Abstract
Multicollinearity is detected via regression models, where independent variables are strongly correlated. Since they entail linear relations between observed or latent variables, the structural equation models (SEM) are subject to the multicollinearity effect, whose numerous consequences include the singularity between the inverse matrices used in estimation methods. Given to this behavior, it is natural to understand that the suitability of these estimators to structural equation models show the same features, either in the simulation results that validate the estimators in different multicollinearity degrees, or in their application to real data. Due to the multicollinearity overview arose from the fact that the matrices inversion is impracticable, the usage of numerical procedures demanded by the maximum likelihood methods leads to numerical singularity problems. An alternative could be the use of the Partial Least Squares (PLS) method, however, it is demanded that the observed variables are built by assuming a positive correlation with the latent variable. Thus, theoretically, it is expected that the load signals are positive, however, there are no restrictions to these signals in the algorithms used in the PLS method. This fact implies in corrective areas, such as the observed variables removal or new formulations of the theoretical model. In view of this problem, this paper aimed to propose adaptations of six generalized ridge estimators as alternative methods to estimate SEM parameters. The conclusion is that the evaluated estimators presented the same performance in terms of accuracy, precision while considering the scenarios represented by model without specification error and model with specification error, different levels of multicollinearity and sample sizes.
Highlights
The existence of a strong correlation between the variables involved in the estimation of parameters of a model characterizes the multicollinearity problem, whose main consequence is the high estimates of standard coefficients and errors, compromising conclusions related to statistical inference (Mori & Suzuki, 2018)
The methodology proposed for the adaptation of ridge estimators in structural equation modeling is described in the following stages: i) Estimators of generalized ridge regression and alternatives; ii) specification of the structural equation model; iii) adaptation of ridge estimators to the structural equation model and iv) scenarios and parametric values used in the Monte Carlo procedure to validate the generalized ridge estimators in structural equation models
Given the same scenarios evaluated by the Monte Carlo simulation, the results described in Table 4 showed that, by considering the specification error, omitting and simultaneously, mean square error estimations were accurate and precise, for all generalized ridge estimators with small oscillations due to the Monte Carlo error
Summary
The existence of a strong correlation between the variables involved in the estimation of parameters of a model characterizes the multicollinearity problem, whose main consequence is the high estimates of standard coefficients and errors, compromising conclusions related to statistical inference (Mori & Suzuki, 2018). In view of this problem, numerous alternatives to detect and solve this problem are reported in literature. Corroborating this statement, some studies on this problem are addressed. Yang and Yuan (2019) mention that the presence of multicollinearity involves obtaining operations of approximate or badly conditioned inverse matrices, causing a problem of numerical nature related to obtaining the estimates of maximum likelihood of a SEM
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