An Alternative Estimation Procedure For Partial Least Squares Path Modeling

Abstract : Since it s incept ion, part ial least squares pat h modeling has suff ered from t he absence of a single opt imizat ion crit erion for est imat ing comp onent weight s. A new est imat ion procedure is proposed t o address t his enduring issue. T he proposed procedure aims t o minimize a single least squares crit erion for est imat ing component weight s under b ot h Mode A and Mode B. An alt ernat ing least squares algorit hm is develop ed t o minimize t he crit erion. T his procedure provides quit e similar or ident ical solut ions t o t hose obt ained from exist ing Lohmöller 's algorit hm in real and simulat ed dat a analyses. T he prop osed procedure can serve as an alt ernat ive t o t he exist ing one in t hat it is well-grounded in t heory as well as performs comparably in pract ice. 1. Int r od u ct ion Part ial least squares pat h modeling (P LSP M) (Wold, 1966, 1973, 1982; Lohmöller 1989) is a long-st anding approach t o st ruct ural equat ion modeling. In paramet er est imat ion, t his approach adopt s a st rat egy of est imat ing a lat ent variable as a component or weight ed composit e of indicat ors. In t his regard, P LSP M can be considered a component-based approach t o st ruct ural equat ion modeling (Tenenhaus, 2008). It carries out two main st ages sequent ially t o est imat e paramet ers. T he first st age es-t imat es latent variables as component s, which requires t he est imat ion of component weight s. T his st age uses an iterative algorit hm t o est imat e t he component weight s. T he second st age est imat es remaining paramet ers in measurement and st ruct ural models (i.e., pat h coeffi cient s and/ or loadings) by means of ordinary linear regression. T hat is, pat h coeffi cient s are est imat ed by regressing each dependent lat ent variable on it s explanat ory lat ent variables, whereas loadings are est imat ed by regressing indi-cat ors on t heir corresponding lat ent variables. T he second st age is t hus non-it erat ive, which is based on t he lat ent variables obt ained from t he first st age. Accordingly, t he first st age is t he most crucial estimat ion procedure in P LSP M (Hanafi, 2007). Lohmöller 's (1989) algorit hm is best known for t he first st age and implement ed int o most software programs for P LSP M, including LVP LS (Lohmöller, 1984), P LS Graph (Chin, 2001), Smart P LS (Ringle et al., 2005), and XLSTAT (Addinsoft , 2009). As will be explained in more det ail in Sect ion 2, t his algorit hm repeat s two st eps, called K ey W ords and Phrases: P art ial least squares pat h modeling, Mode A, Mode B, schemes, opt imizat ion crit erion, alt ernat ing least squares. * McG ill Universit y * * University of Vict oria * * * Cent raleSup elec-L2S, UMR CNR S 8506 and Bioinform at ics/ Biost at ist ics P lat form IHU-A-ICM
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Heungsun Hwang, Yoshio Takane, Arthur Tenenhaus. An Alternative Estimation Procedure For Partial Least Squares Path Modeling. Behaviormetrika, Behaviormetric Society of Japan, 2015, 42 (1), pp.63-78. ⟨10.2333/bhmk.42.63⟩. ⟨hal-01235744⟩

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