A preliminary exploration into the Binomial Logistic Regression Models in R and their potential...

A preliminary exploration into the Binomial Logistic Regression Models in

R and their potential application

Andrew Trant

PPS Arctic - Labrador Highlands Research Group

One presentation in two parts

Part 1 (today)

-comparing binomial logistical regressions in R and Minitab

-binomial GLMs and Odds Ratios

Part 2 (next time)

-using GLMs in conservation biology

-an exploration of the past

Start off small…..

before …and after

type Nrelease NrecapTypical 201 34Melanism 601 205

Kettlewell, H B D (1956)

Research Question:Are the odds of survival higher for dark form (Melanic) than the light form (Typical)?

Odds = e (o) + e (Type) + error (link = logit)

e ( o) = survival odds, typical form

e ( Type) = odds ratio, melanic relative to typical form

e ( o + Type) = survival odds, melanic form

In Minitab:

Predictor Coef SE Coef z P Odds RatioConstant -1.5916 0.1881 -6.54 0.000Type - Melanic 0.9332 0.2069 4.51 0.000 2.54

Log-Likelihood: -477.062Test that all slopes are zero: G=22.977, DF =1, P-value=0.000

95% CILower Upper

1.70 3.81

In R…

glm(formula = Nrecap/Nrel ~ type, family = binomial, data = moth,weights = Nrel) Call:

Coefficients:(Intercept) typeTyp -0.6584 -0.9332

Degrees of Freedom: 1 Total (i.e. Null); 0 ResidualNull Deviance: 22.98 Residual Deviance: 1.592e-13 AIC: 15.93

> summary(moth)

Deviance Residuals: [1] 0 0

Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -0.65840 0.08604 -7.652 1.98e-14 ***typeTyp -0.93323 0.20689 -4.511 6.46e-06 ***---Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 2.2977e+01 on 1 degrees of freedomResidual deviance: 1.5921e-13 on 0 degrees of freedomAIC: 15.929

Number of Fisher Scoring iterations: 3

In Minitab:



95% CILower Upper

1.70 3.81

In R…Estimate Std. Error z-value Pr(>|z|)

(Intercept) -0.6584 0.08604 -7.652 1.98e-14 ***type Typical -0.93323 0.20689 -4.511 6.46e-06 ***

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

Odds = e (o) + e (Type) + error

BUTR assumes that o = melanistic NOT typical

>exp(-0.6584) = 0.5176e ( o) = survival odds, melanistic form R:

Estimate Std. Error z-value Pr(>|z|)(Intercept) -0.6584 0.08604 -7.652 1.98e-14 ***

type Typical -0.93323 0.20689 -4.511 6.46e-06 ***

e ( o + Type) = survival odds, melanic form MINITAB:



95% CILower Upper

1.70 3.81

>exp(-1.5916+0.9332) = 0.5177

Odds = e (o) + e (Type) + error

BUTR assumes that o = melanistic NOT typical

e ( o) = survival odds, melanistic form

>exp(-0.6584) = 0.5176R:


type Typical -0.93323 0.20689 -4.511 6.46e-06 ***

e ( o + Type) = survival odds, melanic form MINITAB:



95% CILower Upper

1.70 3.81

>exp(-1.5916+0.9332) = 0.5177

SAME(ish)

R:


type Typical -0.93323 0.20689 -4.511 6.46e-06 ***

MINITAB: >exp(0.9332) = 2.5426



95% CILower Upper

1.70 3.81

e ( Type) = odds ratio

Odds Ratio

>exp(-0.9332) = 0.3933

>1/exp(-0.9332)=2.5426

Calculating 95% Confidence Intervals

CI = e Estimate±(SE*z-value)

>exp(0.9332±(0.2069*1.96))

Lower = 1.694989

Upper= 3.814174

You have reached the end of part one

But there is a preliminary stab at part two

Dave’s Barnacles

Tetraclita squamosa

Acanthia sp.

>avthickathole<-glm(formula=Npartial/N~AvThickAtHole,family=binomial, weights=N,data=test)

ThickAtHoleN Nlive Npartial Odds ln(Odds) w/wbar ln(w/wbar)0.75 4 0 0 0 * 0 *1.25 5 3 2 1.5 0.40547 1.4 0.336471.75 12 4 5 0.5 -0.69315 0.77778 -0.251312.25 27 9 11 0.5 -0.69315 0.77778 -0.251312.75 32 5 7 0.18519 -1.6864 0.36458 -1.0093.25 25 10 16 0.66667 -0.40547 0.93333 -0.068993.75 17 14 14 4.66667 1.54045 1.92157 0.653144.25 19 14 18 2.8 1.02962 1.7193 0.541924.75 4 3 4 3 1.09861 1.75 0.559625.75 2 1 2 1 0 1.16667 0.15415

Average thickness at hole

LMGLM

Average thickness at hole

General Linear Model:>lm.avthickathole<-lm(w.wbar~AvThickAtHole,data=test)

Estimate Std. Error t value Pr(>|t|)(Intercept) 0.37983 0.39358 0.965 0.3628AvThickAtHole 0.02368 0.01194 1.983 0.0827

Generalized Linear Model:>avthickathole<-glm(formula=Npartial/N~AvThickAtHole,family=binomial, weights=N,data=test)

Estimate Std. Error z value Pr(>|z|)(Intercept) -3.40918 0.72386 -4.71 2.48e-06 ***AvThickAtHole 0.12493 0.02483 5.031 4.88e-07 ***

Odds Ratio: 1.13 (remember…exp(0.1249))

Average thickness residuals plots

LMGLM

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.



Summary of model comparison…GLM vs LM

Trait LM (p-value) GLM (p-value) more sensitive?AvThickAtHole 0.0827 4.88e-07 *** GLM

Height of barnacle

General Linear Model:>lm(w.wbar ~ Ht, data = height)

Generalized Linear Model: >glm.height<-glm(Npartial/N~Ht,family=binomial,weights=N,data=height))

Odds Ratio: 1.26

Estimate Std. Error z value Pr(>|z|)(Intercept) -3.40988 1.16226 -2.934 0.00335 **Ht 0.2431 0.07862 3.092 0.00199 **

Estimate Std. Error t value Pr(>|t|)(Intercept) -0.4576 0.4408 -1.038 0.3263Ht 0.09389 0.02951 3.182 0.0112 *

Height of barnacle residuals plots





LMGLM

Summary of model comparisons…GLM vs LM


Height 0.0112 * 0.00199 ** GLM

Max Diameter

General Linear Model:>lm(w.wbar ~ MaxDiam, data = maxdiam)

Generalized Linear Model:>glm(Npartial/N ~ MaxDiam, family = binomial, data = maxdiam,weights = N)

Odds Ratio: 1.073

Estimate Std. Error t value Pr(>|t|)(Intercept) 0.2427 0.50788 0.478 0.642MaxDiam 0.03485 0.02551 1.366 0.199

Estimate Std. Error z value Pr(>|z|)(Intercept) -1.37102 1.12028 -1.224 0.221MaxDiam 0.07833 0.05714 1.371 0.17

Max Diameter residuals plots

LMGLM





Summary of model comparisons…GLM vs LM


Height 0.0112 * 0.00199 ** GLMMax Diameter 0.199 0.17 GLM

Okay, that’s it…

Date post:	17-Jan-2016
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A preliminary exploration into the Binomial Logistic Regression Models in R and their potential...

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