LCA-2.1: Ten Frequently Asked Questions About Latent Class Analysis

Disclaimer: Reading notes prepared with AI assistance and checked against the source

1. What problem is this paper addressing?
1. 这篇论文解决了什么问题？

Latent class analysis, or LCA, has become increasingly popular in psychological research, but many applied researchers use it without fully understanding the modeling logic behind it.
潜类别分析，或 LCA，在心理学研究中越来越受欢迎，但许多应用研究人员在使用它时并没有完全理解其背后的建模逻辑。

Nylund-Gibson and Choi’s paper addresses a practical problem:
Nylund-Gibson 和 Choi 的论文解决了一个实际问题：

Many researchers want to use LCA to identify hidden subgroups in their data, but they need clearer guidance on how to specify, estimate, interpret, and validate LCA models.
许多研究人员希望使用 LCA 来识别他们数据中的隐藏子群，但他们需要更清晰的指导，说明如何指定、估计、解释和验证 LCA 模型。

The article is written as a methodological guide. Instead of presenting one new statistical estimator, it answers ten common questions that applied researchers often ask when learning LCA.
这篇文章是一份方法论指南。它没有提出一个新的统计估计量，而是回答了应用研究人员在学习 LCA 时常问的十个常见问题。

The paper covers: 论文涵盖了：

• what LCA is LCA 是什么
• how to decide the number of classes
  如何确定类别数量
• how to interpret item probability plots
  如何解读项目概率图
• how to include covariates and distal outcomes
  如何包含协变量和远期结果
• what sample size is needed
  需要多大的样本量
• what software can be used
  有什么软件可以用
• how LCA relates to other latent variable models
  LCA 与其他潜变量模型的关系是什么
• what extensions exist 存在哪些扩展

The paper’s main contribution is educational: it translates the statistical logic of LCA into an applied workflow that researchers can follow.
论文的主要贡献是教育性的：它将 LCA 的统计逻辑转化为研究人员可以遵循的应用工作流程。

2. Why this problem matters
2. 为什么这个问题很重要

LCA is often used when researchers believe a population is not homogeneous.
当研究人员认为一个群体不是同质的时候，LCA 通常会被使用。

For example, youth may not all follow the same developmental pattern. Families may not differ only by “more” or “less” support. People may cluster into qualitatively different profiles.
例如，年轻人可能并不都遵循相同的发展模式。家庭可能不仅仅通过“更多”或“更少”的支持来区分。人们可能会聚集成性质不同的特征群。

This matters because many applied research questions are not only about variable relationships. They are also about types of people, patterns of risk, or distinct profiles of experience.
这很重要，因为许多应用研究问题不仅关于变量关系。它们也关于人的类型、风险的模式或经验的独特特征群。

In social work, public health, psychology, and policy research, this is especially important. Practitioners often need to know:
在社会工作、公共卫生、心理学和政策研究中，这一点尤为重要。从业者通常需要了解：

• Which subgroups are most at risk?
  哪些亚群风险最高？
• Which groups show different combinations of needs?
  哪些群体显示出不同的需求组合？
• Which groups may need different interventions?
  哪些群体可能需要不同的干预措施？
• Are there hidden patterns that average effects obscure?
  是否存在平均效应所掩盖的隐藏模式？

LCA gives researchers a model-based way to identify those hidden groups.
生命周期评估为研究人员提供了一种基于模型的识别这些隐藏群体的方法。

The key phrase is model-based. LCA is not just an informal clustering technique. It estimates a probabilistic model for how observed responses are generated by an underlying categorical latent variable.
关键短语是基于模型的。LCA 不仅仅是一种非正式的聚类技术。它估计了一个概率模型，用于解释观察到的响应是如何由潜在的分类潜变量生成的。

3. Core idea of LCA 3. LCA 的核心思想

The core idea of LCA is simple:
LCA 的核心思想很简单：

People’s observed responses may be explained by membership in unobserved groups.
人们的观察响应可能可以通过属于未观察到的群体来解释。

These hidden groups are called latent classes.
这些隐藏的群体被称为潜在类别。

In LCA, researchers choose a set of observed indicators. These may be survey items, symptoms, behaviors, attitudes, or service-use patterns. The model then estimates whether people can be grouped into a small number of latent classes based on their response patterns.
在 LCA 中，研究人员选择一组观察指标。这些可能是调查项目、症状、行为、态度或服务使用模式。然后模型估计人们是否可以根据他们的反应模式被分组到少数几个潜在类别中。

For example, in the paper’s applied example, the authors use seven items from the Positive Youth Development Inventory Contribution subscale. These items measure whether youth value and engage in social contribution. The authors ask whether college students show qualitatively distinct profiles of positive contribution.
例如，在论文的应用示例中，作者使用了积极青年发展量表贡献子量表的七个项目。这些项目衡量青年是否重视并参与社会贡献。作者询问大学生是否表现出不同质的积极贡献特征。

The model selected four classes:
模型选择了四个类别：

• Holistic–Collaborative 整体–协作
• Altruistic–Low Self-efficacy
  利他–低自我效能
• Low Engagement
• Holistic–Independent

The important point is that these classes are not directly observed. They are inferred from response patterns.

4. How the LCA model works

The paper introduces LCA as a finite mixture model.

Suppose there are:

• (M) observed indicators
• (K) latent classes
• (u_{mi}), the response of person (i) to indicator (m)
• (c_i), the latent class membership of person (i)

The basic unconditional LCA model can be written as:

Pr(u_{i1}, u_{i2}, \ldots, u_{iM})
=
\sum_{k=1}^{K}
\left[
\pi_k
\prod_{m=1}^{M}
Pr(u_{mi} \mid c_i = k)
\right]

Plain-language explanation:

A person’s full response pattern is modeled as a weighted combination of possible class-specific response patterns.
一个人的完整响应模式被建模为可能的类特定响应模式的加权组合。

Each class contributes two things:
每个类有两个贡献：

1. The probability that someone belongs to that class.
   某人属于该类的概率。
2. The probability that someone in that class endorses each item.
   该类中某人对每个项目的支持概率。

The first part is the class proportion.
第一部分是类别比例。

\pi_k = Pr(c_i = k)

This tells us the relative size of class (k).
这告诉我们类别（k）的相对大小。

The second part is the conditional item probability.
第二部分是条件项目概率。

Pr(u_{mi} = 1 \mid c_i = k)

This tells us the probability that a person in class (k) endorses item (m).
这告诉我们类别（k）中的人支持项目（m）的概率。

These two parameter types are the heart of LCA.
这两个参数类型是 LCA 的核心。

Class proportions tell us how common each class is.
类别比例告诉我们每个类别的常见程度。

Conditional item probabilities tell us what each class looks like.
条件项目概率告诉我们每个类别看起来像什么。

5. Local independence 5. 局部独立性

A central assumption in LCA is local independence.
LCA 中的一个核心假设是局部独立性。

The paper explains this as the assumption that once latent class membership is accounted for, the observed indicators are no longer associated with one another.
论文解释这一假设为：一旦考虑了潜在类别成员资格，观察到的指标就不再相互关联。

In plain language: 用简单的话来说：

The latent class variable is supposed to explain the shared pattern among the indicators.
潜在类别变量被认为可以解释指标之间的共享模式。

For example, if several family regulation items are correlated, LCA assumes that this association is due to underlying class membership. Within a given class, the remaining item associations should be small.
例如，如果多个家庭监管项目相关，LCA 假设这种关联是由于潜在的类别成员资格造成的。在给定类别内，其余的项目关联应该较小。

This assumption matters because LCA interprets the latent classes as the main source of response-pattern structure. If strong residual associations remain within classes, the model may be misspecified.
这一假设很重要，因为 LCA 将潜在类别解释为响应模式结构的主要来源。如果类内存在强烈的残差关联，模型可能存在设定错误。

The authors note that local independence can sometimes be relaxed, but this should be done carefully and based on substantive knowledge.
作者指出，有时可以放宽局部独立性，但这应该谨慎进行，并基于实质性知识。

6. Deciding the number of classes
6. 确定类别数量

The paper calls this step class enumeration.
论文称这一步骤为类别枚举。

Class enumeration means estimating models with different numbers of classes and deciding which solution best represents the data.
类别枚举意味着估计具有不同类别数量的模型，并决定哪个解决方案最能代表数据。

The authors recommend starting with a one-class model as a baseline. Then researchers fit models with more classes, usually adding one class at a time.
作者建议以单类模型作为基线开始。然后研究人员拟合更多类的模型，通常每次增加一个类。

A key message is: 一个关键信息是：

There is no single agreed-upon fit index for deciding the number of classes.
没有单一的公认拟合指数用于决定类的数量。

Instead, researchers should jointly consider:
相反，研究人员应该综合考虑：

• statistical fit indices 统计拟合指数
• substantive interpretability
  实质性可解释性
• parsimony 简约性
• classification diagnostics
  分类诊断
• class size 类大小
• model stability 模型稳定性
• theoretical usefulness 理论实用性

The paper discusses several fit indices.
论文讨论了几个拟合指数。

Information criteria include:
信息准则包括：

• BIC
• sample-size adjusted BIC 样本量调整后的 BIC
• CAIC 中海油
• AWE

Lower values indicate better fit.
较低的值表示更好的拟合。

The paper also discusses likelihood-based tests:
该论文还讨论了基于似然的检验：

• VLMR-LRT
• BLRT

These compare neighboring class solutions, such as a three-class model versus a four-class model.
这些检验比较了邻近类别的解决方案，例如一个三分类模型与一个四分类模型。

The authors also discuss Bayesian comparison tools such as Bayes factor and correct model probability.
作者们还讨论了贝叶斯比较工具，如贝叶斯因子和正确模型概率。

The practical lesson is that fit indices often disagree. This is normal in applied LCA.
实际教训是拟合指数经常不一致。这在应用 LCA 中是正常的。

When fit indices disagree, researchers should not mechanically choose the model with the best number in one column. They should compare candidate models and ask whether the additional classes are meaningful, stable, and useful.
当拟合指数不一致时，研究人员不应机械地选择某一列中数值最好的模型。他们应该比较候选模型，并询问附加类别是否有意义、稳定且有用。

7. Interpreting the item probability plot
7. 解释项目概率图

Once a class solution is selected, the next task is interpretation.
一旦选择了一个班级解决方案，下一个任务就是解释。

The paper emphasizes the item probability plot as one of the most useful tools for interpreting LCA results.
论文强调了项目概率图是解释 LCA 结果最有用的工具之一。

An item probability plot shows:
项目概率图显示：

• indicators on the x-axis x 轴上的指标
• conditional item probabilities on the y-axis
  y 轴上的条件项概率
• one line for each latent class
  每条线代表一个潜类别

Each line is a class profile.
每条线是一个类别轮廓。

The researcher interprets each class by examining which items have high or low probabilities within that class.
研究人员通过检查哪个项目在该类别中具有高或低概率来解释每个类别。

In the PYDI example, the authors use the item probability plot to label the four classes.
在 PYDI 示例中，作者使用项目概率图来标记四个类别。

The largest class, Holistic–Collaborative, has high endorsement probabilities across all items. This suggests youth who value contribution broadly and engage collaboratively.
最大类别，整体性-协作类，在所有项目上都具有高支持概率。这表明重视广泛贡献并参与协作的年轻人。

The Altruistic–Low Self-efficacy class values contribution but has low probability on items related to perceived personal effectiveness.
利他性-低自我效能类重视贡献，但在与感知个人效能相关的项目上支持概率较低。

The Low Engagement class has generally low or ambivalent endorsement probabilities.
低参与度类在一般项目上具有低或矛盾的支持概率。

The Holistic–Independent class resembles the Holistic–Collaborative class but differs on items related to interpersonal and community engagement.
整体性-独立类与整体性-协作类相似，但在人际和社区参与相关的项目上有所不同。

This example shows that class labels are not generated automatically. They require substantive interpretation.
这个例子表明类别标签不是自动生成的。它们需要实质性的解释。

8. Classification quality
8. 分类质量

The paper warns that interpreting classes is not enough. Researchers also need to evaluate how well the model classifies people.
论文警告说，解释类别是不够的。研究人员还需要评估模型如何对人类进行分类。

The authors discuss four classification diagnostics.
作者讨论了四种分类诊断方法。

First, entropy. 首先，熵。

Entropy is an omnibus measure of classification quality. Values closer to 1 indicate clearer classification. The paper notes that values around .80 or above are often treated as good.
熵是分类质量的综合指标。值越接近 1 表示分类越清晰。论文指出，值在 0.80 左右或以上通常被认为是好的。

But entropy should not be used as the main model-selection statistic.
但熵不应作为主要的模型选择统计量。

Second, average posterior probabilities, or AvePP.
其次，平均后验概率，或称为 AvePP。

AvePP tells us how likely people assigned to a class are to actually belong to that class. Higher values indicate clearer class assignment.
AvePP 告诉我们被分配到某个类别的人实际上属于该类别的可能性有多大。更高的值表示类别分配更清晰。

Third, class homogeneity.
第三，类别同质性。

Class homogeneity refers to how similar people are within a class. Conditional item probabilities near high or low extremes suggest stronger homogeneity.
类别同质性是指类别内人们的相似程度。条件项目概率接近高低极端表明同质性更强。

Fourth, class separation.
第四，类别分离。

Class separation refers to how different classes are from one another. Some indicators may separate one pair of classes well but not separate other classes.
类分离指的是不同类之间是如何相互区别的。某些指标可能很好地分离一对类，但无法分离其他类。

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In the paper’s example, the Holistic–Independent class overlaps substantially with the Holistic–Collaborative class. This is visible in the item probability plot and in the classification probability table.
在论文的示例中，Holistic–Independent 类与 Holistic–Collaborative 类有显著重叠。这在项目概率图和分类概率表中可见。

This is an important applied lesson:
这是一个重要的应用教训：

A class solution can be statistically defensible but still have classification ambiguity.
一个类解决方案可以是统计上站得住脚的，但仍然存在分类模糊性。

9. Adding covariates 9. 添加协变量

After identifying latent classes, researchers often want to know what predicts class membership.
在识别潜在类别后，研究人员通常想知道是什么预测了类别成员资格。

These predictors are called covariates.
这些预测因素被称为协变量。

The paper expresses the covariate model as a multinomial logistic regression:
论文将协变量模型表示为多项式逻辑回归：

Pr(c_i = k \mid x_i)
=
\frac{
\exp(\gamma_{0k} + \gamma_{1k}x_i)
}{
\sum_{j=1}^{K}
\exp(\gamma_{0j} + \gamma_{1j}x_i)
}

Plain-language explanation:
平话解释：

The covariate (x_i) predicts the probability that person (i) belongs to class (k).
协变量（x_i）预测个体（i）属于类别（k）的概率。

For example, the paper examines whether Hispanic and non-Hispanic youth differ in their likelihood of belonging to the four PYDI classes.
例如，该论文研究了西班牙裔和非西班牙裔青年在属于四个 PYDI 类别上的可能性是否存在差异。

The key idea is that covariates help answer:
核心思想是协变量有助于回答：

Who is more likely to belong to each latent class?
谁更有可能属于每个潜在类别？

10. Adding distal outcomes
10. 添加远期结果

Distal outcomes are variables that researchers compare across latent classes.
远期结果是研究者用来比较潜在类别的变量。

They answer a different question from covariates.
它们与协变量回答的是不同的问题。

Covariates ask: 协变量问：

Who is likely to be in each class?
谁可能会在每个班级中？

Distal outcomes ask: 远期结果询问：

Do the classes differ on an outcome?
这些班级在结果上是否存在差异？

In the paper’s example, life satisfaction is the distal outcome.
在论文的示例中，生活满意度是远期结果。

The authors estimate class-specific means of life satisfaction and compare them across the four classes.
作者们估计了特定类别的生活满意度均值，并将它们在四个类别之间进行比较。

They find that the Holistic–Collaborative class has significantly higher life satisfaction than the other three classes. Other pairwise comparisons are not statistically significant.
他们发现，整体协作类别的成员的生活满意度显著高于其他三个类别。其他成对比较没有统计学意义。

The authors are careful to treat this as a class difference in outcome means, not as proof that class membership causes life satisfaction.
作者们谨慎地将其视为类别结果均值的差异，而不是类别归属导致生活满意度的证明。

11. Why one-step estimation can be risky
11. 为什么单步估计可能存在风险

The paper explains that, in theory, researchers might want to estimate the latent class model and the auxiliary-variable relationships all at once.
该论文解释说，在理论上，研究人员可能希望一次性估计潜类模型和辅助变量关系。

This is called a one-step approach.
这被称为一步法。

However, in mixture modeling, this can be risky because adding covariates or distal outcomes can change the formation of the latent classes themselves.
然而，在混合建模中，这可能存在风险，因为添加协变量或远端结果可能会改变潜类本身的形成。

That means the classes may no longer be defined only by the intended indicators.
这意味着类可能不再仅由预期指标定义。

For this reason, the paper recommends separating class enumeration from later structural analyses.
因此，该论文建议将类别枚举与后续的结构分析分开。

First, estimate the classes using only the selected indicators.
首先，仅使用选定的指标估计类别。

Then, after selecting the final class solution, estimate covariate and distal outcome relations.
然后，在选定最终类别解决方案后，估计协变量和远端结果关系。

12. Three-step and BCH approaches
12. 三步法和 BCH 方法

The paper identifies the three-step method and BCH method as current best-practice approaches for auxiliary-variable analysis.
该论文将三步法和 BCH 方法识别为当前辅助变量分析的现行最佳实践方法。

These approaches share a common logic:
这些方法具有共同的逻辑：

1. Estimate the latent class model using only the indicators.
   仅使用指标估计潜类模型。
2. Assign or summarize class membership while preserving classification information.
   分配或总结类别成员资格，同时保留分类信息。
3. Estimate covariate or distal outcome relations while accounting for classification error.
   估计协变量或远端结果关系，同时考虑分类误差。

The key advantage is that the measurement model is protected.
其主要优势在于测量模型得到了保护。

The latent classes are not reshaped by auxiliary variables.
潜在类别不会受到辅助变量的重塑。

This is one of the most practically important lessons of the paper.
这是本文最 practically important 的一个重要教训。

13. Sample size 13. 样本量

The paper emphasizes that there is no fixed minimum sample size for LCA.
论文强调，对于生命周期评价（LCA）没有固定的最小样本量。

Sample size requirements depend on several conditions:
样本量要求取决于几个条件：

• number of indicators 指标数量
• number of classes 类数量
• how well indicators separate classes
  指标区分类的效果
• how well classes are separated
  类分离的效果
• relative size of the classes
  类的相对大小
• whether rare classes are expected
  是否预期稀有职业
• model complexity 模型复杂度

The paper notes that some prior work has suggested (N = 500) as a heuristic. More generally, the authors state that (N = 300) to (N = 1000) is a range where commonly used mixture-model fit indices may function adequately.
该论文指出，先前的一些研究建议 (N = 500) 作为启发式方法。更普遍地，作者们指出 (N = 300) 到 (N = 1000) 是一个常用混合模型拟合指数可能充分运作的范围。

However, this is not a universal rule.
然而，这并非一条普遍规则。

A simple two-class model with very well-separated classes may need far fewer cases.
一个简单且类别非常分离的两类模型可能需要远少于此数量的案例。

A complex model with many classes, many indicators, weak separation, or rare classes may require much larger samples.
一个复杂的多类别模型、具有多个指标、分离度弱或类别稀有的模型可能需要远大的样本量。

The paper also warns that insufficient sample size can lead to:
该论文还警告说，样本量不足可能导致：

• convergence problems 收敛问题
• low power to detect classes
  检测类别的功效低
• unstable solutions 不稳定解
• failure to identify rare but meaningful classes
  未能识别稀有但具有意义的类别

The practical message is that sample size should be evaluated in relation to model complexity and class separation, not as a fixed checklist number.
实际意义在于样本量应与模型复杂性和类别分离性相关联，而不是作为固定的清单数字。

14. What makes this paper important?
14. 这篇论文的重要性是什么？

This paper is important because it gives applied researchers a clear conceptual map of LCA.
这篇论文之所以重要，是因为它为应用研究人员提供了 LCA 的清晰概念图。

It does not only define the model. It explains the practical decisions that determine whether an LCA study is credible.
它不仅定义了模型，还解释了决定 LCA 研究是否可信的实际决策。

These decisions include: 这些决策包括：

• choosing indicators 选择指标
• fitting multiple class solutions
  适配多重类解决方案
• comparing fit indices 比较拟合指数
• interpreting item probability plots
  解读项目概率图
• evaluating classification quality
  评估分类质量
• avoiding overextracted class solutions
  避免过度提取的类解决方案
• handling covariates and distal outcomes carefully
  谨慎处理协变量和远端结果
• recognizing sample-size limitations
  认识到样本量限制

For technical readers, the paper is useful because it connects the formal mixture-model notation to applied interpretation.
对于技术读者而言，这篇论文是有用的，因为它将形式混合模型符号与实际解释联系起来。

For social work, policy, and applied research readers, the paper is useful because it shows how hidden subgroup analysis can support more nuanced understanding of populations.
对于社会工作、政策及应用研究读者而言，这篇论文是有用的，因为它展示了如何通过隐藏子群分析来支持对人群更细致的理解。

15. Why this matters for social work, policy, and applied AI
15. 这为何对社会工作、政策及应用 AI 至关重要

The paper itself is written for psychological researchers, not specifically for social work or applied AI. But the methodological relevance is clear.
该论文本身是为心理学研究人员撰写的，并非专门针对社会工作或应用人工智能。但方法论的相关性是明确的。

Social work and policy research often deal with heterogeneous populations. Averages can hide meaningful differences.
社会工作和政策研究经常处理异质人群。平均值可能掩盖有意义的差异。

For example, two adolescents may have the same overall level of family risk but very different profiles:
例如，两个青少年可能有相同的总体家庭风险水平，但特征差异很大：

• low monitoring but high warmth
  监控低但温暖高
• high structure but high conflict
  结构高但冲突高
• low support across multiple domains
  多领域支持低
• strong family support but high peer risk
  家庭支持强但同伴风险高

LCA helps researchers model these profiles directly.
LCA 帮助研究人员直接模拟这些特征。

For policy and intervention design, this matters because different profiles may require different supports.
在政策和干预措施设计中，这一点很重要，因为不同的特征可能需要不同的支持。

For applied AI, the relevance is more methodological than direct. The paper reminds us that subgroup discovery should not be treated as automatic pattern extraction. Researchers need transparent model selection, diagnostic checks, interpretability, and caution about classification error.
在应用人工智能领域，其相关性更多地体现在方法论上而非直接关联。该论文提醒我们，子群发现不应被视为自动模式提取。研究人员需要透明的模型选择、诊断检查、可解释性，以及对分类错误的谨慎态度。

That is useful for any applied modeling workflow where hidden groups or risk profiles are used to inform decisions.
这对于任何应用建模工作流程都很有用，其中隐藏的群体或风险特征被用来为决策提供信息。

16. Limitations and things to be careful about
16. 局限性和需要谨慎的事项

The paper is introductory, so it does not provide a full technical treatment of every topic.
这篇论文是入门级的，因此它没有对每个主题进行完整的技术处理。

Important cautions include the following.
重要的注意事项包括以下几点。

First, class enumeration is uncertain.
首先，类别划分不确定。

Fit indices often disagree. Researchers should not treat LCA as a machine that automatically discovers the “true” number of groups.
拟合指数常常不一致。研究人员不应将 LCA 视为一台自动发现“真实”组数的机器。

Second, class labels are interpretive.
其次，类别标签是解释性的。

Researchers name classes based on item-response patterns and theory. Poorly chosen labels can overstate what the model actually shows.
研究人员根据项目反应模式和理论来命名类别。选择不当的标签可能会夸大模型实际显示的内容。

Third, entropy is not a model-selection statistic.
第三，熵不是模型选择统计量。

It can help describe classification quality, but it should not be used as the main reason to choose the number of classes.
它可以帮助描述分类质量，但不应将其作为选择类别数量的主要原因。

Fourth, small classes can be unstable.
第四，小班可能不稳定。

Rare classes may be substantively important, but they are difficult to recover without adequate sample size and strong separating indicators.

Fifth, covariates and distal outcomes can change the class solution if included too early.

This is why the paper recommends three-step or BCH approaches.

Sixth, LCA depends heavily on indicator choice.

The classes that emerge are only as meaningful as the indicators used to define them.

17. Takeaways for readers new to LCA

LCA is a model-based way to identify hidden subgroups from observed response patterns.

The two most important outputs are class proportions and conditional item probabilities.

Class enumeration means deciding how many classes to retain.

There is no single best fit index for class enumeration.

Item probability plots are central for interpretation.

Class labels should come from response patterns, theory, and substantive usefulness.

Classification quality should be checked using entropy, posterior probabilities, homogeneity, and separation.

Covariates predict class membership.

Distal outcomes are compared across classes.

Three-step and BCH methods help analyze auxiliary variables without letting them redefine the classes.

Sample size needs depend on complexity, class separation, and class prevalence.

The best LCA studies combine statistical evidence with theoretical judgment.

References 参考资料

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

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

Collins, L. M., & Lanza, S. T. (2010). Latent class and latent transition analysis: With applications in the social, behavioral, and health sciences. Wiley.
Collins, L. M., & Lanza, S. T. (2010). 隐类分析及隐转移分析：在社会、行为与健康科学中的应用。Wiley。

Lanza, S. T., & Cooper, B. R. (2016). Latent class analysis for developmental research. Child Development Perspectives, 10(1), 59–64. https://doi.org/10.1111/cdep.12163
Lanza, S. T., & Cooper, B. R. (2016). 发展研究中的隐类分析。儿童发展视角，10(1)，59–64。https://doi.org/10.1111/cdep.12163

Masyn, K. E. (2013). Latent class analysis and finite mixture modeling. In T. D. Little (Ed.), The Oxford handbook of quantitative methods: Statistical analysis (Vol. 2, pp. 551–611). Oxford University Press.
Masyn, K. E. (2013). 隐马尔可夫分析及有限混合模型. T. D. Little (编), 牛津定量方法手册：统计分析 (第 2 卷, pp. 551–611). 牛津大学出版社.

Muthén, B. O. (2003). Statistical and substantive checking in growth mixture modeling: Comment on Bauer and Curran. Psychological Methods, 8(3), 369–377. https://doi.org/10.1037/1082-989X.8.3.369
Muthén, B. O. (2003). 成长混合模型中的统计和实质性检验：对 Bauer 和 Curran 的评论. 心理方法, 8(3), 369–377. https://doi.org/10.1037/1082-989X.8.3.369

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
Nylund, K. L., Asparouhov, T., & Muthén, B. O. (2007). 关于潜在类别分析和增长混合模型中类别数量的确定：一项蒙特卡洛模拟研究. 结构方程模型, 14(4), 535–569. https://doi.org/10.1080/10705510701575396

Nylund-Gibson, K., & Choi, A. Y. (2018). Ten frequently asked questions about latent class analysis. Translational Issues in Psychological Science, 4(4), 440–461. https://doi.org/10.1037/tps0000176
Nylund-Gibson, K., & Choi, A. Y. (2018). 关于潜类分析的十个常见问题. 心理科学转化问题, 4(4), 440–461. https://doi.org/10.1037/tps0000176

Nylund-Gibson, K., Grimm, R., Quirk, M., & Furlong, M. (2014). A latent transition mixture model using the three-step specification. Structural Equation Modeling: A Multidisciplinary Journal, 21(3), 439–454. https://doi.org/10.1080/10705511.2014.915375
Nylund-Gibson, K., Grimm, R., Quirk, M., & Furlong, M. (2014). 基于三步规范的一个潜变量转换混合模型. 结构方程模型：一个多学科期刊，21(3), 439–454. https://doi.org/10.1080/10705511.2014.915375

Nylund-Gibson, K., & Masyn, K. E. (2016). Covariates and mixture modeling: Results of a simulation study exploring the impact of misspecified effects on class enumeration. Structural Equation Modeling: A Multidisciplinary Journal, 23(6), 782–797. https://doi.org/10.1080/10705511.2016.1221313
Nylund-Gibson, K., & Masyn, K. E. (2016). 协变量和混合模型：一项模拟研究的结果，探讨了错误指定效应对类别枚举的影响。结构方程建模：一个多学科杂志，23(6), 782–797。https://doi.org/10.1080/10705511.2016.1221313

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. (2010). 带协变量的潜类别模型：两种改进的三步法. 政治分析, 18(4), 450–469. https://doi.org/10.1093/pan/mpq025