Concept Architecture
Concept
Theoretically, the Latent Class Model (LCM) is a finite mixture statistical model used to identify unobserved subgroups within a population that exhibit distinct patterns of preferences or behaviour. It is based on latent variable theory and probabilistic classification, recognising that individuals are heterogeneous and that this heterogeneity can be represented by a finite number of discrete latent classes. In health economics, Latent Class Models are widely used in discrete choice experiments and stated preference studies to estimate preference heterogeneity across population segments.
Mathematically, the Latent Class Model represents the overall likelihood as a weighted combination of class-specific likelihood functions. Each individual is assigned a probability of belonging to each latent class, and separate preference parameters are estimated for every class using maximum likelihood estimation. The model simultaneously estimates class membership probabilities and class-specific utility coefficients.
In practice, Latent Class Models are estimated using discrete choice data collected from surveys or experiments. Statistical software estimates both the probability that respondents belong to each latent class and the preference parameters associated with each class. The resulting classes are interpreted to understand heterogeneity in healthcare preferences, willingness to pay and treatment choice behaviour.
Purpose
Used to identify distinct subgroups with different preference structures, quantify preference heterogeneity and improve the estimation and interpretation of healthcare choices in stated preference and health economic analyses.
Mathematical Formulae
Primary Formula
The unconditional probability that individual n chooses alternative i is
P?? = ????? �?P??|?
where
- P?? = overall probability of choosing alternative i
- C = number of latent classes
- �? = probability of membership in latent class c
- P??|? = conditional choice probability within latent class c
The conditional choice probability is typically specified as the multinomial logit model
P??|? = exp(V??|?) / ?? exp(V??|?)
Supporting Formulae
Class membership probabilities satisfy
????? �? = 1
Overall log-likelihood
LL = ?? ln(????? �?P??|?)
Related Mathematical Methods
- Random Utility Theory
- Finite mixture modelling
- Multinomial logit modelling
- Maximum likelihood estimation
- Expectation-Maximisation algorithm
- Discrete choice experiments
- Information criteria (AIC and BIC) for class selection
Example
A discrete choice experiment evaluates preferences for diabetes treatments among 1,000 respondents.
A two-class Latent Class Model identifies:
- Class 1 (70%) strongly values treatment effectiveness and accepts higher costs.
- Class 2 (30%) places greater importance on reducing treatment burden and minimising adverse effects.
Separate utility coefficients are estimated for each class, allowing policymakers to understand how treatment preferences differ across patient groups and to design interventions targeted to different populations.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| SUMPRODUCT | =SUMPRODUCT(B2:B4,C2:C4) | Calculate weighted probabilities across latent classes |
| SUM | =SUM(B2:B4) | Verify that class membership probabilities sum to one |
| EXP | =EXP(B2) | Calculate exponential utilities for multinomial logit probabilities |
| LN | =LN(B2) | Calculate log-likelihood contributions |
| IF | =IF(B2=MAX($B$2:$B$4),""Assigned Class"","""") | Identify the most likely latent class for an individual |
VBA (Optional)
Automate estimation summaries by importing latent class model outputs, calculating class membership statistics and generating comparative reports for healthcare preference studies.
Sources
- Greene WH, Hensher DA. A Latent Class Model for Discrete Choice Analysis: Contrasts with Mixed Logit. Transportation Research Part B. 2003.
- Train KE. Discrete Choice Methods with Simulation. 2nd ed. Cambridge University Press.
- Louviere JJ, Hensher DA, Swait JD. Stated Choice Methods: Analysis and Applications. Cambridge University Press.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press.
- ISPOR Conjoint Analysis Good Research Practices Task Force Reports.
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press.
Related Concepts (2)
Library
Publications
1
Conjoint Analysis Applications in Health — A Checklist: A Report of the ISPOR Good Research Practices for Conjoint Analysis Task Force — Bridges, Hauber, Marshall, Lloyd, Prosser, Regier, Johnson & Mauskopf, Vol. 14, No. 4 ed., 2011 (Value in Health)
The ISPOR good-practice checklist for conjoint analysis and discrete-choice experiments in health — the stated-preference methods used to elicit patient and public preferences over treatment attributes for value assessment and priority-setting.
Journal ArticleView source →
Frequently Asked Questions (6)
What is a latent class model?
A statistical model that assumes a population consists of unobserved subgroups with distinct preferences, estimating both each subgroup's traits and individual membership probability.
Source: Greene & Hensher 2003
What does a latent class model assume?
That the population consists of a small number of unobserved groups, each with its own set of preference weights, and that every respondent belongs to one of them without the analyst knowing which. Estimation recovers the weights for each class and, for every respondent, the probability of belonging to each class. This differs from assuming preferences vary continuously across individuals, since the model posits discrete types rather than a smooth distribution. Membership probabilities can also be related to observed characteristics within the same estimation, which allows the classes to be described in terms a service could act on rather than remaining purely statistical constructs.
Source: Greene & Hensher 2003
Why use a latent class model rather than a random parameters model?
Because it identifies groups that can be described and acted upon, which a continuous distribution does not. Where a service must be configured for identifiable segments, knowing that one group weighs waiting time heavily and another weighs travel distance is more useful than knowing the population variance of each coefficient. The random parameters approach is more flexible about the shape of heterogeneity and less informative about who differs from whom. The two are not mutually exclusive, and specifications combining discrete classes with continuous variation within each class are used where both kinds of heterogeneity appear to be present.
Source: Greene & Hensher 2003
How is the number of classes chosen in a latent class model?
By estimating models with increasing numbers of classes and comparing them on information criteria that penalise complexity, since adding classes always improves fit. The choice is not settled by the statistics alone, because the criteria frequently disagree and a solution with more classes may be statistically preferred while containing groups too small or too similar to interpret. Practical judgement about whether the classes are distinguishable and meaningful therefore enters the decision. Reporting the criteria examined and the solutions rejected is therefore part of transparent practice, since presenting only the chosen specification conceals how much judgement entered the result.
Source: Greene & Hensher 2003
What is a latent class model used for in health?
To identify segments of patients or the public with systematically different preferences over treatment attributes or service configuration, which supports targeted provision rather than a single design for everyone. It is used to establish whether a minority holds preferences that an average would conceal, which matters where a service is intended to be acceptable to all. And class membership can be related to observed characteristics such as age or condition severity, which indicates who the groups are. It is also used to detect groups whose choices are inconsistent with the assumed decision rule, such as respondents ignoring most attributes, which appears as a class with implausible weights.
Source: Lancsar & Louviere 2008
What are the limitations of a latent class model?
The classes are constructs of the model rather than observed groups, so a different specification or a different sample can produce different classes. Membership is probabilistic, so assigning individuals to a class discards information and can mislead where probabilities are close. The approach requires larger samples than a simple model, since each class is estimated from a subset. And identifying who belongs to each class from observed characteristics is frequently only partially successful, which limits how far the findings can be operationalised. Replication in an independent sample is the strongest check available, and it is rarely performed, which means most published class structures rest on a single dataset.
Source: Greene & Hensher 2003
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 1 Aug 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/latent-class-model
- Term code
- HE-EE-CBA-030
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