Some Cautionary Notes on the Use of Principal Components Regression

Hadi, Ali S.; Ling, Robert F.

doi:10.1080/00031305.1998.10480530

Cited by 114 publications

(41 citation statements)

References 14 publications

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“…For instance, linear combinations of collinear variables (principal components) can be used as synthetic independent predictors in principal component regressions (Vigneau et al 1997). However, this kind of approach may show serious statistical pitfalls (Hadi & Ling 1998), while the new independent variables will often be difficult to interpret (see Dormann et al 2013 for details and a review of other available methods).…”

Section: Dealing With Multicollinearitymentioning

confidence: 99%

Multicollinearity in spatial genetics: separating the wheat from the chaff using commonality analyses

et al. 2015

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Direct gradient analyses in spatial genetics provide unique opportunities to describe the inherent complexity of genetic variation in wildlife species and are the object of many methodological developments. However, multicollinearity among explanatory variables is a systemic issue in multivariate regression analyses and is likely to cause serious difficulties in properly interpreting results of direct gradient analyses, with the risk of erroneous conclusions, misdirected research and inefficient or counterproductive conservation measures. Using simulated data sets along with linear and logistic regressions on distance matrices, we illustrate how commonality analysis (CA), a detailed variance-partitioning procedure that was recently introduced in the field of ecology, can be used to deal with nonindependence among spatial predictors. By decomposing model fit indices into unique and common (or shared) variance components, CA allows identifying the location and magnitude of multicollinearity, revealing spurious correlations and thus thoroughly improving the interpretation of multivariate regressions. Despite a few inherent limitations, especially in the case of resistance model optimization, this review highlights the great potential of CA to account for complex multicollinearity patterns in spatial genetics and identifies future applications and lines of research. We strongly urge spatial geneticists to systematically investigate commonalities when performing direct gradient analyses.

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Section: Dealing With Multicollinearitymentioning

confidence: 99%

Multicollinearity in spatial genetics: separating the wheat from the chaff using commonality analyses

et al. 2015

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“…The problem here is that these three variables are necessarily co-linear due to the relationship t ¼ ðCT max À T 0 Þ=DT. It is well known that (severe) co-linearity creates serious problems if the purpose of the regression is to understand the process, to identify important variables in the process, or to obtain meaningful estimates of the regression coefficients (Rawlings 1988;Hadi & Ling 1998;Jolliffe 2004). Although any of those variables could be taken as a surrogate for the whole set (Thisted 1980), a simple scaling up of metabolic costs with decreasing heating rates may explain why differences in CT max are associated with exposure duration.…”

Section: Discussionmentioning

confidence: 99%

Estimating the adaptive potential of critical thermal limits: methodological problems and evolutionary implications

2010

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Summary1. Current studies indicate that estimates of thermal tolerance limits in ectotherms depend on the experimental protocol used, with slower and presumably more ecologically relevant rates of warming negatively affecting the upper thermal limits (CT max ). Recent empirical evidence also gives credence to earlier speculations suggesting that estimates of heritability could drop with slower heating rates. 2. Using published data from the fruit fly Drosophila melanogaster, we show that empirical patterns can be explained if flies' physical condition decreases with experimental time in thermal tolerance assays. This problem could even overshadow potential benefits of thermal acclimation, also suggesting that a drop in CT max with slower heating rates does not necessarily rule out beneficial acclimatory responses. 3. Numerical results from a simple illustrative model show that no clear conclusions can be obtained on how the phenotypic variance in CT max will be affected with different rates of thermal change. Conversely, the genetic variance and estimated heritabilities are expected to drop with slower heating rates, hence ramping rates in experiments aiming to study the evolutionary potential of thermal tolerance to respond to global warming should be as fast as possible (within the range in which measurement accuracy and physical condition are not affected). 4. Measurements under ecologically realistic warming rates should also consider the impact of other physiological and behavioural strategies that might partly compensate the negative effects of slow heating rates. However, there are situations in which slow heating rates closely mimic natural conditions, as those encountered by some aquatic ectotherms. These heating rates may be an issue of major concern in these species, given its negative impact on CT max and its adaptive potential.Key-words: ectotherms, energy expenditure, evolvability, heritability, phenotypic plasticity, thermal ramping, thermal toleranceThe reason why plants and animals (including men) are so sensitive to temperature is that they are chemical machines …. Many of them do burn even at ordinary temperatures, but so slowly that we don't notice any great change even within a lifetime. (Haldane 1940, pp. 69-70)

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“…Principle components regression (Manly 1990, Chatterjee and Price 1991, Hadi and Ling 1998, testing for the best model based on stand type and the landscape predictor variables summarised in principle components (Tables 3a, b), showed that the stand type in which the site was situated was important in determining the abundance of almost all species for which the whole model was significant (Tables 4a, b). Pairwise t-tests on stand type showed that the abundances of most species differed between clear-cuts and the other stand types, with the majority of species being more common in older forests.…”

Section: Effects Of Cwd Availability and Landscape Composition On Beementioning

confidence: 99%

Effects of landscape composition and substrate availability on saproxylic beetles in boreal forests: a study using experimental logs for monitoring assemblages

Gibb

Hjältén²,

Ball³

et al. 2005

Ecography

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K. 2006. Effects of landscape composition and substrate availability on saproxylic beetles in boreal forests: a study using experimental logs for monitoring assemblages. Á/ Ecography 29: 191 Á/204.Intensive forestry practises in the Swedish landscape have led to the loss and fragmentation of stable old-growth habitats. We investigated relationships between landscape composition at multiple scales and the composition of saproxylic beetle assemblages in nine clear-cut, mature managed and old-growth spruce-dominated forest stands in the central boreal zone of Sweden. We set out fresh spruce and birch logs and created spruce snags in 2001 Á/2002 to experimentally test the effects of coarse woody debris (CWD) type and forest management on the composition of early and late successional, and red-listed saproxylic beetle assemblages. We examined effects of CWD availability at 100 m, and landscape composition at 1 and 10 km on saproxylic beetle abundances. Additionally, we tested whether assemblage similarity decreased with increasing distance between sites. We collected beetles from the experimental logs using eclector and window traps in four periods during 2003. CWD was measured and landscape composition data was obtained from maps of remotely sensed data. The composition of saproxylic beetles differed among different CWD substrates and between clear-cuts and the older stand types, however differences between mature managed and old-growth forests were significant only for red-listed species. Assemblage similarities for red-listed species on clear-cuts were more different at greater distances apart, indicating that they have more localised distributions. CWD availability within 100 m of the study sites was rarely important in determining the abundance of species, suggesting that early successional saproxylic beetles can disperse further than this distance. At a larger scale, a large area of suitable stand types within both 1 and 10 km resulted in greater abundances in the study sites for several common and habitatspecific species. The availability of suitable habitat at scales of 1 Á/10 km is thus likely to be important in the survival of many saproxylic species in forestry-fragmented areas.

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Some Cautionary Notes on the Use of Principal Components Regression

Cited by 114 publications

References 14 publications

Multicollinearity in spatial genetics: separating the wheat from the chaff using commonality analyses

Multicollinearity in spatial genetics: separating the wheat from the chaff using commonality analyses

Estimating the adaptive potential of critical thermal limits: methodological problems and evolutionary implications

Effects of landscape composition and substrate availability on saproxylic beetles in boreal forests: a study using experimental logs for monitoring assemblages

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