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edit approved Mar 27, 2015 at 18:00

My optimal model includes a significant interaction between my first principal component and a predictor variable (external to the PCs) which has a positive regression coefficient. I'm not quite sure how to interpret this two-way interaction. Does Fs_abundanceFs_abundance increase with an unit increase of the positive loadings and decrease of negative loadings of PC1PC1 and that increases the likelihood of success of my response variable?

>a12 a12<<- glmer(Tb_qpcr_status~Tb_qpcr_status ~ (1|River)+Fs_abundance*PC1 + Fs_abundance * PC1,family=binomial 
family = binomial,data=f data = f.data)
>  
summary(a12)

Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod'] Family: binomial ( logit ) Formula: Tb_qpcr_status ~ (1 | River) + Fs_abundance * PC1 Data: f.data


Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: binomial  ( logit )
Formula: Tb_qpcr_status ~ (1 | River) + Fs_abundance * PC1
   Data: f.data

     AIC      BIC   logLik deviance df.resid 
    16.7     19.9     -3.4      6.7        9 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.1975 -0.1143 -0.0185  0.1221  1.4067 

Random effects:
 Groups Name        Variance Std.Dev.
 River  (Intercept) 0        0       
Number of obs: 14, groups:  River, 3

Fixed effects:
                 Estimate Std. Error z value Pr(>|z|)
(Intercept)       -4.6814     3.9753  -1.178    0.239
Fs_abundance       2.1215     2.8837   0.736    0.462
PC1               -0.9542     1.7018  -0.561    0.575
Fs_abundance:PC1   3.5402     2.7761   1.275    0.202

Correlation of Fixed Effects:
            (Intr) Fs_bnd PC1   
Fs_abundanc -0.713              
PC1          0.759 -0.758       
Fs_bndn:PC1 -0.684  0.427 -0.123

Scaled residuals: Min 1Q Median 3Q Max -1.1975 -0.1143 -0.0185 0.1221 1.4067

Random effects: Groups Name Variance Std.Dev. River (Intercept) 0 0
Number of obs: 14, groups: River, 3

Fixed effects: Estimate Std. Error z value Pr(>|z|) (Intercept) -4.6814 3.9753 -1.178 0.239 Fs_abundance 2.1215 2.8837 0.736 0.462 PC1 -0.9542 1.7018 -0.561 0.575 Fs_abundance:PC1 3.5402 2.7761 1.275 0.202

Correlation of Fixed Effects: (Intr) Fs_bnd PC1
Fs_abundanc -0.713
PC1 0.759 -0.758
Fs_bndn:PC1 -0.684 0.427 -0.123

>a13 a13<<- update(a12, ~.- Fs_abundance:PC1)
> anova(a12, a13)

Data: f.data
Models:
a13: Tb_qpcr_status ~ (1 | River) + Fs_abundance + PC1
a12: Tb_qpcr_status ~ (1 | River) + Fs_abundance * PC1
    Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)  
a13  4 19.640 22.197 -5.8201   11.640                           
a12  5 16.721 19.916 -3.3605    6.721 4.9192      1    0.02656 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Data: f.data Models: a13: Tb_qpcr_status ~ (1 | River) + Fs_abundance + PC1 a12: Tb_qpcr_status ~ (1 | River) + Fs_abundance * PC1 Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq) a13 4 19.640 22.197 -5.8201 11.640 a12 5 16.721 19.916 -3.3605 6.721 4.9192 1 0.02656 *

Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1

My optimal model includes a significant interaction between my first principal component and a predictor variable (external to the PCs) which has a positive regression coefficient. I'm not quite sure how to interpret this two-way interaction. Does Fs_abundance increase with an unit increase of the positive loadings and decrease of negative loadings of PC1 and that increases the likelihood of success of my response variable?

> a12<-glmer(Tb_qpcr_status~(1|River)+Fs_abundance*PC1,family=binomial,data=f.data)
> summary(a12)

Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod'] Family: binomial ( logit ) Formula: Tb_qpcr_status ~ (1 | River) + Fs_abundance * PC1 Data: f.data

 AIC      BIC   logLik deviance df.resid 
16.7     19.9     -3.4      6.7        9

Scaled residuals: Min 1Q Median 3Q Max -1.1975 -0.1143 -0.0185 0.1221 1.4067

Random effects: Groups Name Variance Std.Dev. River (Intercept) 0 0
Number of obs: 14, groups: River, 3

Correlation of Fixed Effects: (Intr) Fs_bnd PC1
Fs_abundanc -0.713
PC1 0.759 -0.758
Fs_bndn:PC1 -0.684 0.427 -0.123

> a13<-update(a12,~.-Fs_abundance:PC1)
> anova(a12,a13)

Data: f.data Models: a13: Tb_qpcr_status ~ (1 | River) + Fs_abundance + PC1 a12: Tb_qpcr_status ~ (1 | River) + Fs_abundance * PC1 Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq) a13 4 19.640 22.197 -5.8201 11.640 a12 5 16.721 19.916 -3.3605 6.721 4.9192 1 0.02656 *

Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1

My optimal model includes a significant interaction between my first principal component and a predictor variable (external to the PCs) which has a positive regression coefficient. I'm not quite sure how to interpret this two-way interaction. Does Fs_abundance increase with an unit increase of the positive loadings and decrease of negative loadings of PC1 and that increases the likelihood of success of my response variable?

a12 <- glmer(Tb_qpcr_status ~ (1|River) + Fs_abundance * PC1, 
family = binomial, data = f.data)
 
summary(a12)

Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: binomial  ( logit )
Formula: Tb_qpcr_status ~ (1 | River) + Fs_abundance * PC1
   Data: f.data

     AIC      BIC   logLik deviance df.resid 
    16.7     19.9     -3.4      6.7        9 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.1975 -0.1143 -0.0185  0.1221  1.4067 

Random effects:
 Groups Name        Variance Std.Dev.
 River  (Intercept) 0        0       
Number of obs: 14, groups:  River, 3

Fixed effects:
                 Estimate Std. Error z value Pr(>|z|)
(Intercept)       -4.6814     3.9753  -1.178    0.239
Fs_abundance       2.1215     2.8837   0.736    0.462
PC1               -0.9542     1.7018  -0.561    0.575
Fs_abundance:PC1   3.5402     2.7761   1.275    0.202

Correlation of Fixed Effects:
            (Intr) Fs_bnd PC1   
Fs_abundanc -0.713              
PC1          0.759 -0.758       
Fs_bndn:PC1 -0.684  0.427 -0.123

a13 <- update(a12, ~.- Fs_abundance:PC1)
anova(a12, a13)

Data: f.data
Models:
a13: Tb_qpcr_status ~ (1 | River) + Fs_abundance + PC1
a12: Tb_qpcr_status ~ (1 | River) + Fs_abundance * PC1
    Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)  
a13  4 19.640 22.197 -5.8201   11.640                           
a12  5 16.721 19.916 -3.3605    6.721 4.9192      1    0.02656 *
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

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asked Mar 24, 2015 at 18:44

Ines

Interpretation of interaction between a PC and a continuous predictor on a logical response

I'm using lme4 in R to test the effect of various continuous explanatory variables, some of which I've corrected for their collinearity using PCA, on a logical response variable.

My optimal model includes a significant interaction between my first principal component and a predictor variable (external to the PCs) which has a positive regression coefficient. I'm not quite sure how to interpret this two-way interaction. Does Fs_abundance increase with an unit increase of the positive loadings and decrease of negative loadings of PC1 and that increases the likelihood of success of my response variable?

> a12<-glmer(Tb_qpcr_status~(1|River)+Fs_abundance*PC1,family=binomial,data=f.data)
> summary(a12)

Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod'] Family: binomial ( logit ) Formula: Tb_qpcr_status ~ (1 | River) + Fs_abundance * PC1 Data: f.data

 AIC      BIC   logLik deviance df.resid 
16.7     19.9     -3.4      6.7        9

Scaled residuals: Min 1Q Median 3Q Max -1.1975 -0.1143 -0.0185 0.1221 1.4067

Random effects: Groups Name Variance Std.Dev. River (Intercept) 0 0
Number of obs: 14, groups: River, 3

Correlation of Fixed Effects: (Intr) Fs_bnd PC1
Fs_abundanc -0.713
PC1 0.759 -0.758
Fs_bndn:PC1 -0.684 0.427 -0.123

> a13<-update(a12,~.-Fs_abundance:PC1)
> anova(a12,a13)

Data: f.data Models: a13: Tb_qpcr_status ~ (1 | River) + Fs_abundance + PC1 a12: Tb_qpcr_status ~ (1 | River) + Fs_abundance * PC1 Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq) a13 4 19.640 22.197 -5.8201 11.640 a12 5 16.721 19.916 -3.3605 6.721 4.9192 1 0.02656 *

Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1