Latent Class Analysis and its uses Debbie Cooper

Latent Class Analysis and its uses Debbie Cooper, Office for National Statistics

Summary of Presentation • What is Latent Class Analysis? • Advantages of Latent Class Analysis? • Types and extentions of Latent Class Analysis • Examples of applications and potential applications of Latent Class Analysis

What is Latent Class Analysis? “Latent class analysis provides a powerful, flexible approach to the analysis of categorically-scored data. ” (Mc. Cutcheon & Hagenaars, 1997: 266)

What is Latent Class Analysis (LCA)? X Latent variable (true value or characteristic of interest) Indicator variables A B C D

Example Personal well-being Anxious -High -Medium -Low Happy -High -Medium -Low Satisfied -High -Medium -Low Worthwhile -High -Medium -Low These thresholds are not the ones used in the personal well-being official statistics. They are being used for illustrative purposes only.

Latent variables and latent classes Personal well-being Latent Classes: 1. High happy, high satisfied, high worth, low anxious 2. Medium happy, medium satisfied, medium worth, medium anxious 3. Low happy, medium satisfied, medium worth, low anxious 4. Low happy, low satisfied, low worth, high anxious This is a hypothetical example, it is being used for illustrative purposes only. Analysis of UK personal well-being data has NOT actually been carried out for the purposes of this presentation.

Why use Latent Class Analysis? • Clustering techniques: ØK-means clustering ØHierarchical cluster analysis ØLatent Class Analysis • LCA has a number of advantages over these other types of clustering techniques

LCA vs. other clustering methods • LCA is model-based and there are more formal/rigorous criteria to make decisions about one’s final model (Vermunt & Magidson, 2002) • It is relatively easy to deal with variables having different scale types (Vermunt & Magidson, 2002) • LCA allows for fractional cluster membership

Why use LCA? • Holistic approach to analysis – looking at the bigger picture • Can classify respondents to latent classes using posterior probabilities

Why use LCA cont’d • Can include covariates • Can use bootstrapping with sparse data • LCA and variations of it create a multitude of uses

Types of LCA • Exploratory LCA • Confirmatory LCA (restrictions applied) • Latent Transition Analysis (extension of LCA in longitudinal studies) and there’s more. .

Latent variable analysis • Earlier definition of LCA – focus on categorical data • LCA forms part of a much larger field called Latent variable (or structure) analysis • At least 4 types of models can be distinguished in terms of the assumptions underlying the latent variables and their indicators

Latent variable analysis Indicator variables Latent variable(s) Discrete Continuous Discrete Latent Class Analysis Latent Trait Analysis Continuous Latent Profile Analysis Factor Analysis (Biemer, 2011)

Example Applications of LCA • Latent Class Analysis was used to identify wellbeing profiles in Wales using data from the National Survey for Wales (Chanfreau et al. , 2014). • Study using LCA to develop a model of the relationship between socioeconomic position and ethnicity (Fairly et al. , 2014) • Adjusting for non-response bias on the Italian Survey of Households Income and Wealth (Ranalli et al. , 2013)

Example Applications of LCA • Has been used to estimate one or more parameters of a survey error model e. g. Ø used to evaluate classification errors (measurement error) on the US Labour Force Survey (Biemer & Bushery, 1999); Ø used to assess measurement error in the US Consumer Expenditure Survey (Tucker et al. , 2011) • Used to identify flawed survey questions (Kreuter et al. , 2008) • Used to estimate mode effects on the U. S. National Health Interview Survey (Biemer, 2001)

Example Potential Applications of LCA Basic exploratory LCA to identify: Ø well-being profiles (latent classes) Ø economic profiles Ø health profiles Include covariates to investigate the relationships between: Ø health profiles and level of education Ø well-being profiles and level of income Use LTA to investigate impact of an intervention/policy

Questions Please email any questions to: Methodology@ons. gov. uk

Further Reading • Mc. Cutcheon, A. L. , 1987. Latent Class Analysis. California: Sage Publications. • Magidson, J. and Vermunt, J. K. 2004. Latent Class Models. In: Kaplan, D. eds. The SAGE Handbook of Quantitative Methodology for the Social Sciences. California: Sage Publications. pp. 175 -198.

References [1] Biemer, P. P. and Bushery, J. M. 1999. Estimating the Error in Labor Force Data Using Markov Latent Class Analysis. In: FCSM (Federal Committee on Statistical Methodology), 1999 Research Conference, US, November 15 -17, 1999. Biemer, P. P. , 2001. Nonresponse Bias and Measurement Bias in a Comparison of Face to Face and Telephone Interviewing. Journal of Official Statistics, 17(2), p. 295 -320. Biemer, P. P. , 2011. Latent Class Analysis of Survey Error. New Jersey: Wiley. Chanfreau, J. , Cullinane, C. , Calcutt, E. , and Mc. Manus, S. , 2014. Wellbeing in Wales: Secondary analysis of the National Survey for Wales 2012 -13. [pdf] Welsh Government Social Research. Available at: < https: //www. researchgate. net/publication/266301754_Wellbeing_in_Wales_Secondary_analysis _of_the_National_Survey_for_Wales_2012 -13> [Accessed 16 December 2015]. Fairley, L. , Cabieses, B. , Small, N. , Petherick, E. S. , Lawlor, D. A. and Pirkett, K. E. , 2014. Using latent class analysis to develop a model of the relationship between socioeconomic position and ethnicity: cross-sectional analyses from a multi-ethnic birth cohort study. BMC Public Health, 14: 835.

References [2] Kreuter, F. , Yan, T. and Tourangeau, R. , 2008. Good item or bad—can latent class analysis tell? : the utility of latent class analysis for the evaluation of survey questions. Journal of the Royal Statistical Society A. 171(3). Mc. Cutcheon A. L. and Hagenaars, J. A. , 1997. Simultaneous Latent Class Models for Comparative Social Research. In: Langeheine, R. and Rost, J. (eds) Applications of Latent Trait and Latent Class Models. New York: Waxmann. Pgs. 266 -277. Ranalli, M. G. , Matei, A. , and Neri, A. 2013. Handling nonignorable nonresponse using generalized calibration with latent variables. In: IASS (International Association of Survey Statisticians), 59 th World Statistics Congress. Hong Kong, 25 -30 August 2013. Tucker, C. , Meekins, B. and Biemer, P. 2011. Latent Class Analysis of Measurement Error in the Consumer Expenditure Survey. In: AMSTAT (American Statistical Association), 2011 Joint Statistical Meetings, US, July 30 – August 4 th 2011. Vermunt, J. K. , & Magidson, J. 2002. Latent class cluster analysis. In: J. A. Hagenaars, & A. L. Mc. Cutcheon eds. Applied latent class analysis. Cambridge University Press, New York. pp. 89106.