TY - JOUR
T1 - Algorithms and biplots for double constrained correspondence analysis
AU - Ter Braak, Cajo J.F.
AU - Šmilauer, Petr
AU - Dray, Stéphane
PY - 2018/6
Y1 - 2018/6
N2 - Correspondence analysis with linear external constraints on both the rows and the columns has been mentioned in the ecological literature, but lacks full mathematical treatment and easily available algorithms and software. This paper fills this gap by defining the method as maximizing the fourth-corner correlation between linear combinations, by providing novel algorithms, which demonstrate relationships with related methods, and by making a detailed study of possible biplots and associated approximations. The method is illustrated using ecological data on the abundances of species in sites and where the species are characterized by traits and sites by environmental variables. The trait data and environment data form the external constraints and the question is which traits and environmental variables are associated, how these associations drive species abundances and how they can be displayed in biplots. With microbiome data becoming widely available, these and related multivariate methods deserve more study as they might be routinely used in the future.
AB - Correspondence analysis with linear external constraints on both the rows and the columns has been mentioned in the ecological literature, but lacks full mathematical treatment and easily available algorithms and software. This paper fills this gap by defining the method as maximizing the fourth-corner correlation between linear combinations, by providing novel algorithms, which demonstrate relationships with related methods, and by making a detailed study of possible biplots and associated approximations. The method is illustrated using ecological data on the abundances of species in sites and where the species are characterized by traits and sites by environmental variables. The trait data and environment data form the external constraints and the question is which traits and environmental variables are associated, how these associations drive species abundances and how they can be displayed in biplots. With microbiome data becoming widely available, these and related multivariate methods deserve more study as they might be routinely used in the future.
KW - Biplot
KW - Canonical correlation analysis
KW - Canonical correspondence analysis
KW - Community ecology
KW - Fourth-corner correlation
KW - Multivariate analysis
KW - Trait-environment relations
U2 - 10.1007/s10651-017-0395-x
DO - 10.1007/s10651-017-0395-x
M3 - Article
AN - SCOPUS:85040567232
SN - 1352-8505
VL - 25
SP - 171
EP - 197
JO - Environmental and Ecological Statistics
JF - Environmental and Ecological Statistics
IS - 2
ER -