3 Lord Stats Refs

8/13/2019 3 Lord Stats Refs

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Regression Analysis:

Florida Medical Entomology LabUniversit of Florida

ESA 2010: MUVE Section Symposium

opportunities: Novel statistics for entomologis


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Re ression anal sis

one or more independent variables

u y

Used to explore relationships and ascontri utions

Models developed for explicit predi


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Familiar t es

Logistic regression

tepwise regression

GLM: generalized linear models

GLMM: generalized linear mixed mo


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Traditional Linear re ressi

De endent and inde endent variables

Numerical: continuous or ordinal

Fixed effects model

All levels entire region of interest

Included in x range Normal distribution for errors

Single dependent variable

Can be simple, single variable

Y=b0

+ b1

x +

Or complex

Y=b0 + b1x1 + b2x2 ++ bijxi*xj +

Multivariate, interactions


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Traditional: Criteria for fittin

Hypothesis testing approach

F test, R2

Are coefficients significantly different froDoes variable make a significant contrib

model?


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Model Selection

Interactions to specified level

Full model


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GLM

Extensions of fixed effects linear models

Normal distributions Use a link function to link a linear model to t

Based on distribution of Y

Common distribution

Binomial: logit link


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Lo istic re ression

Binomial distribution

Infected or not Present or not

Probability that y=1

p(y=1) =

Logit link Log( /1-) = b0 + b1x1 + b2x2 +


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Lo istic - inter retation

variables

Odds ratios (or log odds ratios)

More common with levels of X rather than


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Exam le: lo istic ste wise re r

Data from simulation model: St. Louis Ence

Outcome (dependent variable): epidemic o

Epidemic = 1

Not epidemic = 0

14 input parameters as independent varia

amp e rom e ine parameter space

Fixed effects

,

Power of data with n=100 and many indepenvariables


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Exam le: Ste wise lo istic re

Logistic Model R2 = 0.34

Mosquito population

Mosquito mortality (baseline)

k5) 260

280

300

YesVectorSu

mmerPe

(dayssin

ceJan.

1

200

220

240

Epidemic?

No

70 80 90 100

160

180

Total Mosquito Population (x105)

10 100 1000 10000

Time of peak bird re

(days sinc

mosquitoes


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Generalized Linear Mixed M

Fixed effects

Independent variable is considered randolausibl re resent a lar er o ulation w

probability distribution


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GLMM models

Distribution of

variables

Variance structure

Bolker et al. 2008.

TREE 24: 127-135


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Bias in arameter estimation

Hypothesis testing: If coefficient is not significant, it is treate

Simulation study:

Y=1 + 0.5*x +eDistr

frome~N(0,1)

n = 10Regression model fit

Slope tested using

hypothesis testing

Distr

from

ope = accepte

p


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Ste wise re ression

Test for exit of entered variables

selection methods

Penalty for increased complexity

,

entry & exit


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Issues in ste wise re ression

Involves many sequential tests

Also affects distribution of F-statisticOverall si nificance of the final model aff

Fits single model with no assessment of w

others would have similar redictive abi


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Variable selection methods

Stepwise selection with information crite

BIC

All penalize model for increased comple

o me o s as owar s ncrease com


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Models pmethods

ata sets

Reanalyzed using

1: Stepwise F test

2: Ste wise AICSF SIC SSIC

3: Stepwise BIC

4: All subset AIC5: All subset BIC

: egress on ree

7: Regression tree BModels

stepwise

predictiv

Murtaugh. 2009. Ecology

Letters 12:1061-1068


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Issues with re ression

How many models should be considered?

Multiple dependent variables?y

tat st cs are a too


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Acknowled ements

symposium

Jonathan Day


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ESA Symposium References Lord presentation

Bolker, B. M., M. E. Brooks, C. J. Clark, S. W. Geange, J. R. Poulsen, M. H. H. Stevens, andJ. S. White.2008.Generalized linear mixed models: a practical guide for ecology and evolution.Trends Ecol. Evol. 24:127-135.

Littell, R. C., G. A. Milliken, W. W. Stroup, R. D. Wolfinger, and O. Schabenberger. 2006.SAS for mixed models. SAS Institute Inc., Cary, NC.

Murtaugh, P. A.2009.Performance of several variable-selection methods applied to realecological data. Ecol. Lett. 12:1061-1068.

Scheiner, S.M. and J. Gurevitch (eds.). 2001.Design and analysis of ecological experiments.Oxford University Press, New York, NY.

Shoukri, M. M. and C. A. Pause.1999.Statistical methods for health sciences. CRC Press LLC,Boca Raton, FL.

Snedecor, G. W. and W. G. Cochran.1980.Statistical methods. The Iowa State UniversityPress, Ames, Iowa.

Stephens, P. A., S. W. Buskirk, and C. Martnez del Rio.2007.Inference in ecology andevolution. Trends Ecol. Evol. 22:192-197.

Whittingham, M. J., P. A. Stephens, R. B. Bradbury, and R. P. Freckleton. 2006.Why do westill use stepwise modelling in ecology and behaviour? J. Anim. Ecol. 75:1182-1189.

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