INTRODUCTION TO RESOURCE SELECTION BY ANIMALS University of Wyoming 11-12 January, 2003 Module 5 Resource Selection Functions by Logistic Regression Presented by Bryan F.J. Manly Western EcoSystems Technology Inc. Module 2 Logistic Regression.
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INTRODUCTION TO RESOURCESELECTION BY ANIMALSUniversity of Wyoming11-12 January, 2003Module 5Resource Selection Functions byLogistic RegressionPresented byBryan F.J. ManlyWestern EcoSystems TechnologyInc.
One of the simplest ways of estimating aresource selection probability functioninvolves using logistic regression for modelling the probability of use of resourceunits, based on a collection of such units.Logistic regression can also be used withsamples of resource units, although this iscomplicated by the need to vary theestimation procedure according to thesampling protocol that is used.These uses of logistic regression are covered in this module and illustrated using data on the selection of winter habitat by antelopes and nest site selection by fernbirds.
Chapter 5 in Resource Selection by Animals:Statistical Design and Analysis for Field Studies,2nd Edit (RSBA2).
where (z) is the integral from -to z for the standard normal distribution, and the proportional hazards function
for the X variables.
of the model.
(a) The population of interest can be redefined to consist only of those in the smaller area. Nothing can then be said about the resource selection function in other areas.
(b) It can be assumed that the resource selection function is the same everywhere, and can therefore be estimated by a sample from just a part of the total area. Based on this
assumption, the estimated function applies everywhere.
(a) The 256 sampled plots can be regarded as the population of interest.
(b) It can be assumed that the resource selection function is the same on all public land – the estimated function applies to all plots in this population.
(c) It can be assumed that the resource selection function is the same on all public and private land. In that case, the estimated function applies to the whole of the Red Rim area.
variables can be used to replace the single aspect number:
Ind1 = 1 for an E/NE plot or otherwise 0
Ind2 = 1 for a S/SE plot or otherwise 0
Ind3 = 1 for a W/SW plot or otherwise 0.
N/NW aspect treated as the 'standard' aspect,which others differ from.
Nine variables available to characterize each of the 256 study plots:
X1 = density (thousands/ha) of big sagebrush
X2 = density (thousands/ha) of black greasewood
X3 = density (thousands/ha) of Nuttall's saltbush
X4 = density (thousands/ha) of Douglas rabbitbrush
X5 = slope (degrees)
X6 = distance to water(m)
X7 = East/Northeast indicator variable
X8 = South/Southeast indicator variable
X9 = West/Southwest indicator variable
Several approaches that can be used for analysing the data by logistic regression, depending on what definition of 'use' is applied:
(a)A study plot can be considered to be 'used' if antelopes are recorded in either the first or the second winter - application of logistic
regression to approximate the probability of a plot being used is straightforward.
(b) A study plot can be considered to be 'used' if antelopes are recorded in both years -probabilities of 'use' that are smaller than for
definition (a), but an analysis of the data using logistic regression is still straightforward.
(c) A study plot can be considered to be 'used‘ when antelopes are recorded for the first time - requires that the effect of time be
modelled - problems with logistic regression.
(d) The two years can be considered to be replicates - logistic regression can be used separately in each year, or one equation can be fitted to both years of data – more complicated analysis than is needed if one of the definitions (a) and (b) is used but better use is made of the data.
From comparing deviances (goodness of fit statistics) some evidence of selection in 1980-81 (and overall) but not in 1981-82.
equations, again separately for each year, with the vegetation variables and the slope omitted.
not at all significant - simpler model 3 seems better for describing the data.
the types of samples involved.
(a) there is a sample of the available unitsand a sample of the used unitsin the population,
(b) there is a sample of the available unitsand a sample of the unused unitsin the population, and
(c) there is a sample of unused unitsand a sample of used units.
Assume: the population of available units is of size N and ith unit has values xi = (xi1,xi2,...,xip) for the variables X1 to XP, and a corresponding probability of w*(xi) of being used after a certain amount of time.
Prob(ith unit sampled) = Pa + (1 - Pa)w*(xi)Pu.
Assume that the RSPF takes the form
where the argument of the exponential function should be negative.
for the probability of use given that a unit is sampled.
w(x) = exp(b1x1 + ... + bPxP)
and use this to compare resource units.
w*(xi) = exp(b0 +b1xi1 + ... + bPxiP) 1
for all units in the population.
points in the study region) and a sample of used resource units (nest sites).
7.80/3.25 = 2.40 (p = 0.016) for CANOPY
0.21/0.12 = 1.73 (p = 0.083) for EDGE
0.88/0.48 = 1.84 (p = 0.066) for PERIM
if the ratio of sampling probabilities Pu/Pa were known.
is obtained by omitting the terms
-10.73 - loge(Pu/Pa)
from the last equation, i.e.,