Introduction to Profile Analysis: Foundations of the Person-Centred Approach in Health Research

An entry-level (Introduction 101) primer

Abstract

Profile analysis is an umbrella term for a family of multivariate techniques that treat an individual’s scores across several measures as a single, meaningful pattern rather than as a set of separate numbers. This chapter offers an entry-level introduction for health researchers and health management students. It proceeds in four steps. First, it warns the reader about a practical hazard: the phrase “profile analysis” is used in at least six unrelated scientific literatures, ranging from X-ray line profile analysis in materials science to texture profile analysis in food science, so that a naive citation search retrieves a corpus that is largely irrelevant to health research. A structured search of 79 highly cited records showed that roughly six in ten fell outside the behavioural and health sciences. Second, it introduces the classical, ANOVA-based profile analysis of Greenhouse and Geisser (1959) and Nunnally (1962), organised around its three canonical questions: parallelism, level and flatness. Third, it introduces latent profile analysis (LPA), the model-based, person-centred technique that dominates contemporary health applications, covering the underlying finite mixture model, class enumeration criteria (BIC, aBIC, LMR-LRT, BLRT, entropy), variance–covariance specifications, and the three-step approach for auxiliary variables. It then extends these ideas to categorical indicators (latent class analysis) and to four complications common in applied health surveys: checking the local-independence assumption with bivariate residuals and, where needed, adding direct effects; incorporating sampling weights and complex-survey design; correcting for classification error when relating class membership to external variables through bias-adjusted three-step and BCH approaches; and modelling distal outcomes that are counts with Poisson, negative-binomial and hurdle models. Fourth, it works through an illustrative SF-36 example and closes with a reporting checklist, a discussion of common errors, including Watkins’s (2000) caution against over-interpreting subtest profiles, and a software guide. The chapter assumes only introductory statistics and requires no matrix algebra.

Keywords: profile analysis, latent profile analysis, person-centred methods, finite mixture models, health surveys, SF-36, health services research, latent class analysis, local dependence, sampling weights, count data models

1. Introduction: What the Average Hides

Suppose a hospital administers the SF-36 quality-of-life scale to 800 of its discharged patients. The scale yields eight subdimensions: physical functioning, physical role limitation, pain, general health, vitality, social functioning, emotional role limitation and mental health. The researcher sitting down to analyse the data faces 800 rows and 8 columns. The classical reflex is to take the mean of each column and compare these across groups: “The pain score is 58.3 in women and 63.1 in men; the difference is significant (p = 0.012).”

This approach is not wrong, but it is incomplete. Eight separate means answer eight separate questions; none of them answers the question, “How many kinds of patient are there in this population?” A mean pain score of 58.3 could arise from any of three different realities: (a) a homogeneous group in which almost everyone experiences moderate pain; (b) a bipolar group, half of whom feel no pain at all and half of whom are in severe pain; (c) a skewed distribution in which a small but highly painful subgroup pulls the mean down. The managerial decision is entirely different in these three cases. The first calls for a general pain protocol; the second, two separate targeted programmes; the third, intensive-care resources for a small group.

Profile analysis aims precisely at making this distinction. Its core idea can be stated in a single sentence: an individual’s scores across several measures should be treated not as separate numbers but as a single pattern—that is, as a profile. What is of interest is not the individual’s “pain score” but their pattern of “high pain but preserved social functioning.”

Conceptual distinction: Variable-centred analysis asks about relationships among variables (“Is there a correlation between pain and depression?”). Person-centred analysis asks about similarities among individuals (“How many types of individual resembling one another are there in this sample?”). Profile analysis belongs to the second family of questions. The two are not rivals but complements.

2. A Caveat: What “Profile Analysis” Is Not

In writing this chapter, a search was run on Google Scholar for studies with “profile analysis” or “analysis of profile” in the title. The query returned about 301 records; the 79 most highly cited of these were examined. The result produced a warning that every entry-level reader should know: the great majority of these 79 records have nothing to do with health research.

The term is used in at least six entirely unrelated literatures. The table below shows the disciplinary distribution of the searched set and what the concept of a “profile” means in each discipline.

Discipline	Records	Total citations	What “profile” means here
Methodology / Statistics	12	17,776	An individual’s multi-measure pattern (the subject of this chapter)
Materials science & Crystallography	17	9,749	The shape of the X-ray diffraction peak (line profile)
Education & Psychology	15	4,194	An individual’s multi-measure pattern (relevant to the subject)
Health & Life sciences	13	4,910	Mixed: both method and gene/metabolite profile
Food science	10	3,494	Texture profile analysis (TPA): force–time curve
Engineering / Business / Environment	8	1,826	Program-execution profile, supplier profile, life cycle
Earth sciences & Astrophysics	4	4,211	Stream longitudinal profile, mass-distribution profile
TOTAL	79	46,160

The figures are clear: roughly 60% of the searched set (materials, food, earth sciences, engineering) is unrelated to the subject of this chapter. Moreover, looking at the individual most-cited studies makes the picture even more striking. The studies ranked 4th, 5th, 6th and 7th on the list are, respectively, stream longitudinal-profile analysis (Hack, 1973; 1,939 citations), lattice strain in ZnO nanoparticles (Bindu & Thomas, 2014; 1,914 citations), the detection of distantly related proteins by sequence comparison (Gribskov et al., 1987; 1,898 citations), and the effect of dislocation contrast on X-ray line broadening (Ungár & Borbély, 1996; 1,710 citations).

Practical rule: When searching the health-domain profile-analysis literature, “profile analysis” on its own is never a sufficient keyword. Use a query that requires both the method name (“latent profile analysis”) and the domain context (“health survey,” “SF-36,” “quality of life”) together. A full search strategy is given in the appendix to this chapter.

Likewise, expressions common in the clinical literature such as “lipid profile,” “risk factor profile” and “cytokine profile” are not names of a method; they are simply labels given to a bundle of variables measured together. The appearance of “lipid profile analysis” in a study’s title does not mean that the study used the profile analysis method.

3. Two Families: Classical Profile Analysis and Latent Profile Analysis

The methods collected under the heading “profile analysis” fall, for health research, into two large families. Clarifying this distinction from the outset prevents later confusion.

	Classical profile analysis	Latent profile analysis (LPA)
Core question	Do the profiles of known groups resemble one another?	How many unknown subgroups are there in the sample?
Groups	Known in advance (sex, diagnosis, clinic)	Estimated from the data
Statistical framework	Multivariate ANOVA / MANOVA	Finite mixture model (maximum likelihood)
Founding source	Greenhouse & Geisser (1959); Nunnally (1962)	Gibson (1959); Lazarsfeld’s latent structure analysis
Output	F statistics and p-values	Number of classes, class proportions, membership probabilities
Typical software	SPSS GLM, R (profileR), Stata	Mplus, R (tidyLPA, mclust), Latent GOLD
Example question	“Are the SF-36 profiles of diabetic and non-diabetic patients parallel?”	“Into how many types do these patients divide according to their SF-36 scores?”

In practice the terminology is used loosely. In the health literature of the past 15 years, “profile analysis” almost always refers to the second family—latent profile analysis. Yet the first both comes earlier historically and establishes the conceptual foundations; for that reason we begin with it.

4. Classical Profile Analysis: Three Questions

Classical profile analysis compares the mean profiles of two or more groups on the same battery of scales. For example, the means of 200 patients diagnosed with diabetes and 200 people without the diagnosis on the eight subdimensions of the SF-36 are plotted, yielding two lines. The method asks three mutually independent questions about these two lines.

4.1. The parallelism (interaction) test

Are the two profile lines parallel to each other? That is, is the difference between the groups the same magnitude across all subdimensions? If parallelism is rejected, there is an interaction between group and measure: diabetes may, for example, affect physical functioning greatly and mental health only slightly. Statistically, this is the group × measure interaction in a repeated-measures ANOVA, and it is usually the most interesting of the three questions.

4.2. The level test

If the profiles are parallel, is one systematically above the other? This compares the overall means of the groups and reduces to a single independent-samples t-test (or one-way ANOVA).

4.3. The flatness test

If the profiles are parallel and at the same level, is the common profile horizontal? That is, is there no difference at all among the subdimensions? This question is rarely of interest in practice, because the means of subdimensions with different content are not expected to be equal.

4.4. Assumptions and the Greenhouse–Geisser correction

When classical profile analysis is carried out within a repeated-measures framework, it requires the sphericity assumption: the variances of the differences between pairs of measures must be equal. In scales such as the SF-36, whose subdimensions differ in structure, this assumption is almost never met.

Greenhouse and Geisser’s 1959 Psychometrika paper—while also the most highly cited study in the literature searched for this chapter (6,675 citations)—addresses precisely this problem. The authors propose an epsilon (ε) coefficient that summarises the degree to which sphericity is violated, and correct the degrees of freedom of the F test by multiplying them by this coefficient. ε = 1 indicates that sphericity holds exactly; the further ε departs from 1, the more severe the violation.

Application note: When Mauchly’s sphericity test gives p < 0.05, a correction must be applied. If ε > 0.75, the Huynh–Feldt correction (less conservative) is preferred; if ε ≤ 0.75, the Greenhouse–Geisser correction. SPSS reports both automatically; which one was used and the ε value must always be stated in reporting.

Nunnally’s (1962) paper in Psychological Bulletin, in turn, offers a conceptual contribution; in it a profile is decomposed into three components: level (the individual’s overall score elevation), scatter (the variability of their scores) and shape (which subdimension is high relative to which). This threefold distinction is the source of the language still used today in interpreting LPA results: profile labels common in the literature, such as “high level–flat shape” or “low level–jagged shape,” come directly from this framework.

5. Latent Profile Analysis (LPA)

Classical profile analysis assumes you know the groups. But the most interesting questions in health research are often these: the groups are unknown. We do not know which patients fall into which type; indeed we do not even know how many types there are. Latent profile analysis fills this gap.

5.1. The basic idea

The assumption of LPA is this: the heterogeneous population we observe is in fact a mixture of several homogeneous subpopulations. Each subpopulation (class, profile) has its own characteristic mean pattern on the indicator variables. Class membership cannot be observed directly; this is why the model is called “latent.” Nevertheless, class membership can be inferred backward from the distribution of the observed scores.

The model sits within the finite mixture framework. In a K-class model, the probability density of an individual’s observed score vector y is written as:

f(y) = Σ(k=1..K) πₖ · fₖ(y | μₖ, Σₖ)

Here πₖ is the proportion of the k-th class in the population (Σπₖ = 1), μₖ is that class’s mean vector on the indicator variables, and Σₖ is the within-class variance–covariance matrix. In standard LPA, fₖ is the multivariate normal distribution. Estimation is by maximum likelihood, usually via the EM (expectation–maximisation) algorithm.

In practice this means that, for each individual, the probability of belonging to each class is computed. A patient receives a probability vector such as “probability of belonging to profile 1 = 0.92; to profile 2 = 0.07; to profile 3 = 0.01.” This probabilistic membership is the most important feature distinguishing LPA from traditional cluster analysis.

5.2. The difference between LPA, LCA and cluster analysis

Method	Indicator variables	Model-based?	Membership
Latent class analysis (LCA)	Categorical (yes/no, present/absent)	Yes	Probabilistic
Latent profile analysis (LPA)	Continuous (scale scores)	Yes	Probabilistic
k-means clustering	Continuous	No	Hard (0/1)
Hierarchical clustering	Continuous or mixed	No	Hard (0/1)

Williams and Kibowski’s (2016) introduction to LCA/LPA elaborates this distinction. For the health researcher, the practical upshot is this: if your indicators are continuous scale scores (SF-36 subdimensions, WHOQOL domains, PHQ-9 total score), use LPA; if they are binary/categorical (symptom present/absent), use LCA. If the two are mixed, a “factor mixture model” or mixed-indicator models are required.

This second route, which works with categorical indicators—latent class analysis (LCA)—has a substantial literature of its own. Collins and Lanza (2010) set out the theoretical and applied foundations of the method—item-response probabilities, class proportions, the naming of classes and the inclusion of covariates in the model—systematically; Hagenaars and McCutcheon (2002), with their applied examples, are a complementary reference. For the general framework of categorical-data analysis, Agresti (2019) is the standard text. The bridge between LPA and LCA is conceptual: both belong to the finite mixture family, and the problems of class enumeration, local independence and classification error discussed below are common to both models. For this reason, throughout the rest of the chapter the terms “class” and “profile” will be used interchangeably unless otherwise noted.

The superiority of LPA over k-means is not merely philosophical. Being model-based means that statistical criteria (BIC, likelihood-ratio tests) can be used to decide on the number of classes. In k-means there is no statistical answer to the question “how many clusters?”; one looks at the elbow plot and decides. The simulation study of Wang et al. (2017) and the power study of Tein, Coxe and Cham (2013) show under what conditions these criteria are reliable.

5.3. How many profiles? Deciding on the number of classes

This is the most critical and most contested step in an LPA application. The standard approach is to start from a 1-class model, increase the number of classes one at a time, and compare each model on the criteria below.

Criterion	What it tells you	Decision rule
BIC (Bayesian Information Criterion)	Balance of model fit and complexity	Lowest BIC is preferred; regarded as the single most reliable criterion
aBIC (sample-size-adjusted BIC)	More accurate in small samples	Lowest value is preferred
AIC	Similar to BIC, penalises complexity less	Should not be used alone; tends to suggest too many classes
LMR-LRT (Lo–Mendell–Rubin)	Does the K-class model improve significantly over K−1?	p < 0.05 → prefer K classes; p > 0.05 → stop at K−1
BLRT (Bootstrap LRT)	Same question, via bootstrap	The most accurate test in simulations; high computational cost
Entropy	The sharpness of the classification	> 0.80 good; > 0.90 very good. It is NOT a criterion for the number of classes
Smallest-class proportion	Is the class usable in practice?	< 5% warrants caution; that solution is usually abandoned

The most common error: Mistaking entropy for a criterion for the number of classes. Entropy tells you how clear the classification is in the chosen solution; it does not tell you how many classes there should be. The simulation study of Wang et al. (2017) shows that using entropy for this purpose is misleading. A high entropy can lead to the wrong number of classes being chosen.

Statistical criteria do not always converge on a single solution. BIC may suggest 4 classes, BLRT 5, and LMR-LRT 3. In that case the rule is this: theoretical interpretability has the final word. A fourth class that you cannot name and that is clinically meaningless should be abandoned even if its BIC is lowest. Spurk et al.’s (2020) guide treats reporting this decision transparently—that is, presenting the fit criteria of all models in a single table—as mandatory.

How much to trust which criteria in deciding on the number of classes is the subject of a distinct literature. The Monte Carlo study of Nylund, Asparouhov and Muthén (2007) showed that AIC frequently overestimates the number of classes, whereas BIC and especially the bootstrap likelihood-ratio test (BLRT) are more reliable in recovering the correct number; this finding provides the methodological basis for fine choices such as that between four- and five-class solutions. Weller, Bowen and Faubert (2020) offer an accessible best-practice guide to how these criteria should be reported together; Bartolucci, Pandolfi and Pennoni (2022), in turn, place discrete latent-variable models within a broader theoretical framework. The shared emphasis of these sources is clear: the number of classes should not be chosen on the basis of the lowest BIC or AIC alone. Information criteria should be evaluated together with the reproducibility of the solution across different starting values, the size of the smallest class, entropy, the distinguishability of the classes from one another, and theoretical interpretability.

5.4. Variance–covariance structure: the overlooked decision

When an LPA is set up, most software applies the following two constraints by default: (a) the within-class variances are equal across all classes, and (b) the within-class covariances are zero (local independence). This is the most restrictive and most easily converging model; but in health data it is often unrealistic.

For example, in a severely ill patient group the variance of SF-36 scores may differ markedly from that of a healthy group. Freeing the variances across classes gives a better fit in such cases; but because it increases the number of parameters, it can lead to convergence problems. Ferguson, Moore and Hull (2020) and Spurk et al. (2020) recommend that the variance–covariance specification be reported explicitly, because different specifications on the same data can yield different numbers of classes.

5.5. Local Independence, Residual Dependence and Direct Effects

Most mixture models rest on a critical assumption: local independence. Under this assumption, once class membership is known the indicators are independent of one another; that is, all association among the indicators is explained by the latent class structure. When the assumption is violated—that is, when certain pairs of indicators remain associated even after conditioning on class—the model often tries to absorb this residual association by “inventing” an extra class. The result is more classes than warranted and artificial profiles that resist interpretation. Hagenaars (1988) proposed, as an early solution to this problem, adding direct effects between indicators to the model; Asparouhov and Muthén (2015) detailed how residual associations are to be handled in latent class and latent transition models. Berzofsky, Biemer and Kalsbeek (2014) showed that local dependence is especially problematic for rare and sensitive events; Nagelkerke, Oberski and Vermunt (2016), in turn, showed how model fit is to be tested in multilevel structures.

The procedure to follow in practice is summarised compactly in the guide by Visser and Depaoli (2022). First, bivariate residuals (BVR) are computed and reported for all pairs of indicators; alongside the raw p-values, p-values adjusted for multiple comparisons are also given. Direct effects are added to pairs showing high residual dependence and the model is re-estimated. This is followed by sensitivity analyses in which one of the problematic indicators is removed. Finally, it is examined whether the class sizes and class structure change when local dependence is allowed; if the structure remains stable, confidence in the solution increases.

5.6. Complex Sample Design and Weighted Estimation

A substantial share of health research rests not on simple random sampling but on stratified and clustered complex sampling designs, and the observations carry sampling weights. If these weights are ignored, both the class proportions and the parameters may be estimated with bias. Vermunt and Magidson (2007) show how sampling weights can be incorporated into a mixture model within the maximum-likelihood framework—via a weighted EM algorithm; this is the direct basis of “weighted LCA” applications. For the effect of weights, clustering and stratification on standard errors, Lumley (2010) is the reference to consult.

A limitation must be stated explicitly here. Correct design-based variance estimation requires access to the primary sampling units (PSUs) and stratum information. When this information is not available in the data set, the standard errors obtained from weighted estimation are not “full complex-survey variances”; this should be noted as a limitation in interpreting the findings.

5.7. Auxiliary Variables, Classification Error and the Three-Step Approach

The natural question after finding the profiles is: “Which patients fall into which profile, and does profile membership predict outcomes?” There is a serious methodological trap here.

The naive approach—assigning each individual to their most likely class and using this assignment as an ordinary categorical variable—ignores classification error and systematically weakens the associations. The correct approach is three-step: (1) an LPA model is built with the indicators only; (2) the classification error is computed; (3) the auxiliary-variable analysis is carried out taking this error into account.

In Mplus this is done with the BCH command for continuous outcomes, DU3STEP for categorical outcomes and R3STEP for antecedent variables. When entropy is above 0.90, the difference between simple assignment and the three-step approach shrinks; but when entropy is below 0.80, the three-step approach is mandatory.

The statistical basis of the three-step approach is well established. Bolck, Croon and Hagenaars (2004) compared one-step and three-step estimators and exposed the bias caused by naive assignment; Vermunt (2010) proposed two improved three-step approaches for models with covariates. Bakk, Tekle and Vermunt (2013) examined methods that estimate the association between class membership and external variables while correcting for classification error; Bakk and Kuha (2021), in turn, offer a recent review comparing one-step, three-step, BCH and similar corrected approaches. The robustness of the BCH method for continuous distal outcomes has been examined by Bakk and Vermunt (2016) and Bakk, Oberski and Vermunt (2016); the implementation details in Mplus can be found in Asparouhov and Muthén (2014), and a recent overall assessment of this whole family in Vermunt (2025). The practical upshot is this: assigning individuals to a class solely on the basis of the highest posterior probability and then using that class as an error-free observed variable produces biased results. Posterior-draw (pseudo-class) based approaches provide a useful sensitivity check; but confirming the main distal outcomes with the BCH or a corrected three-step method offers stronger evidence.

5.8. Distal Outcomes: Count Data Models

The distal outcome to which profile membership is related is not always continuous or binary; a common situation is that the outcome is a count—such as the number of activities an individual took part in, or a number of visits. Count data do not meet the assumptions of ordinary linear regression and require their own models. Cameron and Trivedi (2013) are the basic reference for these models; Zeileis, Kleiber and Jackman (2008) present their implementation in R, and Mullahy (1986) the theory of modified count models.

The appropriate model changes with the structure of the outcome. For the distinction between not taking part in any activity and taking part in at least one, a logistic model is used; for the number of activities among participants, a zero-truncated Poisson or negative binomial; for the total number of activities, Poisson, or negative binomial if there is overdispersion. If the zeros are thought to be generated by a separate process—that is, if the decision “not to take part at all” and the decision “how many times to take part” are different mechanisms—hurdle (two-part) models are appropriate.

6. An Illustrative Application: Quality-of-Life Profiles with the SF-36

To make the method concrete, let us work through a fictitious but realistic example. Suppose the SF-36 is administered to 612 patients in the chronic-disease outpatient clinic of a university hospital. The aim is to classify patients according to their quality-of-life patterns and to examine the relationship of profile membership with health-service use.

Step 1: Data preparation

The eight subdimension scores are transformed to the 0–100 range. The missing-data pattern is examined; for missingness below 5%, full-information maximum likelihood (FIML) is used. Highly skewed distributions (|skewness| > 2) are noted. The indicators may be standardised; standardisation does not change the class structure but makes the profile plots easier to read.

Step 2: Model comparison

Models with 1 to 6 classes are fitted. Each model is estimated with 500 random starting values (to avoid getting stuck in a local maximum; this setting must be reported). The results are gathered in a table like the one below.

Classes	LL	BIC	aBIC	LMR-LRT p	BLRT p	Entropy	Smallest class %
1	−18,412	36,927	36,876	None	None	None	100.0
2	−17,203	34,573	34,470	<0.001	<0.001	0.88	38.2
3	−16,641	33,506	33,351	0.004	<0.001	0.84	21.4
4	−16,402	33,086	32,879	0.041	<0.001	0.82	11.7
5	−16,338	33,075	32,816	0.318	<0.001	0.76	4.1
6	−16,309	33,134	32,823	0.624	0.082	0.74	2.3

The values in the table are illustrative; they are not taken from a real study. The aim is to show how the decision process works.

Decision: BIC is lowest at 5 classes (33,075), but the improvement over 4 classes is negligible (Δ = 11), and the proportion of the 5th class is 4.1%, which corresponds to only 25 of the 612 patients. In addition, the LMR-LRT becomes non-significant at the 5th class (p = 0.318) and entropy falls from 0.82 to 0.76. Together, these three signals point to the 4-class solution.

Step 3: Naming the profiles

Naming follows Nunnally’s (1962) level–shape distinction: first the overall elevation of the profile, then the distinguishing shape feature, is reflected in the name.

Profile	Proportion	Pattern	Name
1	34.1%	High and flat across all subdimensions	Preserved quality of life
2	31.8%	Physical dimensions low, mental dimensions preserved	Physical-limitation dominant
3	22.4%	Mental dimensions low, physical dimensions preserved	Psychosocial-burden dominant
4	11.7%	Low across all subdimensions	Widespread impairment

A point to note: profiles 2 and 3 are close to each other in mean score but opposite in shape. A variable-centred analysis could never separate these two groups; it is inevitable that both would appear as “moderate quality of life.” This is exactly where profile analysis contributes, and the managerial counterpart of that contribution is direct: profile 2 calls for physiotherapy and rehabilitation resources, profile 3 for psychosocial support resources.

Step 4: Auxiliary-variable analysis

The antecedents of profile membership (age, sex, number of comorbidities, income) are examined in a multinomial logistic regression with R3STEP; the outcomes (annual number of outpatient visits, emergency-department use) are compared with the BCH method. Effect sizes (OR and 95% CI) must always be reported.

7. Sample Size and Power

There is no single sample-size formula for LPA; the required n depends on how well separated the classes are from one another, the number of indicators, and the expected proportion of the smallest class. Tein, Coxe and Cham (2013) show that when class separation is good (standardised mean difference ≈ 1.5 SD), n = 300 is sufficient in most cases; when separation is weak (≈ 0.8 SD), even n = 1,000 can be inadequate.

Three practical rules of thumb for the practitioner:

1. Aim for at least 50 observations for the smallest expected class. If you expect a 5% class, that means n ≥ 1,000.
2. Increasing the number of indicators can reduce the sample-size requirement; but this holds only if the indicators genuinely distinguish the classes. Adding an indicator that does not distinguish them adds noise.
3. If a precise power analysis is needed, use Monte Carlo simulation (the Mplus MONTECARLO command). Define the expected profile structure, generate 500–1,000 replications, and compute the rate of recovering the correct number of classes.

8. Common Errors

The most important warning of this section comes from the most highly cited critical study in profile analysis. Watkins (2000) characterises the clinical interpretation of intelligence-test subtest profiles as “a shared professional myth.” For decades, psychologists made diagnostic inferences from an individual’s subtest pattern; but although the reliability of the subtests individually is high, the reliability of the DIFFERENCES between them is low. The standard error of the difference between two scores is larger than the standard errors of either score.

Critical principle: The peaks and troughs in a profile can also arise from measurement error. For a pattern to be clinically interpretable, it must be larger and more reproducible than what could be explained by measurement error. This is a far stricter requirement when interpreting a single individual’s profile (individual diagnosis) than when finding profiles at the group level (LPA).

Other common errors:

• Mistaking profiles for real entities. The classes found by LPA are statistical constructs; they are not proof that there exist, in nature, patient “types” separated by sharp boundaries. A continuous distribution, too, often yields a well-fitting multi-class solution.
• Relying on a single fit criterion. BIC alone, or LMR-LRT alone, is not enough; the criteria are evaluated together and alongside interpretability.
• Ignoring classification error. Assigning the most likely class and running an ordinary ANOVA estimates the associations with a downward bias. Use the three-step approach.
• Failing to validate. Split the sample in two (split-sample cross-validation) and test whether the profile structure emerges in both halves. If possible, replicate in an independent sample.
• Ignoring the local-maximum problem. A model estimated with an insufficient number of starting values may not have found the best solution. Verify that the best log-likelihood is replicated.
• Fixing the number of classes before the analysis. Starting out saying “we expect to find three profiles” and stopping at three is using an exploratory method as if it were confirmatory.
• Failing to check for local dependence. Residual dependence between indicators can lead the model to produce more classes than warranted. Examine the bivariate residuals (BVR); add direct effects to pairs with high dependence where needed.
• Modelling count outcomes incorrectly. Analysing distal outcomes such as the number of activities or visits with ordinary linear regression—and failing to use Poisson/negative binomial or hurdle models when there is overdispersion and zero-inflation—produces misleading results.

9. Reporting Checklist

The following list contains the minimum elements that should appear in the methods and results sections of an LPA study. These are the omissions most often requested in reviewer reports.

1. Indicator variables: which ones, from which scale, with what scoring, and whether standardised.
2. Missing data: proportion, pattern and method of handling (FIML, multiple imputation).
3. Estimation details: software and version, estimator (MLR recommended), number of random starts, convergence verification.
4. Variance–covariance specification: whether the variances are equal or free across classes; whether the covariances are zero.
5. Model-comparison table: for all models from 1 to K+1, the LL, number of free parameters, AIC, BIC, aBIC, LMR-LRT p, BLRT p, entropy and smallest-class proportion.
6. Justification of the number-of-classes decision: statistical criteria and theoretical interpretability should be discussed separately.
7. Average classification-probability matrix (diagonal values > 0.80 are expected).
8. Profile plot: indicator means (preferably standardised) and class proportions.
9. The approach used in the auxiliary-variable analysis (BCH / DU3STEP / R3STEP) and its justification.
10. Effect sizes and 95% confidence intervals.
11. Local-independence check: BVR values for all pairs of indicators, raw and adjusted p-values; direct effects added and sensitivity analyses performed.
12. Sampling weights and design: whether weights were used, how clustering and stratification were handled, and the nature of the standard errors.
13. Distal-outcome model: the model chosen for count outcomes (Poisson, negative binomial, zero-truncated or hurdle) and the rationale for the choice.
14. Limitations: cross-sectional design, sample representativeness, and whether cross-validation was performed.

10. Software Guide

Software	Package / Command	Note
Mplus	TYPE = MIXTURE	The field standard. BCH, DU3STEP, R3STEP and Monte Carlo power analysis are built in. Commercial.
R	tidyLPA	The easiest way to start; works with an mclust or Mplus back end (Rosenberg et al., 2018). Free.
R	mclust	Gaussian mixture models; automatically compares 14 different variance–covariance specifications.
R	poLCA	For categorical indicators (LCA).
R	profileR	Classical profile analysis, PAMS and moderated profile analysis (Bulut & Desjardins, 2020).
Stata	gsem, lclass()	Mixture models within the generalised SEM framework.
SPSS	Two-Step Cluster	It is NOT LPA. It is not model-based; its fit criteria cannot be compared with those of LPA.
Latent GOLD	None	Commercial software dedicated to latent class modelling.

11. Conclusion

Profile analysis gives the health researcher the ability to see what the average hides. In situations where a population can be described not by a single number but by several distinguishing patterns, the person-centred approach produces more informative results, both theoretically and managerially; such situations are frequently encountered in health-services research.

The method is, however, also open to misuse because of how easily it can be applied. The software always returns a solution; even in data with no heterogeneity, several classes will be “found.” For this reason the three principles emphasised throughout the chapter form the backbone of practice: (1) use the criteria together, do not trust a single number; (2) interpretability comes before statistical fit; (3) validate the profiles you find, if possible in an independent sample.

Finally, the warning from the opening of this chapter bears repeating. When conducting a literature search, the cross-disciplinary polysemy of the term “profile analysis” causes a serious waste of time. The search strategy in the appendix can be used to reach the health-focused literature directly.

References

Agresti, A. (2019). An introduction to categorical data analysis (3rd ed.). Wiley.

Asparouhov, T., & Muthén, B. (2014). Auxiliary variables in mixture modeling: Three-step approaches using Mplus. Structural Equation Modeling, 21(3), 329–341. https://doi.org/10.1080/10705511.2014.915181

Asparouhov, T., & Muthén, B. (2015). Residual associations in latent class and latent transition analysis. Structural Equation Modeling, 22(2), 169–177. https://doi.org/10.1080/10705511.2014.935844

Bakk, Z., & Kuha, J. (2021). Relating latent class membership to external variables: An overview. British Journal of Mathematical and Statistical Psychology, 74(2), 340–362. https://doi.org/10.1111/bmsp.12227

Bakk, Z., Oberski, D. L., & Vermunt, J. K. (2016). Relating latent class membership to continuous distal outcomes: Improving the LTB approach and a modified three-step implementation. Structural Equation Modeling, 23(2), 278–289. https://doi.org/10.1080/10705511.2015.1049698

Bakk, Z., Tekle, F. B., & Vermunt, J. K. (2013). Estimating the association between latent class membership and external variables using bias-adjusted three-step approaches. Sociological Methodology, 43(1), 272–311. https://doi.org/10.1177/0081175012470644

Bakk, Z., & Vermunt, J. K. (2016). Robustness of stepwise latent class modeling with continuous distal outcomes. Structural Equation Modeling, 23(1), 20–31. https://doi.org/10.1080/10705511.2014.955104

Bartolucci, F., Pandolfi, S., & Pennoni, F. (2022). Discrete latent variable models. Annual Review of Statistics and Its Application, 9, 425–452. https://doi.org/10.1146/annurev-statistics-040220-091910

Berzofsky, M. E., Biemer, P. P., & Kalsbeek, W. D. (2014). Local dependence in latent class analysis of rare and sensitive events. Sociological Methods & Research, 43(1), 137–170. https://doi.org/10.1177/0049124113506407

Bindu, P., & Thomas, S. (2014). Estimation of lattice strain in ZnO nanoparticles: X-ray peak profile analysis. Journal of Theoretical and Applied Physics, 8(4), 123–134.

Bolck, A., Croon, M., & Hagenaars, J. (2004). Estimating latent structure models with categorical variables: One-step versus three-step estimators. Political Analysis, 12(1), 3–27. https://doi.org/10.1093/pan/mph001

Bulut, O., & Desjardins, C. D. (2020). Profile analysis of multivariate data: A brief introduction to the profileR package. OSF Preprints. https://doi.org/10.31219/osf.io/sgy8m

Cameron, A. C., & Trivedi, P. K. (2013). Regression analysis of count data (2nd ed.). Cambridge University Press. https://doi.org/10.1017/CBO9781139013567

Collins, L. M., & Lanza, S. T. (2010). Latent class and latent transition analysis: With applications in the social, behavioral, and health sciences. Wiley. https://doi.org/10.1002/9780470567333

Ferguson, S. L., Moore, E. W. G., & Hull, D. M. (2020). Finding latent groups in observed data: A primer on latent profile analysis in Mplus for applied researchers. International Journal of Behavioral Development, 44(5), 458–468.

Gibson, W. A. (1959). Three multivariate models: Factor analysis, latent structure analysis, and latent profile analysis. Psychometrika, 24(3), 229–252.

Greenhouse, S. W., & Geisser, S. (1959). On methods in the analysis of profile data. Psychometrika, 24(2), 95–112.

Gribskov, M., McLachlan, A. D., & Eisenberg, D. (1987). Profile analysis: Detection of distantly related proteins. Proceedings of the National Academy of Sciences, 84(13), 4355–4358.

Hack, J. T. (1973). Stream-profile analysis and stream-gradient index. Journal of Research of the U.S. Geological Survey, 1(4), 421–429.

Hagenaars, J. A. (1988). Latent structure models with direct effects between indicators: Local dependence models. Sociological Methods & Research, 16(3), 379–405. https://doi.org/10.1177/0049124188016003002

Hagenaars, J. A., & McCutcheon, A. L. (Eds.). (2002). Applied latent class analysis. Cambridge University Press. https://doi.org/10.1017/CBO9780511499531

Lumley, T. (2010). Complex surveys: A guide to analysis using R. Wiley.

Mullahy, J. (1986). Specification and testing of some modified count data models. Journal of Econometrics, 33(3), 341–365. https://doi.org/10.1016/0304-4076(86)90002-3

Nagelkerke, E., Oberski, D. L., & Vermunt, J. K. (2016). Goodness-of-fit of multilevel latent class models for categorical data. Sociological Methodology, 46(1), 252–282. https://doi.org/10.1177/0081175015581379

Nunnally, J. (1962). The analysis of profile data. Psychological Bulletin, 59(4), 311–319.

Nylund, K. L., Asparouhov, T., & Muthén, B. O. (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study. Structural Equation Modeling, 14(4), 535–569. https://doi.org/10.1080/10705510701575396

Rosenberg, J. M., Beymer, P. N., Anderson, D. J., van Lissa, C. J., & Schmidt, J. A. (2018). tidyLPA: An R package to easily carry out latent profile analysis (LPA) using open-source or commercial software. Journal of Open Source Software, 3(30), 978. https://doi.org/10.21105/joss.00978

Spurk, D., Hirschi, A., Wang, M., Valero, D., & Kauffeld, S. (2020). Latent profile analysis: A review and “how to” guide of its application within vocational behavior research. Journal of Vocational Behavior, 120, 103445.

Tein, J.-Y., Coxe, S., & Cham, H. (2013). Statistical power to detect the correct number of classes in latent profile analysis. Structural Equation Modeling, 20(4), 640–657.

Ungár, T., & Borbély, A. (1996). The effect of dislocation contrast on x-ray line broadening: A new approach to line profile analysis. Applied Physics Letters, 69(21), 3173–3175.

Vermunt, J. K. (2010). Latent class modeling with covariates: Two improved three-step approaches. Political Analysis, 18(4), 450–469. https://doi.org/10.1093/pan/mpq025

Vermunt, J. K. (2025). Stepwise estimation of latent variable models: An overview of approaches. Statistical Modelling, 25(6), 530–551. https://doi.org/10.1177/1471082X251355693

Vermunt, J. K., & Magidson, J. (2007). Latent class analysis with sampling weights: A maximum-likelihood approach. Sociological Methods & Research, 36(1), 87–111. https://doi.org/10.1177/0049124107301965

Visser, M., & Depaoli, S. (2022). A guide to detecting and modeling local dependence in latent class analysis models. Structural Equation Modeling, 29(6), 971–982. https://doi.org/10.1080/10705511.2022.2033622

Wang, M.-C., Deng, Q., Bi, X., Ye, H., & Yang, W. (2017). Performance of the entropy as an index of classification accuracy in latent profile analysis: A Monte Carlo simulation study. Acta Psychologica Sinica, 49(11), 1473–1482.

Watkins, M. W. (2000). Cognitive profile analysis: A shared professional myth. School Psychology Quarterly, 15(4), 465–479.

Weller, B. E., Bowen, N. K., & Faubert, S. J. (2020). Latent class analysis: A guide to best practice. Journal of Black Psychology, 46(4), 287–311. https://doi.org/10.1177/0095798420930932

Williams, G. A., & Kibowski, F. (2016). Latent class analysis and latent profile analysis. In L. A. Jason & D. S. Glenwick (Eds.), Handbook of Methodological Approaches to Community-Based Research (pp. 143–151). Oxford University Press.

Zeileis, A., Kleiber, C., & Jackman, S. (2008). Regression models for count data in R. Journal of Statistical Software, 27(8), 1–25. https://doi.org/10.18637/jss.v027.i08

 Appendix: Search Strategy

The literature base of this chapter was constructed through the following steps (accessed: 19 August 2026).

Step	Query	Result
1. Broad search (Google Scholar)	allintitle: “profile analysis” OR “analysis of profile”	~301 records; the first 80 were screened, 79 unique records
2. Health-focused narrowing (Google Scholar)	“latent profile analysis” (“health survey” OR “SF-36” OR “EQ-5D” OR NHANES OR BRFSS)	Method + data source required together
3. PubMed primary query	(“latent profile analysis”[tiab] OR “profile analysis”[tiab]) AND (“health survey”[tiab] OR “SF-36″[tiab] OR “SF-12″[tiab] OR “EQ-5D”[tiab] OR “NHANES”[tiab] OR “BRFSS”[tiab] OR “WHOQOL”[tiab])	69 records; the first 30 were taken
4. PubMed supplementary query	“latent profile analysis”[Title] AND (health[tiab] OR “quality of life”[tiab])	855 records; 15 records were taken

Exclusion criteria: X-ray/diffraction context; texture profile analysis (TPA); protein or gene sequence profiles; stream, mass and depth profiles; and labels for bundles of variables that are not method names, such as “lipid profile” and “risk factor profile.”