Stepwise Multivariate Linear Regression

Kabe, D. G.

doi:10.1080/01621459.1963.10500886

Cited by 24 publications

(13 citation statements)

References 7 publications

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“…The set of standardised attributes were then regressed against each retained EOF to allow the estimation of each retained EOF from a given DEM. Stepwise multiple linear regression was used (Kabe, ), which adds the most significant attribute to the equation relating the attributes to the EOFs until a local minimum of the root mean square error is reached. Therefore, not all attributes will be used in the final empirical equation.…”

Section: Methodsmentioning

confidence: 99%

Evaluation of an empirical orthogonal function–based method to downscale soil moisture patterns based on topographical attributes

Busch

Niemann

Coleman

2011

Hydrological Processes

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Abstract:Soil moisture influences many hydrologic applications including agriculture, land management and flood prediction. Most remote-sensing methods that estimate soil moisture produce coarse resolution patterns, so methods are required to downscale such patterns to the resolutions required by these applications (e.g. 10-to 30-m grid cells). At such resolutions, topography is known to affect soil moisture patterns. Although methods have been proposed to downscale soil moisture based on topography, they usually require the availability of past high-resolution soil moisture patterns from the application region. The objective of this article is to determine whether a single topographic-based downscaling method can be used at multiple locations without relying on detailed local observations. The evaluated downscaling method is developed on the basis of empirical orthogonal function (EOF) analysis of space-time soil moisture data at a reference catchment. The most important EOFs are then estimated from topographic attributes, and the associated expansion coefficients are estimated on the basis of the spatial-average soil moisture. To test the portability of this EOF-based method, it is developed separately using four data sets (Tarrawarra, Tarrawarra 2, Cache la Poudre and Satellite Station), and the relationships that are derived from these data sets to estimate the EOFs and expansion coefficients are compared. In addition, each of these downscaling methods is applied not only for the catchment where it was developed but also to the other three catchments. The results suggest that the EOF downscaling method performs well for the location where it is developed, but its performance degrades when applied to other catchments.

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Section: Methodsmentioning

confidence: 99%

Evaluation of an empirical orthogonal function–based method to downscale soil moisture patterns based on topographical attributes

Busch

Niemann

Coleman

2011

Hydrological Processes

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“…Initially the idea of nested sequences of models was used in stepwise multiple regression (Kabe, 1963) and multivariate multiple regression, described in Mulaik (1972, pp. 411-417).…”

Section: Background For the Four-step Methodsmentioning

confidence: 99%

Doing the Four-Step Right

Mulaik¹,

Millsap²

2000

Structural Equation Modeling: A Multidisciplinary Journal

252

140

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Our response to Hayduk and Glaser will principally focus on their critique of the four-step procedure. Hayduk and Glaser project things into the four-step procedure that are not part of its conception. They fail to see the implicit context in which those who use this particular four-step procedure operate, which qualifies its application. They also have misunderstandings about the rationale for the procedure and read too much of exploratory factor analysis into its use. Hayduk (1996) proposed a method for doing structural equation modeling with as few as one or two indicators per latent variable, which he feels is incompatible with the factor-analytic underpinnings of the four-step procedure and which motivates him further to seek its overthrow. He did not clarify this sufficiently on SEMNET, so we have been compelled to read Hayduk (1996) to better understand his position, and we will point out some limitations of it from our own point of view. We further argue that Hayduk's (1996) advocacy of the use of fixed parameters in sparse measurement models is not a viable general alternative to the use of multiple indicators. Hayduk also believed the usual .05 level of significance in testing the exact fit of models favors the null hypothesis. He recommended that the significance level for a chi-square test be set at .75. We show this recommendation to be incoherent with the idea of a significance test and further show it to be unnecessary because, on the contrary, in most studies the null hypothesis is likely to be rejected.

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“…The Kruskal-Wallis nonparametric test (Kruskal and Wallis, 1952) followed by Dunn test (Dunn, 1964) were applied to obtain the statistically significant differences. An automatic linear modelling (IBM SPSS Statistics 24) by stepwise with a significance of 0.05 and a removal probability of 0.1 was also used (Agostinelli, 2002;Grego, 1993;Hastie et al, 2009;Kabe, 1963).…”

Section: Additional Data and Data Analysismentioning

confidence: 99%

Characterization of aerosol sources in León (Spain) using Positive Matrix Factorization and weather types

Oduber

Calvo

Castro

et al. 2021

Science of The Total Environment

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A one-year aerosol sampling period was conducted in León (Spain) to label the sources.• The PMF found 6 main aerosol contributors, from traffic (29%) to biomass burning (3%). • A linear model estimates each source supply to PM 10 from tracer elements and airflows. • PMF analysis along with circulation weather types provide a good estimation for PM 10 . • MLR models built offer a simplification for determining source apportionment.

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Stepwise Multivariate Linear Regression

Abstract: 4] have given some results for the st,epwise estimation of the parameters of a univariate regremion model. We give here similar results for a multivariate linear regression model.

Cited by 24 publications

References 7 publications

Evaluation of an empirical orthogonal function–based method to downscale soil moisture patterns based on topographical attributes

Evaluation of an empirical orthogonal function–based method to downscale soil moisture patterns based on topographical attributes

Doing the Four-Step Right

Characterization of aerosol sources in León (Spain) using Positive Matrix Factorization and weather types

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