Acrola
Kasia Wojczulanis-Jakubas
19 września 2016
Option 1 - Logistic regression
Dependent: male/female (dummy)
Predictors: latitude (continuous) + age + age latitude + date*
Sub-option 1.1: raw date included in the model (JULIAN DAY):
## glm(formula = SxDum ~ NewLat + Age + Age:NewLat + Jul, family = binomial(link = "probit"),
## data = ACROLA_comb)## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.90858637 2.63566039 -0.7241397 0.46897996
## NewLat -0.05067702 0.04125648 -1.2283410 0.21931900
## AgeI -0.92134141 2.16038742 -0.4264705 0.66976507
## Jul 0.01607116 0.00702242 2.2885498 0.02210552
## NewLat:AgeI 0.02074509 0.04837955 0.4287987 0.66806971## Analysis of Deviance Table
##
## Model: binomial, link: probit
##
## Response: SxDum
##
## Terms added sequentially (first to last)
##
##
## Df Deviance Resid. Df Resid. Dev Pr(>Chi)
## NULL 465 584.06
## NewLat 1 5.7345 464 578.33 0.01663 *
## Age 1 1.0150 463 577.31 0.31372
## Jul 1 5.1987 462 572.11 0.02260 *
## NewLat:Age 1 0.1851 461 571.93 0.66707
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Assesing the model fit:
## index.orig training test optimism index.corrected n
## Dxy 0.1917 0.2108 0.1693 0.0415 0.1502 1000
## R2 0.0360 0.0468 0.0282 0.0186 0.0174 1000
## Intercept 0.0000 0.0000 -0.1325 0.1325 -0.1325 1000
## Slope 1.0000 1.0000 0.8196 0.1804 0.8196 1000
## Emax 0.0000 0.0000 0.0682 0.0682 0.0682 1000
## D 0.0239 0.0319 0.0182 0.0137 0.0102 1000
## U -0.0043 -0.0043 0.0012 -0.0055 0.0012 1000
## Q 0.0282 0.0362 0.0170 0.0192 0.0090 1000
## B 0.2118 0.2098 0.2141 -0.0044 0.2162 1000
## g 0.3989 0.4451 0.3460 0.0991 0.2998 1000
## gp 0.0853 0.0938 0.0741 0.0196 0.0657 1000
##
## n=466 Mean absolute error=0.012 Mean squared error=0.00019
## 0.9 Quantile of absolute error=0.019The most insignificat factors: Age + Age:NewLat (P>0.6), excluded from the model:
## glm(formula = SxDum ~ NewLat + Jul, family = binomial(link = "probit"),
## data = ACROLA_comb)## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.54825944 1.999494107 -1.274452 0.20250324
## NewLat -0.03597969 0.022183095 -1.621942 0.10481580
## Jul 0.01604409 0.006432541 2.494207 0.01262389## Analysis of Deviance Table
##
## Model: binomial, link: probit
##
## Response: SxDum
##
## Terms added sequentially (first to last)
##
##
## Df Deviance Resid. Df Resid. Dev Pr(>Chi)
## NULL 465 584.06
## NewLat 1 5.7345 464 578.33 0.01663 *
## Jul 1 6.2132 463 572.11 0.01268 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Assesing the model fit:
## index.orig training test optimism index.corrected n
## Dxy 0.1942 0.2038 0.1857 0.0182 0.1760 1000
## R2 0.0355 0.0415 0.0324 0.0092 0.0263 1000
## Intercept 0.0000 0.0000 -0.0161 0.0161 -0.0161 1000
## Slope 1.0000 1.0000 0.9807 0.0193 0.9807 1000
## Emax 0.0000 0.0000 0.0071 0.0071 0.0071 1000
## D 0.0235 0.0281 0.0213 0.0068 0.0167 1000
## U -0.0043 -0.0043 0.0002 -0.0045 0.0002 1000
## Q 0.0278 0.0324 0.0211 0.0113 0.0165 1000
## B 0.2119 0.2108 0.2133 -0.0025 0.2144 1000
## g 0.3947 0.4154 0.3752 0.0402 0.3546 1000
## gp 0.0848 0.0886 0.0807 0.0079 0.0769 1000
##
## n=466 Mean absolute error=0.005 Mean squared error=6e-05
## 0.9 Quantile of absolute error=0.013Sub-option 1.2: latitud-adjusted date included in the model (DAY OF MIGRATION):
## glm(formula = SxDum ~ NewLat + Age + Age:NewLat + Dmigr, family = binomial(link = "probit"),
## data = ACROLA_comb)## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.776157e+01 88.31797478 -0.20110930 0.8406131
## NewLat 4.135861e-01 2.09674843 0.19725118 0.8436310
## AgeI 2.904688e+01 91.15290801 0.31866106 0.7499835
## Dmigr -3.988923e-04 0.01551108 -0.02571661 0.9794834
## NewLat:AgeI -6.870071e-01 2.16530153 -0.31728010 0.7510311## Analysis of Deviance Table
##
## Model: binomial, link: probit
##
## Response: SxDum
##
## Terms added sequentially (first to last)
##
##
## Df Deviance Resid. Df Resid. Dev Pr(>Chi)
## NULL 103 138.59
## NewLat 1 0.87327 102 137.71 0.3501
## Age 1 0.21721 101 137.50 0.6412
## Dmigr 1 0.00415 100 137.49 0.9487
## NewLat:Age 1 0.10101 99 137.39 0.7506Assesing the model fit:
## index.orig training test optimism index.corrected n
## Dxy 0.1917 0.2135 0.1709 0.0426 0.1490 1000
## R2 0.0360 0.0478 0.0286 0.0192 0.0168 1000
## Intercept 0.0000 0.0000 -0.1330 0.1330 -0.1330 1000
## Slope 1.0000 1.0000 0.8190 0.1810 0.8190 1000
## Emax 0.0000 0.0000 0.0685 0.0685 0.0685 1000
## D 0.0239 0.0327 0.0185 0.0142 0.0097 1000
## U -0.0043 -0.0043 0.0015 -0.0058 0.0015 1000
## Q 0.0282 0.0370 0.0171 0.0200 0.0082 1000
## B 0.2118 0.2095 0.2141 -0.0046 0.2164 1000
## g 0.3989 0.4502 0.3487 0.1014 0.2975 1000
## gp 0.0853 0.0948 0.0747 0.0200 0.0653 1000
##
## n=466 Mean absolute error=0.013 Mean squared error=2e-04
## 0.9 Quantile of absolute error=0.019The most insignificat factors: Age + Age:NewLat (P>0.6), excluded from the model:
## glm(formula = SxDum ~ NewLat + Dmigr, family = binomial(link = "probit"),
## data = ACROLA_comb)## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 9.932094214 18.06000134 0.5499498 0.5823538
## NewLat -0.243902229 0.42876487 -0.5688484 0.5694590
## Dmigr 0.002214197 0.01358626 0.1629733 0.8705394## Analysis of Deviance Table
##
## Model: binomial, link: probit
##
## Response: SxDum
##
## Terms added sequentially (first to last)
##
##
## Df Deviance Resid. Df Resid. Dev Pr(>Chi)
## NULL 103 138.59
## NewLat 1 0.87327 102 137.71 0.3501
## Dmigr 1 0.02606 101 137.69 0.8718Assesing the model fit:
## index.orig training test optimism index.corrected n
## Dxy 0.1942 0.2037 0.1858 0.0179 0.1762 1000
## R2 0.0355 0.0415 0.0324 0.0090 0.0264 1000
## Intercept 0.0000 0.0000 0.0109 -0.0109 0.0109 1000
## Slope 1.0000 1.0000 1.0033 -0.0033 1.0033 1000
## Emax 0.0000 0.0000 0.0029 0.0029 0.0029 1000
## D 0.0235 0.0280 0.0213 0.0067 0.0168 1000
## U -0.0043 -0.0043 -0.0001 -0.0042 -0.0001 1000
## Q 0.0278 0.0323 0.0214 0.0109 0.0169 1000
## B 0.2119 0.2102 0.2132 -0.0031 0.2150 1000
## g 0.3947 0.4158 0.3755 0.0403 0.3544 1000
## gp 0.0848 0.0885 0.0808 0.0077 0.0770 1000
##
## n=466 Mean absolute error=0.005 Mean squared error=5e-05
## 0.9 Quantile of absolute error=0.011Option 2 - GLM
Dependent: male/total for the site (proportion) Predictors: latitude (continuous) + age + age:latitude
Testing the model assumptions:
##
## Call:
## lm(formula = Mprop ~ NewLat + Age + NewLat:Age, data = ACROLA_prop_total)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.17250 -0.06567 -0.02505 0.04498 0.28136
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.175533 0.602139 -0.292 0.774
## NewLat 0.019656 0.013237 1.485 0.154
## AgeI -0.121797 0.790632 -0.154 0.879
## NewLat:AgeI 0.001468 0.017311 0.085 0.933
##
## Residual standard error: 0.1138 on 19 degrees of freedom
## Multiple R-squared: 0.2611, Adjusted R-squared: 0.1445
## F-statistic: 2.238 on 3 and 19 DF, p-value: 0.1168Deleting the outlier [both NewLat (AI) records associated with 19], and re-testing the model fit: 
##
## Call:
## lm(formula = Mprop ~ NewLat + Age + NewLat:Age, data = ACROLA_prop_total[-c(10,
## 11), ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.156678 -0.053237 -0.009386 0.044282 0.164771
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.190791 0.412044 -0.463 0.649
## NewLat 0.019303 0.009058 2.131 0.048 *
## AgeI -0.162599 0.541339 -0.300 0.768
## NewLat:AgeI 0.002634 0.011849 0.222 0.827
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07788 on 17 degrees of freedom
## Multiple R-squared: 0.4462, Adjusted R-squared: 0.3485
## F-statistic: 4.566 on 3 and 17 DF, p-value: 0.01602## Analysis of Variance Table
##
## Response: Mprop
## Df Sum Sq Mean Sq F value Pr(>F)
## NewLat 1 0.073543 0.073543 12.1261 0.002852 **
## Age 1 0.009239 0.009239 1.5234 0.233902
## NewLat:Age 1 0.000300 0.000300 0.0494 0.826751
## Residuals 17 0.103102 0.006065
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The insignificat factors: Age + Age:NewLat (P>0.2), excluded from the model (data set as for the model with all predictors included - doble representation for each location!):
## [1] "Testing the model assumptions"
##
## Call:
## lm(formula = Mprop ~ NewLat, data = ACROLA_prop_total[-c(10,
## 11), ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.168737 -0.050373 0.007571 0.042149 0.150044
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.258864 0.263363 -0.983 0.33800
## NewLat 0.020271 0.005755 3.522 0.00228 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.077 on 19 degrees of freedom
## Multiple R-squared: 0.395, Adjusted R-squared: 0.3632
## F-statistic: 12.41 on 1 and 19 DF, p-value: 0.002278
The insignificat factors: Age + Age:NewLat (P>0.2), excluded from the model (rormated data set - single representation for each location!):
##
## Call:
## lm(formula = Mprop ~ NewLat, data = ACROLA_Mprop_total)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.12318 -0.05643 -0.01042 0.02887 0.23383
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.059200 0.444054 -0.133 0.896
## NewLat 0.016311 0.009669 1.687 0.120
##
## Residual standard error: 0.09864 on 11 degrees of freedom
## Multiple R-squared: 0.2055, Adjusted R-squared: 0.1333
## F-statistic: 2.846 on 1 and 11 DF, p-value: 0.1197Deleting the outliers [NewLat: 12 and 22] re-testing the model fit:
##
## Call:
## lm(formula = Mprop ~ NewLat, data = ACROLA_Mprop_total[-c(6,
## 11), ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.08223 -0.02779 -0.01716 0.03837 0.08054
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.011741 0.244527 0.048 0.9628
## NewLat 0.014051 0.005341 2.631 0.0273 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.05326 on 9 degrees of freedom
## Multiple R-squared: 0.4347, Adjusted R-squared: 0.3719
## F-statistic: 6.921 on 1 and 9 DF, p-value: 0.02733