20-mile-an-hour zone. There are no other
witnesses. His lawyer says if you testify under oath the speed was
only 20 miles an hour, it may save him from serious consequences.
What right has your friend to expect you to protect him?”
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
19 / 58
Stouffer and Toby (1951)
I
Four set of situations “involving conflict between obligations to a
friend and more general social obligations” (p. 396).
I
Example item: “You are riding in a car that your close friend is
driving, and he hits a pedestrian. You know that he was going at
least 35 miles an hour in a 20-mile-an-hour zone. There are no other
witnesses. His lawyer says if you testify under oath the speed was
only 20 miles an hour, it may save him from serious consequences.
What right has your friend to expect you to protect him?”
I
Universalistic response: “He has no right as a friend to expect me
to testify to the lower figure.”
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
19 / 58
Stouffer and Toby (1951)
I
Four set of situations “involving conflict between obligations to a
friend and more general social obligations” (p. 396).
I
Example item: “You are riding in a car that your close friend is
driving, and he hits a pedestrian. You know that he was going at
least 35 miles an hour in a 20-mile-an-hour zone. There are no other
witnesses. His lawyer says if you testify under oath the speed was
only 20 miles an hour, it may save him from serious consequences.
What right has your friend to expect you to protect him?”
I
Universalistic response: “He has no right as a friend to expect me
to testify to the lower figure.”
I
Particularistic response: “He has a right as a friend to expect me
to testify to the lower figure.”
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
19 / 58
Cross-classification of 216 respondents
Observed Variables
I
A: Auto passenger
I
B: Insurance doctor
I
C: Drama critic
I
D: Board of directors
→ Responses
+ Universalistic value
– Particularistic value
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
20 / 58
Cross-classification of 216 respondents
Observed Variables
I
A: Auto passenger
I
B: Insurance doctor
I
C: Drama critic
I
D: Board of directors
→ Responses
+ Universalistic value
– Particularistic value
Response pattern:
2x2x2x2 = 16 possibilities
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
20 / 58
Cross-classification of 216 respondents
Response
Observed Variables
I
A: Auto passenger
I
B: Insurance doctor
I
C: Drama critic
I
D: Board of directors
→ Responses
+ Universalistic value
– Particularistic value
Response pattern:
2x2x2x2 = 16 possibilities
Anja Neundorf (Nottingham)
A
B
C
D
Obs. N
+
+
+
+
+
+
+
+
–
–
–
–
–
–
–
–
+
+
+
+
–
–
–
–
+
+
+
+
–
–
–
–
+
+
–
–
+
+
–
–
+
+
–
–
+
+
–
–
+
–
+
–
+
–
+
–
+
–
+
–
+
–
+
–
42
23
6
25
6
24
7
38
1
4
1
6
2
9
2
20
Using latent class analysis in survey research
20 / 58
Reduction of information
I
LCA helps us to reduce this number to a few (optimal) types of
respondents to these 16 possible responses.
I
Allowing some of the response patters as measurement error –
treating them as ‘mis-classifications’ – rather than as true response
types.
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
21 / 58
Reduction of information
I
LCA helps us to reduce this number to a few (optimal) types of
respondents to these 16 possible responses.
I
Allowing some of the response patters as measurement error –
treating them as ‘mis-classifications’ – rather than as true response
types.
→ Aim: Identify a set of mutually exclusive latent classes that account
for the distribution of cases that occur within a cross-tab of observed
discrete variables.
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
21 / 58
The latent class model (LCM)
Basic unrestricted LCM
A|X
B|X
ABCDX
πijklt
= πtX πit πjt
Anja Neundorf (Nottingham)
C |X
D|X
πkt πlt
Using latent class analysis in survey research
22 / 58
The latent class model (LCM)
Basic unrestricted LCM
A|X
B|X
ABCDX
πijklt
= πtX πit πjt
C |X
D|X
πkt πlt
I
Latent variable Xt : (t=1,...,T)
I
Item Ai : (i=1,...,I) ... Item Dl : (l=1,...,L)
I
ABCDX
πijklt
: Probability of a specific response pattern, depending on
class membership in t
I
πtX : Latent class probability
I
πit ...πlt
A|X
D|X
: Conditional probabilities
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
22 / 58
The latent class model (LCM)
πtX : Latent class probability
I
Describes the distribution of classes of the latent variable within
which the observed measures are locally independent of one another
I
Two important aspects: 1) Number of classes; 2) relative size of
these classes
Identification restriction:
T
X
πtX = 1
t=1
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
23 / 58
The latent class model (LCM)
A|X
D|X
πit ...πlt
: Conditional probabilities
I
Comparable to factor loadings in factor analysis
I
Probability of a respondent to give a specific response to survey
items A-D
I
Gives information about the character of each class t
I
Number of distinct probabilities for each indicator depends on
number of response-options
Identification restriction:
I
X
A|X
πit
= 1 ...
i=1
Anja Neundorf (Nottingham)
L
X
D|X
πlt
=1
l=1
Using latent class analysis in survey research
24 / 58
Estimation procedure
Maximum likelihood estimation (introduced by Goodman 1972)
I
EM (Expectation Maximization)
I
Newton-Raphson
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
25 / 58
Cross-classification of 216 respondents
Response
Observed Variables
I
A: Auto passenger
I
B: Insurance doctor
I
C: Drama critic
I
D: Board of directors
→ Responses
+ Universalistic value
– Particularistic value
Response pattern:
2x2x2x2 = 16 possibilities
Anja Neundorf (Nottingham)
A
B
C
D
Obs. N
+
+
+
+
+
+
+
+
–
–
–
–
–
–
–
–
+
+
+
+
–
–
–
–
+
+
+
+
–
–
–
–
+
+
–
–
+
+
–
–
+
+
–
–
+
+
–
–
+
–
+
–
+
–
+
–
+
–
+
–
+
–
+
–
42
23
6
25
6
24
7
38
1
4
1
6
2
9
2
20
Using latent class analysis in survey research
26 / 58
Results Example I
Probability of ‘Universalistic Response’ (+) and relative frequency
for two-class model
Observed
Variables
Response Type
Universalistic Particularistic
Auto passenger
Drama critic
Insurance doctor
Board of directors
0.99
0.93
0.94
0.77
0.71
0.35
0.33
0.13
Relative Class
Frequency
0.28
0.72
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
27 / 58
Results Example I
Probability of Universalistic Response (+) and relative frequency
for two-class model
Observed
Variables
Response Type
Universalistic Particularistic
Auto passenger
Drama critic
Insurance doctor
Board of directors
0.99
0.93
0.94
0.77
0.71
0.35
0.33
0.13
Relative Class
Frequency
0.28
0.72
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
28 / 58
Judging the goodness of this model?
Model evaluation
I
Pearson’s Chi2
I
Likelihood Ratio Chi2
I
Akaike Information Criteria (AIC)
I
Bayesian Information Criteria (BIC)
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
29 / 58
Judging the goodness of this model?
Model evaluation
Chi2
Model
M0: Independence
M1: Latent class
M2: Latent class
No. of Latent
Classes
Degrees of
Freedom
Goodness
of Fit
Likelihood
Ratio
1
2
3
11
6
2
104.11
2.72
0.42
81.08
2.72
0.39
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
30 / 58
Using restrictions
Hypotheses are tested by imposing restrictions and determining
how these restrictions affect the fit of the model to the data.
Examples:
I
Equality constraint, e.g. parallel indicators or equal error rate
I
Deterministic, e.g. setting conditional probability to specific value
(usually 1 or 0 )
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
31 / 58
Judging the goodness of this model?
Model evaluation
Chi2
Model
M0:
M1:
M2:
M3:
Independence
Latent class
Latent class
Restricted LC
No. of Latent
Classes
Degrees of
Freedom
Goodness
of Fit
Likelihood
Ratio
1
2
3
3
11
6
2
9
104.11
2.72
0.42
2.28
81.08
2.72
0.39
2.28
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
32 / 58
Results Example I
Probability of Universalistic Response (+) and relative frequency
for three-class model
Observed
Variables
Auto passenger
Drama critic
Insurance doctor
Board of directors
Relative Class
Frequency
Response Type
Strict
Mixed
Strict
Universalistic
Particularistic
1
1
1
1
0.80
0.42
0.44
0.18
0
0
0
0
0.17
0.78
0.05
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
33 / 58
Example II
Religiosity in post-Socialist Europe
(with Tim Mueller; Social Forces 2012, 91(2): 559-582)
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
34 / 58
Forced Secularization in Eastern Europe?
Religion in Socialism:
I
Based on Marxism-Leninism ideology of ‘scientific materialism’ →
suppression of religion.
I
Examples: Churches did not play a role in public education, religious
organizations were monitored or prohibited (Froese 2004), pastors
were imprisoned and individual restrictions of university access
(Burgess 1997).
I
Success of suppression differs in Protestant, Catholic, and Orthodox
countries.
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
35 / 58
Problem of measurement
I
People in socialist societies grew up with a suppression of religion
I
Overt religiosity lead to direct disadvantages
I
Respondents will be reluctant to openly confess religious belief
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
36 / 58
Problem of measurement
I
People in socialist societies grew up with a suppression of religion
I
Overt religiosity lead to direct disadvantages
I
Respondents will be reluctant to openly confess religious belief
→ Measurement model needed to measure latent belief
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
36 / 58
Data and analysis
I
Data: International Social Survey Programme (1991, 1998, and
2008)
I
Dependent variable: Believe in God
I
Method: Latent class analysis (using three indicators)
I
Number of latent classes: 3 (atheist, agnostic, religious)
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
37 / 58
Question wording: Item 1
I
“Please tick one box below to show which statement comes closest
to expressing what you believe about God.“ [Express]
(1) I don’t believe in God.
(2) I don’t know whether there is a God and I don’t believe
there is any way to find out.
(3) I don’t believe in a personal God, but I do believe in a
Higher Power of some kind.
(4) I find myself believing in God some of the time, but not at
others.
(5) While I have doubts, I feel that I do believe in God.
(6) I know God really exists and I have no doubts about it.
(8) Can’t choose, don’t know; (9) NA.
(1) is coded as ‘atheist’; (2)-(3) and (8) ‘agnostic’; (4)-(6)
‘religious’ response; (9) are set to missing.
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
38 / 58
Question wording: Item 2
I
“Which best describes your beliefs about God?” [Describe]
(1)
(2)
(3)
(4)
(8)
I don’t believe in God now and I never have.
I don’t believe in God now, but I used to.
I believe in God now, but I didn’t used to.
I believe in God now and I always have.
Can’t choose, don’t know; (9) NA, refused.
(1) is coded as ‘atheist’; (2) and (8) ‘agnostic’; (3)-(4) ‘religious’
response; (9) are set to missing.
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
39 / 58
Question wording: Item 3
I
“How much do you agree or disagree with each one of the
followings? There is a God who concerns Himself with every human
being personally.” [Concern]
(1)
(2)
(3)
(4)
(5)
(8)
Strongly agree.
Agree.
Neither agree or disagree.
Disagree.
Strongly disagree.
Can’t choose, don’t know; (9) NA, refused.
(4)-(5) is coded as ‘atheist’; (3) and (8) ‘agnostic’; (1)-(2)
‘religious’ response; (9) are set to missing.
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
40 / 58
Conditional Probabilities on Indicator Variables
Latent Class
(Size)
C1: ???
C2: ???
C3: ???
(0.26)
(0.27)
(0.47)
Item
Response
Express
atheist
agnostic
religious
0.53
0.45
0.02
0.01
0.58
0.41
0.01
0.04
0.96
Describe
atheist
agnostic
religious
0.83
0.17
0.00
0.05
0.35
0.60
0.00
0.00
1.00
Concern
atheist
agnostic
religious
0.84
0.14
0.01
0.47
0.45
0.08
0.10
0.23
0.68
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
41 / 58
Conditional Probabilities on Indicator Variables (all countries; 1991)
Latent Class
Atheist
Agnostic
Religious
(Size)
(0.26)
(0.27)
(0.47)
Item
Response
Express
atheist
agnostic
religious
0.53
0.45
0.02
0.01
0.58
0.41
0.01
0.03
0.96
Describe
atheist
agnostic
religious
0.83
0.17
0.00
0.05
0.35
0.60
0.00
0.00
1.00
Concern
atheist
agnostic
religious
0.84
0.15
0.01
0.47
0.45
0.08
0.10
0.22
0.68
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
42 / 58
Comparing the fit of the latent class model
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
43 / 58
Model fit by year
1991
1998
2008
N (cases)
N (parameter)
18,128
72
15,042
96
16,296
96
Classif. errors
Entropy R 2
0.11
0.75
0.07
0.81
0.08
0.79
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
44 / 58
Comparing latent classes among different groups
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
45 / 58
Comparing Religiosity in East and West Germany
West Germany
Religious
Atheist
East Germany
Religious
Atheist
Pre-CW Cohort
(born before 1932)
1991
1998
2008
64.2
62.4
73.9
5.7
11.9
5.9
32.0
35.2
32.3
36.8
44.6
50.2
48.9
43.0
50.7
13.8
16.2
10.2
14.2
15.7
14.7
65.9
68.8
68.4
27.9
39.6
25.9
18.7
15.1
3.3
75.9
76.7
Cold War Cohort
(born 1932-1976)
1991
1998
2008
Post-CW Cohort
(born after 1976)
1998
2008
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
46 / 58
Using latent classes probabilities as dependent variable
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
47 / 58
Explaining Trends in Religiosity
Revival or decline of religiosity?
Positive Economic
Development
Thighter ChurchState Relation
Decline
Increase
Modernization Theory
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
48 / 58
Model fit
Table: Fixed Effects Regression Model on Religiosity for Cohorts
GDP (in 1000s)
Legislations
Intercept
Western Europe
Eastern Europe
-0.21∗
[-0.41;
-0.02]
0.08
[-0.39;
6.32
[-7.07;
19.71]
6.76∗∗
[1.47; 12.06]
24.48
0.54]
14.99
σu
σ
23.63
7.05
29.79
7.35
R 2 (within)
R 2 (between)
0.207
0.015
0.359
0.186
56
21
40
15
N (obs)
N (cohorts)
Significance levels: ∗ p<.05, ∗∗ p<.01. Data: ISSP (1991, 1998 and 2008).
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
49 / 58
Summary: What is this all good for?
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
50 / 58
Summary
The opportunities of LCA
I
Classifying people’s opinions and behaviour in descriptive types
(latent classes)
I
Use these classifications as independent or dependent variables
I
Use either latent class probability of sample or post-estimation
classification of respondents
I
Compare different groups
I
Investigating sources of confounding and non-independence among
a set of categorical variables
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
51 / 58
Problems of LCA
Sparseness
I
Too many items with too many response-options can lead to
sparseness
I
Leads to difficulties in model evaluation (determining the degrees of
freedom)
I
Ideally all cells in a cross-table are filled
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
52 / 58
Problems of LCA
Sparseness
I
Too many items with too many response-options can lead to
sparseness
I
Leads to difficulties in model evaluation (determining the degrees of
freedom)
I
Ideally all cells in a cross-table are filled
→ Large-N is needed
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
52 / 58
Problems of LCA
Number of classes
I
Aim is reduction of information from full response-pattern (= K N ;
K=number of response-options; N=number of items) to smaller
number of distinct types (=latent classes)
I
But what is the exact number of optimal classes?
I
Two options to determine this:
1
2
Theory
Model fit
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
53 / 58
Practical issues: Where to go from here?
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
54 / 58
Reading
I Collins, L.M. and Lanza, S.T. (2010). Latent class and latent transition
analysis for the social, behavioral, and health sciences. New York: Wiley.
I McCutcheon, A.L. (1987) Latent class analysis. Quantitative Applications
in the Social Sciences Series No. 64.Thousand Oaks: Sage.
I Hagenaars, J. A. and McCutcheon, A.L. (2002) Applied latent class
analysis . Cambridge: CUP.
I Skrondal, A. and Rabe-Hesketh, S. (2004). Generalized latent variable
modeling : multilevel, longitudinal, and structural equation models.
London : Chapman & Hall/CRC.
I Lazarsfeld P.F. and Henry, N.W. (1968) Latent structure analysis.
Boston: Houghton Mifflin
I Goodman, L.A. (1974) "Exploratory latent structure analysis using both
identifiable and unidentifiable models". Biometrika 61 (2): 215–231.
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
55 / 58
Software
I
R (package poLC) (free)
I
SAS (add-on: PROC LCA & PROC LTA) (free)
I
Lem (free)
I
MPlus
I
Latent Gold
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
56 / 58
Workshops
I
Essex Summer School in Data Analysis and Collection
I
Course Convenor: Allan McCutcheon
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
57 / 58
Thank you for your attention!
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
58 / 58
Modelling heterogeneity in attitude dynamics
Issues to deal with:
I
State dependence
I
Measurement error
I
Initial condition
I
Heterogeneity
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
59 / 58
Modelling heterogeneity in attitude dynamics
Issues to deal with:
I
State dependence
I
Measurement error
I
Initial condition
I
Heterogeneity
→ Mixed Latent Markov Model
P(y i |x i )
=
M X
T
X
···
ξ=1 θ0 =1
T
X
T
X
P(ξ|x i ) P(θ0 |ξ, x i 0 ) ×
θT =1
P(θt |θt−1 , ξ)
t=1
Anja Neundorf (Nottingham)
T
X
[P(yit |θt , ξ)]Iit
t=1
Using latent class analysis in survey research
59 / 58
Simple Markov Model
yt=0
Anja Neundorf (Nottingham)
yt=1
yt=2
...
Using latent class analysis in survey research
60 / 58
Latent Markov Model
I
Measurement error equation:
P(yit = l |θ = s)
log
= δls
P(yit = s|θ = s)
θt=0
θt=1
θt=2
...
yt=0
yt=1
yt=2
...
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
61 / 58
Mover Stayer Model
θ1,t=0
1
θ1,t=1
1
θ1,t=2
...
yt=0
yt=1
yt=2
...
θ2,t=0
θ2,t=1
θ2,t=2
...
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
62 / 58
Mover Stayer Model
θ1,t=0
1
θ1,t=1
1
θ1,t=2
...
Covariates:
Soc. Class
Union
Housing
Age
Gender
Education
Region
yt=0
yt=1
yt=2
...
θ2,t=0
θ2,t=1
θ2,t=2
...
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
63 / 58
Modelling heterogeneity in attitude dynamics II
I
Transition dynamics equation:
P(θt = r |θt−1 = s, ξ)
log
= β0rs + β1rst timeit + β2rs Dξ=2 ,
P(θt = s|θt−1 = s, ξ)
I
Initial state equation:
P
X
P(θ0 = 1|x i0 , ξi )
= α0 +
αp xi0p + ηs ξ
log
P(θ0 = 2|x i0 , ξi )
p=1
I
Mixture allocation equation:
log
Q
X
P(ξi = 2)
= γ0 +
γq xi
P(ξi = 1)
q=1
Anja Neundorf (Nottingham)
Using latent class analysis in survey research
64 / 58