Applied Psychometric Strategies Lab Applied Quantitative and Psychometric
Applied Psychometric Strategies Lab Applied Quantitative and Psychometric Series Caihong R. Li, MS Latent Class Analysis in Mplus November 7, 2017
What will we learn today? 1. 2. 3. 4. 5. Describe latent class analysis (LCA) Identify questions that can be answered by LCA Differentiate between LCA and factor analysis Describe LCA steps in Mplus Provide an empirical example using LCA 2
What is LCA? • LCA is a latent variable modeling approach • LCA identifies unseen (latent) subgroups within a population, using responses from a set of variables • Variables in a LCA can be nominal, ordinal, or continuous 3
What are common applications of LCA? • Identify subgroups of students (e. g. , over-confident students vs. lessconfident students) • LCA could also be used as a diagnostic test in clinical settings (e. g. , assessing the validity of scores from a cognitive assessment) • LCA could also be used to classify a sample into subgroups when we don’t have a “gold standard”(e. g. , the cut score between “self-regulators” and “procrastinators”) • LCA could also be used to adjust for noise caused by invalid responding, nonresponse bias, etc. 4
What research questions can be answered by LCA? 1. Are there different latent classes of students based on their responses to a set of items measuring a variable? 2. If we hypothesize that the participants in my sample can be grouped into two latent classes, how do we confirm this hypothesis? 3. If two latent classes are identified, what is the sample size per latent class? 4. Given someone’s response pattern, what is the probability that a person belongs to a certain class? 5
What is modeled in LCA? Item 1 • The “latent classes” variable Item 2 Item 3 • The “latent classes” variable is a categorical latent variable and the categories being the types of latent classes Latent Classes Item 4 Item 5 • Latent classes differ from each other in their response patterns Item 1 Item 2 • Individuals in each class are similar to each other in their response patterns Item 3 Item 4 Item 5 Latent Class 1 Latent Class 2 Item 3 Item 4 Item 5 6
What is the difference between LCA and factor analysis (FA)? Item 1 Item 2 Item 3 Latent classes Item 3 Item 4 Item 5 LCA: Person-centered A latent continuous construct FA: Item-centered 7
Let’s Review • LCA identifies unseen subgroups within a population, using responses from a set of variables/items • LCA is commonly used when it’s necessary to identify latent classes from a sample or a “gold rule” of classifying people is NOT readily available • The only variable modeled in LCA is the “latent classes” variable • LCA classifies people NOT items 8
What are the BASIC steps when conducting a LCA in Mplus? 1 Identify LCA indicators 2 3 4 Estimate LCA models Evaluate LCA models Interpret LCA results 9
1: Identify LCA indicators • Determine the items/variables you want to use and that make sense for your purposes – Existing instrument – Write a set of items for your purpose – A combination of the above options 10
Example: Do we have invalid respondents in online survey responses? Data (FAKE!) N = 1, 000 Mplus Code Indicator/Item Categories Options 1. Speedy Average response time to an item is less than 3 s 2 1 = less than 3 s; 0 = equal or greater than 3 s 2. Lying I have told the truth on this survey. 2 1 = NO; 0 = YES 3. Careless I was careless when I answered this survey. 2 1 = YES; 0 = NO 4. Disable I have more than two types of disabilities. 2 1 = YES; 0 = NO 5. Extreme Mean score ranked 99 percentile or higher 2 1 = 99 th percentile or higher; 0 = lower than 99 th percentile 1 1 1 1 0 0 0 0 1 0 0 0 11
2:Estimate LCA models Speedy Lying Careless Speedy 2 Latent Classes Lying Careless Disable Extreme Speedy Lying Careless 4 Latent Classes Lying Careless Disable Extreme 3 Latent Classes 5 Latent Classes 12
Create Mplus syntax 1. Create the syntax for a 2 -class LCA model 2. Make sure the syntax runs properly 3. Using the 2 -class LCA model syntax as a template, create syntaxes for LCA models with 3 latent classes, 4 latent classes, and 5 latent classes, separately 4. Run the rest of the syntaxes 13
Create syntax for 2 -latent-class model 14
Create syntax for 2 -latent-class model (con. ) 15
Create syntax for 2 -latent-class model (con. ) 16
Create syntaxes for other models If we want to specify a 3 -class LCA model, where do we make changes? 17
Mplus files for each LCA model Mplus files for LCA • For each LCA model, 4 files are connected with it: – Input file – Output file – Graph file – New data file 18
3: Evaluate LCA models Q: How many classes should we retain? A: Multiple statistical criteria 1. Bayesian Information Criterion (BIC) 2. Adjusted BIC (ABIC) 3. Lo-Mendell-Rubin likelihood ratio test (LMR LRT) 4. The bootstrap likelihood ratio test (Bootstrap LRT) 5. Interpretability 19
BIC & ABIC LCA Models BIC ABIC 2 -Class 2311. 414 2276. 477 3 -Class 2342. 577 2288. 584 4 -Class 2371. 190 2298. 140 5 -Class 2405. 083 2312. 977 20
LMR LRT LCA Models p for LMR 2 -Class vs. 1 -Class <. 001 3 -Class vs. 2 -Class . 0244 4 -Class vs. 3 -Class . 0017 5 -Class vs. 4 -Class . 0089 21
Bootstrap LRT LCA Models p for Bootstrap 2 -Class vs. 1 -Class <. 001 3 -Class vs. 2 -Class . 1765 4 -Class vs. 3 -Class . 0698 5 -Class vs. 4 -Class . 1923 22
Which model is the best? LCA Models BIC ABIC 2 -Class 2311. 414 2276. 477 3 -Class 2342. 577 4 -Class 5 -Class LCA Models p for LMR p for Bootstrap 2 -Class vs. 1 -Class <. 001 2288. 584 3 -Class vs. 2 -Class . 0244 . 1765 2371. 190 2298. 140 4 -Class vs. 3 -Class . 0017 . 0698 2405. 083 2312. 977 5 -Class vs. 4 -Class . 0089 . 1923 23
4: Interpret LCA Results • Given a person belongs to a certain class, what is this person’s probability of saying “yes” to each item? • What should we label each latent class? • Given a person’s response pattern, what is the probability that person belongs to a certain class? • What is the sample size of each latent class? 24
Given a person belongs to a certain class, what is this person’s probability of saying “yes” to each item? 25
What should we label each latent class? 26
Given a person’s response pattern, what is the probability that person belongs to a certain class? lca 2_save. txt: 27
What is the sample size of each latent class? Intervention? Sensitivity analysis 28
All in one plot Speedy Lying Careless Disable Extreme Figure 1. Item probability profiles for 2 -class latent class model (N = 1, 000) 29
How to get the item probability profile plot? 30
What does a bad model look like? Figure 2. Item probability profiles for 3 -class latent class model (N = 1, 000) 31
How can we use the “latent classes” variable? Relationship with covariates Speedy Lying Careless Relationship with outcome variables Latent classes Disable Gender Lying Careless Race Disable Gender Latent classes Selfefficacy Race Extreme c on gender race; SE on c gender race; 32
Troubleshooting bootstrap LRT 33
Common problem with bootstrap LRT 34
How to solve it? LRTSTARTS = 0 0 40 8; by default LRTSTARTS = 0 0 300 20; 35
Problem solved! 36
Things to keep in mind when doing LCA • LCA classifies people (not items) into unseen subgroups • A large dataset is required • With many indicators, consider the full version of Mplus • Other software to complete LCA: – Latent. Gold, Proc LCA in SAS, po. LCA in R 37
References • Asparouhov, T. & Muthén, B. (2012). Using Mplus TECH 11 and TECH 14 to test the number of latent classes. Mplus Web Notes: No. 14. May 22, 2012 • Denson, N. , & Ing, M. (2014). Latent class analysis in higher education: An illustrative example of pluralistic orientation. Research in Higher Education, 55, 508 -526. doi: 10. 1007/s 11162 -013 -9324 -5 • Porcu, M. & Giambona, F. (2017). Introduction to latent class analysis with applications. Journal of Early Adolescence, 37, 129158. doi: 10. 1177/0272431616648452 38
How do I cite and reference this talk? • If you wish to cite the video of this AQPS Talk, please use this reference and citation: Reference: Li, C. R. (2017, November). Latent class analysis in Mplus. [Video file]. Retrieved from http: //sites. education. uky. edu/apslab/upcoming-events/ In-text citation: Li (2017) or (Li, 2017) • This Power. Point Handout can be found at the APS Lab website: http: //sites. education. uky. edu/apslab/upcoming-events/ • You can download the fake raw data and Mplus input and output syntax used in this talk from the APS Lab website. You are encouraged to adapt our syntax for your own research—please use this reference and citation when doing so: Reference: Li, C. R. (2017). Name of specific syntax file you adapted from us goes here [Data file]. Retrieved from http: //sites. education. uky. edu/apslab/upcoming-events/ In-text citation: Li (2017) or (Li, 2017) 39
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