Course Text: Pages 5-7
We refer to LC Cluster models with categorical indicators as traditional LC models, because these were the first LC models, as defined by Leo Goodman in 1974. In LatentGOLD we refer to these models as LC Cluster models to distinguish them from many other types of LC models that we will also learn about throughout this course.
Specifically, the LC Cluster model includes a K-category latent variable X, each category of which represents a latent class (cluster, segment). Later, in Topic J, we will see how the traditional LC cluster model is extended to include continuous and count variables.
The formal representation of the traditional LC model, expresses the fundamental concept of local independence, which states that indicators are mutually independent of each other conditional on class membership. The LC Cluster model can be expressed in terms of either probability parameters (in LatentGOLD’s Profile output) or log-linear parameters (in LatentGOLD’s Parameters output). Because probability parameters are easier to interpret than log-linear parameters1, in this introductory course we will primarily use the probability representation of the model, as provided in Equation (3) on page 7 of the course text.
With four categorical indicators, we have:
P(y1,y2,y3,y4 )=∑ P(y1 |X=k)P(y2 |X=k)P(y3 |X=k)P(y4 |X=k)
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1 For an example of the log-linear form of the LC model with four categorical variables, see section 2.1 of Magidson, J., and Vermunt, J.K. (2001).
Magidson, J., and Vermunt, J.K. (2001). Latent class factor and cluster models, bi-plots and related graphical displays. Sociological Methodology, 31, 223-264. Click to view
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Use of LatentGOLD to estimate a traditional 3-class LC model is illustrated in LG Tutorial 1, where traditional model fitting strategies result in 3 latent classes. Topic C addresses these model fitting strategies in more detail.
LG Tutorial #1 link: LG Tutorial 1
1: Model Setup (pages 1-6)
2: Model Estimation (pages 7)
3: Summary Output, Parameters, Profile and ProbMeans Output: (pages 8-15)
4: Assigning Cases to Latent Classes (pages 16-17)
In Topic D we will return to LG Tutorial 1 when we address the Classification step of LC modeling in more detail.
Optional (Advanced Topic)
Note: While the traditional LC model is introduced in a manner analogous to cluster analysis (LC Cluster Model), alternatively it could be introduced in a manner analogous to factor analysis (Discrete Factor Model). For an introduction to LC Discrete Factor (DFactor) models, see Course Text (pages 15-20). This topic can be safely omitted without jeopardizing the rest of this course.
DFactor models, implemented in the LatentGOLD DFactor Module, are illustrated in LG tutorial 2 using the same data as used in LG tutorial 1. The DFactor models provide new insights into these data. Tutorial 2 also illustrates the use of the ordinal scale type with the categorical indicators that contain more than two categories. (Dichotomous indicators may be treated as Nominal or Ordinal without any differences in the model statistics. This choice is simply a matter of preference regarding display of the parameters (as effect vs. dummy coding) and category labels differs, while the model itself (e.g., model predictions, classifications of cases) is identical.
LG Tutorial #2 link: LG Tutorial 2
B4: Introduction (pages 5-6)
B5: Ordinal Scale Type (pages 5-6)
B2: Discrete Factor (DFactor) model basics (pages 7-19)