HANOI UNIVERSITY OF SCIENCE Final exam scientific report Course V370: Research Methods and Statistical Modelings Vu Tuan Tai- K55TT KHMT- 10000792 " Analysis of presence or absence of species The data to be analyzed is the data on the abundance of Faramea occidentalis (in attached text file) Please explain the influence of precipitation, altitude, age and geology parameters on the presenceabsence of Faramea occidentalis species The calculation and the numerical results are required " Contents Analysis an influence of age category on the presence-absence of Faramea occidentalis 1.1 Analysis by using quasi-binomial GLM > Presabs.model3 0 ~ Age.cat, family = quasibinomial(link=logit) , data = faramea, na.action = na.exclude) > summary(Presabs.model3) Call: glm(formula = Faramea.occidentalis > ~ Age.cat, family = quasibinomial(link = logit), data = faramea, na.action = na.exclude) Deviance Residuals: Min 1Q Median 3Q Max -1.4350 -1.0008 -0.9005 1.0979 1.4823 Coefficients: Estimate Std Error t value Pr(>|t|) (Intercept) 0.5878 0.5783 1.016 0.316 Age.cat[T.c2] -0.7701 0.8536 -0.902 0.372 Age.cat[T.c3] -1.2809 0.7767 -1.649 0.107 (Dispersion parameter for quasibinomial family taken to be 1.075) Null deviance: 59.401 on 42 degrees of freedom Residual deviance: 56.322 on 40 degrees of freedom (2 observations deleted due to missingness) AIC: NA Number of Fisher Scoring iterations: > anova(Presabs.model3,test="F") Analysis of Deviance Table Model: quasibinomial, link: logit Response: Faramea.occidentalis > Terms added sequentially (first to last) Df Deviance Resid Df Resid Dev F Pr(>F) NULL 42 59.401 Age.cat 3.0793 40 56.322 1.4322 0.2508 > predict(Presabs.model3, type="response", se.fit=T) $fit B0 B49 p1 p2 p3 p4 p5 p6 0.3333333 0.3333333 0.4545455 0.3333333 0.6428571 0.6428571 0.4545455 0.4545455 p7 p8 p9 p10 p11 p12 p13 p14 0.6428571 0.3333333 0.3333333 0.3333333 0.3333333 0.4545455 0.4545455 0.3333333 p15 p16 p17 p18 p19 p20 p21 p22 0.3333333 0.3333333 0.3333333 0.4545455 0.6428571 0.6428571 0.6428571 0.6428571 p23 p24 p25 p26 p27 p28 p29 p30 0.4545455 0.4545455 0.4545455 0.4545455 0.6428571 0.6428571 0.6428571 0.6428571 p31 p32 p33 p34 p35 p36 p37 p38 0.3333333 0.3333333 0.3333333 0.3333333 0.3333333 0.3333333 0.3333333 0.6428571 p39 p40 p41 C1 S0 0.6428571 NA NA 0.6428571 0.4545455 $se.fit B0 B49 p1 p2 p3 p4 p5 p6 0.1152024 0.1152024 0.1556596 0.1152024 0.1327757 0.1327757 0.1556596 0.1556596 p7 p8 p9 p10 p11 p12 p13 p14 0.1327757 0.1152024 0.1152024 0.1152024 0.1152024 0.1556596 0.1556596 0.1152024 p15 p16 p17 p18 p19 p20 p21 p22 0.1152024 0.1152024 0.1152024 0.1556596 0.1327757 0.1327757 0.1327757 0.1327757 p23 p24 p25 p26 p27 p28 p29 p30 0.1556596 0.1556596 0.1556596 0.1556596 0.1327757 0.1327757 0.1327757 0.1327757 p31 p32 p33 p34 p35 p36 p37 p38 0.1152024 0.1152024 0.1152024 0.1152024 0.1152024 0.1152024 0.1152024 0.1327757 p39 p40 p41 C1 S0 0.1327757 NA NA 0.1327757 0.1556596 $residual.scale [1] 1.036822 > null.model 0 ~ 1, family = quasibinomial(link=logit) , data = faramea, na.action = na.exclude) > anova(null.model, Presabs.model3, test="Chi") > plot(Presabs.model3) > termplot(Presabs.model3, se=T, partial.resid=T, rug=T, terms="Age.cat") > library(effects) > plot(effect("Age.cat", Presabs.model3)) 1.2 Graphical results 1.3 Discussion We can see that the quasi-binomial model estimated the dispersion parameter to be 1.075 Moreover, the ANOVA table provides a large significant level P=0.25 The ANOVA table also provides important information on the deviance that is explained: the model only explains 3.079 per 59.401 of null deviance ( approximately 5.2%- small percentage) So that we can conclude there is no evidence for an influence of age on the presence-absence of Faramea occidentalis Analysis an influence of precipitation on the presence-absence of Faramea occidentalis 2.2 Analysis by using quasi-binomial GLM > Presabs.model4 0 ~ Precipitation, family = quasibinomial(link=logit) , data = faramea, na.action = na.exclude) > summary(Presabs.model4) Call: glm(formula = Faramea.occidentalis > ~ Precipitation, family = quasibinomial(link = logit), data = faramea, na.action = na.exclude) Deviance Residuals: Min 1Q Median 3Q Max -1.7303 -1.0431 -0.3289 1.1157 1.7268 Coefficients: Estimate Std Error t value Pr(>|t|) (Intercept) 6.948352 2.828385 2.457 0.0183 * Precipitation -0.002721 0.001095 -2.484 0.0172 * Signif codes: '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' (Dispersion parameter for quasibinomial family taken to be 0.9878704) Null deviance: 59.401 on 42 degrees of freedom Residual deviance: 50.561 on 41 degrees of freedom (2 observations deleted due to missingness) AIC: NA Number of Fisher Scoring iterations: > summary(Presabs.model4) Call: glm(formula = Faramea.occidentalis > ~ Precipitation, family = quasibinomial(link = logit), data = faramea, na.action = na.exclude) Deviance Residuals: Min 1Q Median 3Q Max -1.7303 -1.0431 -0.3289 1.1157 1.7268 Coefficients: Estimate Std Error t value Pr(>|t|) (Intercept) 6.948352 2.828385 2.457 0.0183 * Precipitation -0.002721 0.001095 -2.484 0.0172 * Signif codes: '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' (Dispersion parameter for quasibinomial family taken to be 0.9878704) Null deviance: 59.401 on 42 degrees of freedom Residual deviance: 50.561 on 41 degrees of freedom (2 observations deleted due to missingness) AIC: NA Number of Fisher Scoring iterations: > anova(Presabs.model4,test="F") Analysis of Deviance Table Model: quasibinomial, link: logit Response: Faramea.occidentalis > Terms added sequentially (first to last) Df Deviance Resid Df Resid Dev F Pr(>F) NULL 42 59.401 Precipitation 8.8406 41 50.561 8.9492 0.004682 ** Signif codes: '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' > predict(Presabs.model4, type="response", se.fit=T) $fit B0 B49 p1 p2 p3 p4 p5 0.51585260 0.51585260 0.23199505 0.19599449 0.22518137 0.22881035 0.59346000 p6 p7 p8 p9 p10 p11 p12 0.60691110 0.57754510 0.56615226 0.28611341 0.51632834 0.52570000 0.53836922 p13 p14 p15 p16 p17 p18 p19 0.48436383 0.51265767 0.56648644 0.53498590 0.55603305 0.52888801 0.40957580 p20 p21 p22 p23 p24 p25 p26 0.42958718 0.59536260 0.52692120 0.69682041 0.67793630 0.64473891 0.69428486 p27 p28 p29 p30 p31 p32 p33 0.66272350 0.66962240 0.83081979 0.77620128 0.11822036 0.11782378 0.05264970 p34 p35 p36 p37 p38 p39 p40 0.18149948 0.01904871 0.21490787 0.17079990 0.52441063 0.60248775 NA p41 C1 S0 NA 0.85958830 0.21628851 $se.fit B0 B49 p1 p2 p3 p4 p5 0.08456340 0.08456340 0.10310235 0.10255668 0.10318186 0.10314912 0.09028002 p6 p7 p8 p9 p10 p11 p12 0.09175142 0.08867379 0.08763705 0.10019974 0.08457920 0.08494578 0.08560342 p13 p14 p15 p16 p17 p18 p19 0.08413929 0.08446438 0.08766594 0.08541010 0.08680929 0.08509405 0.08779233 p20 p21 p22 p23 p24 p25 p26 0.08625142 0.09048256 0.08500118 0.10200951 0.10003257 0.09618903 0.10175731 p27 p28 p29 p30 p31 p32 p33 0.09830953 0.09910199 0.10311570 0.10641589 0.09025501 0.09013959 0.05987074 p34 p35 p36 p37 p38 p39 p40 0.10157356 0.03010363 0.10314943 0.10051629 0.08488917 0.09125797 NA p41 C1 S0 NA 0.09818365 0.10316496 $residual.scale [1] 0.9939167 > null.model 0 ~ 1, family = quasibinomial(link=logit) , data = faramea, na.action = na.exclude) > anova(null.model, Presabs.model4, test="Chi") Error in anova.glmlist(c(list(object), dotargs), dispersion = dispersion, : models were not all fitted to the same size of dataset > plot(Presabs.model4) Waiting to confirm page change Waiting to confirm page change Waiting to confirm page change Waiting to confirm page change > termplot(Presabs.model4, se=T, partial.resid=T, rug=T, terms="Precipitation") > library(effects) > plot(effect("Precipitation", Presabs.model4)) > 2.2 Graphical results 2.3 Discussion From the result above, we can see that the dispersion parameter is estimated to be 0.987, very close to In addition, we can obtain that there is evidence that precipitation has an effect on the presence-absence of Faramea, because the significant level calculated for the coefficient is low (P=0.0172) and the model can explain 8.84 per 59.401 of null deviance We can also notice that there is an effect of precipitation from the low significance level of the ANOVA table (P=0.005) Here we need to calculate the inverse logit function y= exp(x)/(1+exp(x)) Where: x= intercept So the value of y= exp(6.9483)/(1 + exp(6.9483-0.00272))= 1.0017 Analysis an influence of elevation (altitude) on the presenceabsence of Faramea occidentalis 3.1 Analysis by using quasi-binomial GLM > Presabs.model4 0 ~ Elevation, family = quasibinomial(link=logit) , data = faramea, na.action = na.exclude) > summary(Presabs.model4) Call: glm(formula = Faramea.occidentalis > ~ Elevation, family = quasibinomial(link = logit), data = faramea, na.action = na.exclude) Deviance Residuals: Min 1Q Median 3Q Max -1.5768 -1.0960 -0.1003 0.9853 1.3298 Coefficients: Estimate Std Error t value Pr(>|t|) (Intercept) 1.059522 0.548718 1.931 0.0604 Elevation -0.007838 0.003608 -2.172 0.0357 * Signif codes: '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' (Dispersion parameter for quasibinomial family taken to be 0.9235897) Null deviance: 59.401 on 42 degrees of freedom Residual deviance: 49.469 on 41 degrees of freedom (2 observations deleted due to missingness) AIC: NA Number of Fisher Scoring iterations: > summary(Presabs.model4) Call: glm(formula = Faramea.occidentalis > ~ Elevation, family = quasibinomial(link = logit), data = faramea, na.action = na.exclude) Deviance Residuals: Min 1Q Median 3Q Max -1.5768 -1.0960 -0.1003 0.9853 1.3298 Coefficients: Estimate Std Error t value Pr(>|t|) (Intercept) 1.059522 0.548718 1.931 0.0604 Elevation -0.007838 0.003608 -2.172 0.0357 * Signif codes: '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' (Dispersion parameter for quasibinomial family taken to be 0.9235897) Null deviance: 59.401 on 42 degrees of freedom Residual deviance: 49.469 on 41 degrees of freedom (2 observations deleted due to missingness) AIC: NA Number of Fisher Scoring iterations: > anova(Presabs.model4,test="F") Analysis of Deviance Table Model: quasibinomial, link: logit Response: Faramea.occidentalis > Terms added sequentially (first to last) Df Deviance Resid Df Resid Dev F Pr(>F) NULL 42 59.401 Elevation 9.9317 41 49.469 10.753 0.002127 ** Signif codes: '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' > predict(Presabs.model4, type="response", se.fit=T) $fit B0 B49 p1 p2 p3 p4 0.529708571 0.529708571 0.711517145 0.568499634 0.413067396 0.413067396 p5 p6 p7 p8 p9 p10 0.678307798 0.695166342 0.643192603 0.660971608 0.103956639 0.587614191 p11 p12 p13 p14 p15 p16 0.643192603 0.727334914 0.652135099 0.643192603 0.625010199 0.451517474 p17 p18 p19 p20 p21 p22 0.529708571 0.646782001 0.451517474 0.451517474 0.549178826 0.413067396 p23 p24 p25 p26 p27 p28 0.695166342 0.660971608 0.549178826 0.660971608 0.413067396 0.451517474 p29 p30 p31 p32 p33 p34 0.568499634 0.413067396 0.163984396 0.143608856 0.025500776 0.357453005 p35 p36 p37 p38 p39 p40 0.004295295 0.375649093 0.025500776 0.005020600 0.016087593 NA p41 C1 S0 NA 0.660971608 0.490555259 $se.fit B0 B49 p1 p2 p3 p4 p5 0.08146756 0.08146756 0.10112096 0.08255982 0.09403845 0.09403845 0.09628896 p6 p7 p8 p9 p10 p11 p12 0.09880798 0.09097973 0.09364622 0.10141856 0.08406130 0.09097973 0.10316293 p13 p14 p15 p16 p17 p18 p19 0.09230903 0.09097973 0.08840591 0.08774458 0.08146756 0.09150956 0.08774458 p20 p21 p22 p23 p24 p25 p26 0.08774458 0.08166658 0.09403845 0.09880798 0.09364622 0.08166658 0.09364622 p27 p28 p29 p30 p31 p32 p33 0.09403845 0.08774458 0.08255982 0.09403845 0.11807371 0.11418257 0.04360614 p34 p35 p36 p37 p38 p39 p40 0.10458585 0.01101142 0.10109007 0.04360614 0.01250399 0.03114841 NA p41 C1 S0 NA 0.09364622 0.08327455 $residual.scale [1] 0.9610358 > null.model 0 ~ 1, family = quasibinomial(link=logit) , data = faramea, na.action = na.exclude) > anova(null.model, Presabs.model4, test="Chi") > plot(Presabs.model4) > termplot(Presabs.model4, se=T, partial.resid=T, rug=T, terms="Elevation") > library(effects) > plot(effect("Elevation", Presabs.model4)) 3.2 Graphical results 3.3 Discussion According to the above results, the model explain 9.9317 or 16.72% of total deviance Furthermore, the Pr-value ~ 0.0357 is very low implies there is evidence so that the elevation has effect on the presence/absence of Faramea Here we must calculate the inverse logit y= exp(x)/(1+(1+exp(x)) So, y=exp(1.0595)/(1+exp(1.0595-0.00784))= 0.747 Analysis an influence of geology on the presence-absence of Faramea occidentalis 4.1 Analysis by using quasi-binomial GLM > Presabs.model4 0 ~ Geology, family = quasibinomial(link=logit) , data = faramea, na.action = na.exclude) > summary(Presabs.model4) Call: glm(formula = Faramea.occidentalis > ~ Geology, family = quasibinomial(link = logit), data = faramea, na.action = na.exclude) Deviance Residuals: Min 1Q Median 3Q Max -1.7941 -0.4854 -0.4854 0.6681 2.0963 Coefficients: Estimate Std Error t value Pr(>|t|) (Intercept) -2.0794 0.7395 -2.812 0.00792 ** Geology[T.Tb] 3.4657 1.3275 2.611 0.01309 * Geology[T.Tbo] 20.6455 6431.4085 0.003 0.99746 Geology[T.Tc] 2.3671 1.0555 2.243 0.03116 * Geology[T.Tcm] 20.6455 2876.2134 0.007 0.99431 Geology[T.Tgo] 1.6740 1.1649 1.437 0.15936 Geology[T.Tl] 20.6455 4547.6926 0.005 0.99640 Signif codes: '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' (Dispersion parameter for quasibinomial family taken to be 0.9722222) Null deviance: 59.401 on 42 degrees of freedom Residual deviance: 33.853 on 36 degrees of freedom (2 observations deleted due to missingness) AIC: NA Number of Fisher Scoring iterations: 17 > summary(Presabs.model4) Call: glm(formula = Faramea.occidentalis > ~ Geology, family = quasibinomial(link = logit), data = faramea, na.action = na.exclude) Deviance Residuals: Min 1Q Median 3Q Max -1.7941 -0.4854 -0.4854 0.6681 2.0963 Coefficients: Estimate Std Error t value Pr(>|t|) (Intercept) -2.0794 0.7395 -2.812 0.00792 ** Geology[T.Tb] 3.4657 1.3275 2.611 0.01309 * Geology[T.Tbo] 20.6455 6431.4085 0.003 0.99746 Geology[T.Tc] 2.3671 1.0555 2.243 0.03116 * Geology[T.Tcm] 20.6455 2876.2134 0.007 0.99431 Geology[T.Tgo] 1.6740 1.1649 1.437 0.15936 Geology[T.Tl] 20.6455 4547.6926 0.005 0.99640 Signif codes: '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' (Dispersion parameter for quasibinomial family taken to be 0.9722222) Null deviance: 59.401 on 42 degrees of freedom Residual deviance: 33.853 on 36 degrees of freedom (2 observations deleted due to missingness) AIC: NA Number of Fisher Scoring iterations: 17 > anova(Presabs.model4,test="F") Analysis of Deviance Table Model: quasibinomial, link: logit Response: Faramea.occidentalis > Terms added sequentially (first to last) Df Deviance Resid Df Resid Dev F Pr(>F) NULL 42 59.401 Geology 25.548 36 33.853 4.3797 0.002027 ** Signif codes: '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' > predict(Presabs.model4, type="response", se.fit=T) $fit B0 B49 p1 p2 p3 p4 p5 p6 0.8000000 0.8000000 0.5714286 0.5714286 0.5714286 0.5714286 0.4000000 0.4000000 p7 p8 p9 p10 p11 p12 p13 p14 0.4000000 0.1111111 0.1111111 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 p15 p16 p17 p18 p19 p20 p21 p22 0.4000000 0.1111111 0.1111111 1.0000000 0.1111111 0.1111111 0.4000000 0.8000000 p23 p24 p25 p26 p27 p28 p29 p30 0.5714286 0.5714286 0.1111111 0.1111111 1.0000000 1.0000000 0.8000000 0.8000000 p31 p32 p33 p34 p35 p36 p37 p38 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111 0.1111111 p39 p40 p41 C1 S0 0.1111111 NA NA 0.1111111 0.5714286 $se.fit B0 B49 p1 p2 p3 p4 1.763834e-01 1.763834e-01 1.844278e-01 1.844278e-01 1.844278e-01 1.844278e-01 p5 p6 p7 p8 p9 p10 2.160247e-01 2.160247e-01 2.160247e-01 7.303802e-02 7.303802e-02 2.487024e-05 p11 p12 p13 p14 p15 p16 2.487024e-05 5.561155e-05 2.487024e-05 2.487024e-05 2.160247e-01 7.303802e-02 p17 p18 p19 p20 p21 p22 7.303802e-02 2.487024e-05 7.303802e-02 7.303802e-02 2.160247e-01 1.763834e-01 p23 p24 p25 p26 p27 p28 1.844278e-01 1.844278e-01 7.303802e-02 7.303802e-02 3.932330e-05 3.932330e-05 p29 p30 p31 p32 p33 p34 1.763834e-01 1.763834e-01 7.303802e-02 7.303802e-02 7.303802e-02 7.303802e-02 p35 p36 p37 p38 p39 p40 7.303802e-02 7.303802e-02 7.303802e-02 7.303802e-02 7.303802e-02 NA p41 C1 S0 NA 7.303802e-02 1.844278e-01 $residual.scale [1] 0.9860133 > null.model 0 ~ 1, family = quasibinomial(link=logit) , data = faramea, na.action = na.exclude) > anova(null.model, Presabs.model4, test="Chi") Error in anova.glmlist(c(list(object), dotargs), dispersion = dispersion, : models were not all fitted to the same size of dataset > plot(Presabs.model4) Warning: not plotting observations with leverage one: 14 Waiting to confirm page change Waiting to confirm page change Waiting to confirm page change Warning: not plotting observations with leverage one: 14 Waiting to confirm page change > termplot(Presabs.model4, se=T, partial.resid=T, rug=T, terms="Geology") > library(effects) > plot(effect("Geology", Presabs.model4)) > 4.2 Graphical results 4.3 Discussion Accordingly, the variance of presence- absence of Faramea occidentalis is 25.548 per 59.401 of total deviance (43%) Moreover, the Pr-value~ 0.002027 in the ANOVA table implies that geology has significant effect on the presence-absence of species The inverse logit function must be y=exp(x)/ (1+exp(x)) For example: with Geology[T.Tb]: y=exp(-2.0794)/(1+exp(-2.0794+3.4657))=0.025 Analysis the influence of several explanatory variables on the presence-absence of Faramea occidentalis by using binomial GLM 5.1 Results > Presabs.model6 ~ Precipitation + I(Precipitation^2) + Geology + Age.cat + Elevation + I(Elevation^2), family = binomial(link = logit) , data = faramea, na.action = na.exclude) Warning: glm.fit: fitted probabilities numerically or occurred > summary(Presabs.model6) Call: glm(formula = Faramea.occidentalis > ~ Precipitation + I(Precipitation^2) + Geology + Age.cat + Elevation + I(Elevation^2), family = binomial(link = logit), data = faramea, na.action = na.exclude) Deviance Residuals: Min 1Q Median 3Q Max -2.03069 -0.02753 0.00000 0.08387 1.97738 Coefficients: Estimate Std Error z value Pr(>|z|) (Intercept) -1.137e+02 8.737e+01 -1.302 0.193 Precipitation 1.006e-01 7.594e-02 1.324 0.185 I(Precipitation^2) -2.223e-05 1.644e-05 -1.352 0.176 Geology[T.Tb] 1.401e+00 1.718e+00 0.815 0.415 Geology[T.Tbo] 2.962e+01 1.075e+04 0.003 0.998 Geology[T.Tc] 1.266e+01 8.055e+00 1.572 0.116 Geology[T.Tcm] 2.642e+01 4.153e+03 0.006 0.995 Geology[T.Tgo] -1.270e+00 2.709e+00 -0.469 0.639 Geology[T.Tl] 1.792e+01 7.274e+03 0.002 0.998 Age.cat[T.c2] -9.695e+00 1.024e+01 -0.946 0.344 Age.cat[T.c3] -2.983e+00 2.458e+00 -1.214 0.225 Elevation 8.701e-02 1.161e-01 0.749 0.454 I(Elevation^2) -4.493e-04 5.293e-04 -0.849 0.396 (Dispersion parameter for binomial family taken to be 1) Null deviance: 59.401 on 42 degrees of freedom Residual deviance: 17.376 on 30 degrees of freedom (2 observations deleted due to missingness) AIC: 43.376 Number of Fisher Scoring iterations: 18 > anova(Presabs.model6,test="Chi") Warning: glm.fit: fitted probabilities numerically or occurred Warning: glm.fit: fitted probabilities numerically or occurred Analysis of Deviance Table Model: binomial, link: logit Response: Faramea.occidentalis > Terms added sequentially (first to last) NULL Df Deviance Resid Df Resid Dev Pr(>Chi) 42 59.401 Precipitation 8.8406 41 50.561 0.002946 ** I(Precipitation^2) 0.7224 40 49.838 0.395367 Geology 21.1442 34 28.694 0.001728 ** Age.cat 7.6046 32 21.089 0.022320 * Elevation 2.8375 31 18.252 0.092088 I(Elevation^2) 0.8761 30 17.376 0.349285 Signif codes: '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' > drop1(Presabs.model6, test="Chi") Warning: glm.fit: fitted probabilities numerically or occurred Warning: glm.fit: fitted probabilities numerically or occurred Warning: glm.fit: fitted probabilities numerically or occurred Warning: glm.fit: fitted probabilities numerically or occurred Warning: glm.fit: fitted probabilities numerically or occurred Single term deletions Model: Faramea.occidentalis > ~ Precipitation + I(Precipitation^2) + Geology + Age.cat + Elevation + I(Elevation^2) Df Deviance AIC LRT Pr(>Chi) 17.376 43.376 Precipitation 20.871 44.871 3.4952 0.0615481 I(Precipitation^2) 21.441 45.441 4.0652 0.0437749 * Geology 40.674 54.674 23.2984 0.0007025 *** Age.cat 24.799 46.799 7.4234 0.0244364 * Elevation 18.020 42.020 0.6445 0.4220785 I(Elevation^2) 18.252 42.252 0.8761 0.3492853 Signif codes: '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' > 5.2 Discussion More specific, the complex model in which all explanatory variable is much better in demonstrating the impact on the presence-absence of Faramea occidentalis As the result, we get the logit link function X=Logit(µ)= a + b1 x1+ b2.x2+b3.x3… Where a= intercept b1, b2,b3 = coefficient estimate value of each category So, that the inverse logit Y= exp(X)+(1+exp(X)) Conclusion We can see that each category variable (age, precipitation, altitude, geology) has its own influence on response variable as the presence-absence of Faramea occidentalis at certain level (even maybe at zero-level) Howeve, in order to get more exact result analysis, the complex model in which include both categories in the GLM should be used