Data

\(n = 89\) sites, \(d = 4\) covariates \(x_{ij}\):

response variable: \(y_i =\) presence of Reinhardtius hippoglossoides (flétan)

Barents map
Barents map
##     Latitude Longitude Depth Temperature Presence
## 356    71.10     22.43   349        3.95        0
## 357    71.32     23.68   382        3.75        0
## 358    71.60     24.90   294        3.45        0
## 359    71.27     25.88   304        3.65        0
## 363    71.52     28.12   384        3.35        0
## 364    71.48     29.10   344        3.65        1
## 
##  0  1 
## 34 55

Logistic regression model for the abundance

Setting \(x_{i0} \equiv 1\) and \(\beta = [\beta_0 \dots \beta_d]^\intercal\), \[ Y_i \sim \mathcal{B}(\pi_i), \qquad \log\frac{\pi_i}{1-\pi_i} = x_i^\intercal \beta. \]

bernGlm <- glm(Presence ~ Latitude + Longitude + Depth + Temperature, data=barents, family='binomial')
summary(bernGlm)
## 
## Call:
## glm(formula = Presence ~ Latitude + Longitude + Depth + Temperature, 
##     family = "binomial", data = barents)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.1707  -0.4024   0.1544   0.4743   1.9112  
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -43.45610   32.47644  -1.338  0.18087    
## Latitude      0.23210    0.41554   0.559  0.57647    
## Longitude     0.44160    0.13786   3.203  0.00136 ** 
## Depth         0.04809    0.01115   4.314  1.6e-05 ***
## Temperature  -0.61923    0.54730  -1.131  0.25787    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 118.38  on 88  degrees of freedom
## Residual deviance:  60.07  on 84  degrees of freedom
## AIC: 70.07
## 
## Number of Fisher Scoring iterations: 6