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1989 | Buch

Basic Principles of Model Building Kapitel lesen Erstes Kapitel lesen

Latent Variable Path Modeling with Partial Least Squares

verfasst von: Dr. Jan-Bernd Lohmöller

Verlag: Physica-Verlag HD

Enthalten in: Professional Book Archive

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Über dieses Buch

Partial Least Squares (PLS) is an estimation method and an algorithm for latent variable path (LVP) models. PLS is a component technique and estimates the latent variables as weighted aggregates. The implications of this choice are considered and compared to covariance structure techniques like LISREL, COSAN and EQS. The properties of special cases of PLS (regression, factor scores, structural equations, principal components, canonical correlation, hierarchical components, correspondence analysis, three-mode path and component analysis) are examined step by step and contribute to the understanding of the general PLS technique. The proof of the convergence of the PLS algorithm is extended beyond two-block models. Some 10 computer programs and 100 applications of PLS are referenced. The book gives the statistical underpinning for the computer programs PLS 1.8, which is in use in some 100 university computer centers, and for PLS/PC. It is intended to be the background reference for the users of PLS 1.8, not as textbook or program manual.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Basic Principles of Model Building
Abstract
Scientific knowledge of reality comes in form of models. As distinguished from everyday knowledge, scientific knowledge is characterized by the clear distinction between theoretical and empirical aspects. Because the distinction between the two cannot be part of the theoretical or the empirical, the frame of reference has to be introduced as a third element of the model for scientific knowledge. The frame of reference, formulated (more or less) in everyday language, contains a mixture of theoretical (“T”) and empirical (“E”) contents, as shown in Eq.1.1 which is taken from Wold (1969b): Scientific Knowlesge=
$$\boxed{\boxed{T \Leftrightarrow E}}$$
(1.1)
where the rectangle marks the frame of reference.
Jan-Bernd Lohmöller
Chapter 2. The Basic and the Extended PLS Method
Abstract
This chapter is devoted to the description of the PLS method and will be followed by chapter 3 which describes the theoretical foundations of the method. The first subchapter, Sc.2.1, gives a very short outline of what Herman Wold calls his Basic Method of PLS Soft Modeling (Wold 1979c, 1980c, 1982d). Because PLS is a rigorously founded, simply structured, and comprehensibly described methodology, it has provoked extensions, generalizations, re-interpretation and reformulations, e.g. by Bookstein (1980, 1982a, 1982c), Noonan and Wold (1982, 1983, 1986), Hui (1978), Apel (1978a, 1978b, 1979), Apel and Wold (1982) and Knepel (1980, 1981). For overviews cf. Falk (1988) Fornell (1982), and Valette-Florence (1986). The extensions proposed by Lohmöller (1979b, 1981a) will be outlined here in detail, starting in Sc.2.2 with the description of the extended model, followed in Sc.2.3 by the extended estimation facilities and in Sc.2.4 with methods of assessing the estimation results, and closing in Sc.2.5 by an application.
Jan-Bernd Lohmöller
Chapter 3. Foundations of Partial Least Squares
Abstract
The description of the Latent Variables Path (LVP) model and the Partial Least Squares (PLS) estimation procedure is now in chapter 3 followed by the reflection on the statistical foundations of the method. Thereby, simple cases of LVP model serve as examples for general features of the PLS method.
Jan-Bernd Lohmöller
chapter 4. Mixed Measurement Level Multivariate Data
Abstract
Linear equations are applicable only to interval-scaled variables which are the only ones to allow for linear transformations (Stevens 1951). Thus the standard procedures cannot be used for the categorical and the ordinal-scaled variables that are often encountered in the behavioral sciences. This chapter considers the extensions of LVP analysis so as to include categorical variables.
Jan-Bernd Lohmöller
chapter 5. Predictive vs. Structural Modeling: PLS vs. ML
Abstract
The Latent Variables Path (LVP) model and also the first viable estimation technique were developed by Karl Jöreskog (from 1973 onwards). Right from the beginning his LISREL method was of the utmost elegance and perfection, as regards the deductive properties of the model. The LISREL program has since been gradually improved (LISREL III: Jöreskog & van Thillo 1973; LISREL VII: Jöreskog & Sörbom 1987), as regards convenience for the user, additional estimation criteria and model diagnostics. However, one inconvenient side of LISREL, well known to all users, is incurable: LISREL tends to produce improper solutions characterized by negative variance estimates and LV correlations greater than unity (van Driel 1978, Jöreskog 1981, Fornell & Bookstein 1982, Rindskopf 1983, 1984).
Jan-Bernd Lohmöller
Chapter 6. Latent Variables Three-Mode Path (LVP3) Analysis
Abstract
Three-mode data y ktn are indexed by elements of three different sets of indices. Thus, y ktn may denote the score of case n ∈ N at time t ∈ T with respect to 61ttribute k ∈ K The term “three-mode” as well as the first three-mode structural model, the three-mode factor model (FA3 model), was introduced by Tucker (1963, 1964, 1965, 1966, 1967, 1972). The three-mode path model with latent variables (LVP3 model), introduced by Lohmöller and Wold (1980), uses a three-mode factor model as outer and a three-mode path model as inner model. An application of LVP3 analysis was presented by Lohmöller and Wold (1982). The program for LVP3 analysis is called PLS3 and is written by Lohmöller (1981a:chapter 6).
Jan-Bernd Lohmöller
Chapter 7. PLS Programs and Applications
Abstract
Except for special cases and simple models, PLS models require special PLS programs Principal component and canonical correlation analysis can be performed by nearly all standard statistical computer packages (like SPSS, BMDP, OSIRIS, SAS). How simple models can be estimated by SPSS is shown in Table 7.1. For every iteration cycle the program has to be restarted, with new weight coefficients for the LVs each time.
Jan-Bernd Lohmöller
Backmatter
Metadaten
Titel
Latent Variable Path Modeling with Partial Least Squares
verfasst von
Dr. Jan-Bernd Lohmöller
Copyright-Jahr
1989
Verlag
Physica-Verlag HD
Electronic ISBN
978-3-642-52512-4
Print ISBN
978-3-642-52514-8
DOI
https://doi.org/10.1007/978-3-642-52512-4