Types of model outcomes

Nonlinear Modeling with Generalized Additive Models (GAMs) in R

Noam Ross

Senior Research Scientist, EcoHealth Alliance

Types of outcomes

Continuous outcomes

Speed of a motorcycle (mph)
Fuel efficiency of a car (mpg)
Level of pollution in soil (g/kg)

Binary outcomes

Presence or absence of an organism in a location
Whether a purchase was made
Yes/No answer on a survey

Probabilities and log-odds: logistic function

Probabilities and log-odds: logit function

Logistic and logit functions in R

plogis() # Logistic
qlogis() # Logit

qlogis(plogis(0.5))

0.5

qlogis(0.25) == log(1/3)

TRUE

Logistic GAMs with mgcv

gam(y ~ x1 + s(x2),
   data = dat,
   family = binomial,
   method = "REML")

Family: binomial 
Link function: logit 
Formula:
y ~ s(x1) + s(x2)
Parametric coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)   0.7330     0.1208    6.07 1.28e-09 ***
 ---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Approximate significance of smooth terms:
        edf Ref.df Chi.sq  p-value    
s(x1) 1.367  1.646  25.83 1.23e-05 ***
s(x2) 5.754  6.890  51.37 8.12e-09 ***

plogis(0.733)

0.6754633

head(csale)

  purchase n_acts bal_crdt_ratio avg_prem_balance retail_crdt_ratio
1        0     11        0.00000         2494.414           0.00000
2        0      0       36.09506         2494.414          11.49123
3        0      6       17.60000         2494.414           0.00000
4        0      8       12.50000         2494.414           0.80000
5        0      8       59.10000         2494.414          20.80000
6        0      1       90.10000         2494.414          11.49123
  avg_fin_balance mortgage_age cred_limit
1        1767.197     182.0000      12500
2        1767.197     138.9601          0
3           0.000     138.9601          0
4        1021.000     138.9601          0
5         797.000      93.0000          0
6        4953.000     138.9601          0

Let's practice!

Nonlinear Modeling with Generalized Additive Models (GAMs) in R