Finite-mixture structural equation models for response-based segmentation and unobserved heterogeneity
Finite-mixture structural equation models for response-based segmentation and unobserved heterogeneity
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DOI：
10.1287/mksc.16.1.39
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发表时间：
1997-01-01
影响因子：
5
通讯作者：
DESarbo, WS
中科院分区：
文献类型：
--
作者：
Jedidi, K;Jagpal, HS;DESarbo, WS
社会科学研究人员面临两个特有的问题（例如，市场营销，经济学，心理学和金融）：未观察到的异质性和数据的测量误差。结构方程模型是一个强大的工具，用于处理这些困难，使用一个联立方程框架与不可观察的结构和明显的指标，这是容易出错的。然而，在估计结构方程模型时，研究人员经常将数据视为从单个人群中收集的数据（Muthen 1989）。这种同质性的假设往往是不现实的。例如，在多维期望值模型中，来自不同细分市场的消费者可能具有不同的信念结构（Bagozzi，1982）。满意度的研究表明，消费者的决策过程各不相同的细分市场（Day 1977）。本文表明，聚合分析，忽略异质性的结构方程模型产生误导性的结果，传统的拟合统计是没有用的检测未观察到的异质性的数据。此外，序列分析，首先形成组使用聚类分析，然后应用多组结构方程modeling是不令人满意的，我们开发了一个通用的有限混合结构方程模型，同时对待异质性和形式的市场细分的背景下，一个指定的模型结构，所有观察到的变量进行测量误差。该模型比聚类分析、多组验证性因子分析和多组结构方程模型更具有普遍性。特别是，该模型包含几个专业模型，包括有限混合物联立方程模型，有限混合物验证性因子分析和有限混合物二阶因子分析。有限混合物结构方程模型应该引起广泛学科学者的兴趣（例如，消费者行为学、市场营销学、经济学、金融学、心理学和社会学），其中未观察到的异质性和测量误差是有问题的。此外，市场研究人员和产品经理应该对该模型感兴趣，原因有二。首先，该模型允许经理使用消费者决策过程模型执行基于响应的细分，同时明确允许测量和结构错误。第二，该模型允许管理人员发现未观察到的调节因素，占异质性。一旦管理者确定了调节因素，他们就可以将细分成员资格与可观察到的个人层面特征联系起来（例如，我们将有限混合结构方程模型应用于客户满意度的直接营销研究，并估计了一个具有未观察结构和23个显性指标的大型模型。结果表明，有三个消费者细分，他们重视的满意度的各个方面的重要性方面有很大的不同。相比之下，聚合分析是误导性的，因为它错误地表明，除了价格，所有满意度的维度对所有消费者都很重要。从方法上讲，有限混合模型是稳健的;也就是说，参数估计在双重交叉验证下是稳定的，并且该方法可用于测试大型模型。此外，双重交叉验证的结果表明，有限混合模型是上级优于序列数据分析策略的拟合优度和可解释性。我们进行了四个模拟实验，以测试使用递归和非递归模型规格的算法的鲁棒性。具体来说，我们研究了不同的模型选择标准（例如，CAIC，BIG和GFI）的鲁棒性，在选择正确数量的集群的准确识别和过度识别模型假设的分布形式是正确指定的。我们还研究了分布错误指定的影响（即，偏离多变量正态性）对模型性能的影响。结果表明，当数据是异质的，聚集模型的标准拟合优度统计量是没有用的检测异质性。此外，参数恢复较差。然而，对于有限混合模型，BIC和CAIC准则在检测异质性和识别真实的段数方面表现良好。特别是，测量和结构模型的参数恢复是非常令人满意的。有限混合方法对分布误指定具有鲁棒性;此外，当异质性的形式被误指定时（即，只有当结构方程模型得到了实质性理论的支持，先验分割不可行，并且理论表明数据是异质的并且属于有限数量的未观察组时，研究人员和从业人员才应该使用混合方法。我们期望这些条件在许多社会科学领域，应用，特别是市场细分研究中成立。未来的研究应该集中在大规模的模拟研究，以测试使用广泛的模型和统计分布的结构方程混合模型。理论研究应该通过允许混合比例取决于先验信息和/或特定于主题的变量来扩展该模型。最后，为了提供一个脱壳机处理的异质性，我们需要开发一个通用的随机系数结构方程模型。这样的模型是目前在统计和心理测量学文献中不可用的。
Two endemic problems face researchers in the social sciences (e.g., Marketing, Economics, Psychology, and Finance): unobserved heterogeneity and measurement error in data. Structural equation modeling is a powerful tool for dealing with these difficulties using a simultaneous equation framework with unobserved constructs and manifest indicators which are error-prone. When estimating structural equation models, however, researchers frequently treat the data as if they were collected from a single population (Muthen 1989). This assumption of homogeneity is often unrealistic. For example, in multidimensional expectancy value models, consumers from different market segments can have different belief structures (Bagozzi 1982). Research in satisfaction suggests that consumer decision processes vary across segments (Day 1977).This paper shows that aggregate analysis which ignores heterogeneity in structural equation models produces misleading results and that traditional fit statistics are not useful for detecting unobserved heterogeneity in the data. Furthermore, sequential analyses that first form groups using cluster analysis and then apply multigroup structural equation modeling are not satisfactory.We develop a general finite mixture structural equation model that simultaneously treats heterogeneity and forms market segments in the context of a specified model structure where all the observed variables are measured with error. The model is considerably more general than cluster analysis, multigroup confirmatory factor analysis, and multigroup structural equation modeling. In particular, the model subsumes several specialized models including finite mixture simultaneous equation models, finite mixture confirmatory factor analysis, and finite mixture second-order factor analysis.The finite mixture structural equation model should be of interest to academics in a wide range of disciplines (e.g., Consumer Behavior, Marketing, Economics, Finance, Psychology, and Sociology) where unobserved heterogeneity and measurement error are problematic. In addition, the model should be of interest to market researcher; and product managers for two reasons. First, the model allows the manager to perform response-based segmentation using a consumer decision process model, while explicitly allowing for both measurement and structural error. Second, the model allows managers to detect unobserved moderating factors which account for heterogeneity. Once managers have identified the moderating factors, they can link segment membership to observable individual-level characteristics (e.g., socioeconomic and demographic variables) and improve marketing policy.We applied the finite mixture structural equation model to a direct marketing study of customer satisfaction and estimated a large model with unobserved constructs and 23 manifest indicators. The results show that there are three consumer segments that vary considerably in terms of the importance they attach to the various dimensions of satisfaction. In contrast, aggregate analysis is misleading because it incorrectly suggests that except for price all dimensions of satisfaction are significant for all consumers. Methodologically, the finite mixture model is robust; that is, the parameter estimates are stable under double cross-validation and the method can be used to test large models. Furthermore, the double cross-validation results show that the finite mixture model is superior to sequential data analysis strategies in terms of goodness-of-fit and interpretability.We performed four simulation experiments to test the robustness of the algorithm using both recursive and nonrecursive model specifications. Specifically, we examined the robustness of different model selection criteria (e.g, CAIC, BIG, and GFI) in choosing the correct number of clusters for exactly identified and overidentified models assuming that the distributional form is correctly specified. We also examined the effect of distributional misspecification (i.e., departures from multivariate normality) on model performance. The results show that when the data are heterogeneous, the standard goodness-of-fit statistics for the aggregate model are not useful for detecting heterogeneity. Furthermore parameter recovery is poor. For the finite mixture model, however, the BIC and CAIC criteria perform well in detecting heterogeneity and in identifying the true number of segments. In particular, parameter recovery for both the measurement and structural models is highly satisfactory. The finite mixture method is robust to distributional misspecification; in addition, the method significantly outperforms aggregate and sequential data analysis methods when the form of heterogeneity is misspecified (i.e., the true model has random coefficients).Researchers and practitioners should only use the mixture methodology when substantive theory supports the structural equation model, a priori segmentation is infeasible, and theory suggests that the data are heterogeneous and belong to a finite number of unobserved groups. We expect these conditions to hold in many social science ay,plications and, in particular, market segmentation studies.Future research should focus on large-scale simulation studies to test the structural equation mixture model using a wide range of models and statistical distributions. Theoretical research should extend the model by allowing the mixing proportions to depend on prior information and/or subject-specific variables. Finally, in order to provide a huller treatment of heterogeneity, we need to develop a general random coefficient structural equation model. Such a model is presently unavailable in the statistical and psychometric literatures.