OxBoatRace: Oxford-Cambridge Boat Race

In glarma: Generalized Linear Autoregressive Moving Average Models

Description

Results of the boat race between Oxford and Cambridge from 1829–2011.

Usage

data(OxBoatRace)

Format

A data frame containing the following columns:

[, 1]	Year	Year in which the race occurred. Some years are missing when the race was not run.
[, 2]	Intercept	A vector of ones, providing the intercept in the model.
[, 3]	Camwin	A binary response, zero for an Oxford win, one for a Cambridge win.
[, 4]	WinnerWeight	Weight of winning team's crew.
[, 5]	LoserWeight	Weight of losing team's crew.
[, 6]	Diff	Difference between winning team's weight and losing team's weight.

Source

Klingenberg, Bernhard (2008) Regression models for binary time series with gaps. Computational Statistics & Data Analysis, 52, 4076–4090.

Examples

### Example with Oxford-Cambridge Boat Race
data(OxBoatRace)

y1 <- OxBoatRace$Camwin
n1 <- rep(1, length(OxBoatRace$Year))
Y <- cbind(y1, n1 - y1)
X <- cbind(OxBoatRace$Intercept, OxBoatRace$Diff)
colnames(X) <- c("Intercept", "Weight Diff")

oxcamglm <- glm(Y ~ Diff + I(Diff^2),
                data = OxBoatRace,
                family = binomial(link = "logit"), x = TRUE)
summary(oxcamglm)

X <- oxcamglm$x

glarmamod <- glarma(Y, X, thetaLags = c(1, 2), type = "Bin", method = "NR",
                    residuals = "Pearson", maxit = 100, grad = 1e-6)

summary(glarmamod)
likTests(glarmamod)

## Plot Probability of Cambridge win versus Cambridge Weight advantage:
beta <- coef(glarmamod, "beta")
par(mfrow = c(1, 1))
plot(OxBoatRace$Diff, 1 / (1 + exp(-(beta[1] + beta[2] * OxBoatRace$Diff +
                                       beta[3] * OxBoatRace$Diff^2))),
     ylab = "Prob", xlab = "Weight Diff")
title("Probability of Cambridge win \n versus Cambridge weight advantage")

## Residuals and fit plots
par(mfrow=c(3, 2))
plot.glarma(glarmamod)

Example output

Call:
glm(formula = Y ~ Diff + I(Diff^2), family = binomial(link = "logit"), 
    data = OxBoatRace, x = TRUE)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.4850  -1.2109   0.8953   1.0055   1.9305  

Coefficients:
             Estimate Std. Error z value Pr(>|z|)   
(Intercept)  0.382472   0.202334    1.89  0.05872 . 
Diff         0.114623   0.037331    3.07  0.00214 **
I(Diff^2)   -0.010097   0.004855   -2.08  0.03756 * 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 216.16  on 155  degrees of freedom
Residual deviance: 198.62  on 153  degrees of freedom
AIC: 204.62

Number of Fisher Scoring iterations: 5


Call: glarma(y = Y, X = X, type = "Bin", method = "NR", residuals = "Pearson", 
    thetaLags = c(1, 2), maxit = 100, grad = 1e-06)

Pearson Residuals:
    Min       1Q   Median       3Q      Max  
-1.8865  -0.7968   0.4395   0.8436   2.9658  

GLARMA Coefficients:
        Estimate Std.Error z-ratio Pr(>|z|)    
theta_1   0.3396    0.1709   1.987 0.046975 *  
theta_2   0.5552    0.1459   3.804 0.000142 ***

Linear Model Coefficients:
             Estimate Std.Error z-ratio Pr(>|z|)   
(Intercept)  0.349954  0.267249   1.309  0.19038   
Diff         0.114755  0.038238   3.001  0.00269 **
I(Diff^2)   -0.011333  0.004916  -2.305  0.02114 * 

    Null deviance: 216.16  on 155  degrees of freedom
Residual deviance: 148.53  on 151  degrees of freedom
AIC: 193.0553 

Number of Newton Raphson iterations: 5

LRT and Wald Test:
Alternative hypothesis: model is a GLARMA process
Null hypothesis: model is a GLM with the same regression structure
          Statistic  p-value    
LR Test       15.56 0.000417 ***
Wald Test     17.51 0.000158 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

          Statistic   p-value    
LR Test      15.564 0.0004173 ***
Wald Test    17.510 0.0001577 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

glarma documentation built on May 2, 2019, 6:33 a.m.