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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