A Comparative Analysis with Oxalis continued Abigail Mazie and C cile An April 26 2011 Goals Comparative analysis of Oxalis data continued Using R for comparative analysis Illustrating multiple regression and principal component analysis PCA Reading the Data library ape library picante library phylobase oxalis dat read csv oxalis data csv rownames oxalis dat oxalis dat species oxalis dat oxalis dat 1 add column with natural log of scales mm oxalis dat log scales mm log oxalis dat scales mm oxalis dat OadenophyllaADEPH1 ObrasiliensisBRAS2 OperdicariaMV79 OdebilisEE171 OhispidulaMV44MV342 ObipartitaMV59MV320 alt precip seasonality scales mm lat abslat region log scales mm 2081 785 72 40 40 1 40 1 Basal 3 688879 79 1097 17 7 30 5 30 5 SESouthAmerican 1 945910 275 1262 63 64 30 7 30 7 SESouthAmerican 4 158883 684 1613 62 10 20 4 20 4 SESouthAmerican 2 302585 79 1211 31 8 28 2 28 2 SESouthAmerican 2 079442 803 1510 28 5 27 0 27 0 SESouthAmerican 1 609438 Visualizing the data altitude 0 1700 abslat 3700 7 20 seasonality 40 17 74 110 Possible Variables Temperature minimum maximum mean Precipitation Latitude Altitude Bioclimatic Variables Bioclimatic Variables BIO1 Annual Mean Temperature BIO2 Mean Diurnal Range Mean of monthly max temp min temp BIO3 Isothermality BIO2 BIO7 100 BIO4 Temperature Seasonality standard deviation 100 BIO5 Max Temperature of Warmest Month BIO6 Min Temperature of Coldest Month BIO7 Temperature Annual Range BIO5 BIO6 BIO8 Mean Temperature of Wettest Quarter BIO9 Mean Temperature of Driest Quarter BIO10 Mean Temperature of Warmest Quarter BIO11 Mean Temperature of Coldest Quarter BIO12 Annual Precipitation BIO13 Precipitation of Wettest Month BIO14 Precipitation of Driest Month BIO15 Precipitation Seasonality Coefficient of Variation BIO16 Precipitation of Wettest Quarter BIO17 Precipitation of Driest Quarter BIO18 Precipitation of Warmest Quarter BIO19 Precipitation of Coldest Quarter Why use principal component analysis Too many variables for direct multiple regression little power PCA will allow us to reduce number of predictor variables to a few components while retaining most information from all predictor variables Can use PCA on groups of predictor variables to reduce to one component Bioclimatic Variables Temperature Group BIO1 Annual Mean Temperature BIO2 Mean Diurnal Range Mean of monthly max temp min temp BIO3 Isothermality BIO2 BIO7 100 BIO4 Temperature Seasonality standard deviation 100 BIO5 Max Temperature of Warmest Month BIO6 Min Temperature of Coldest Month BIO7 Temperature Annual Range BIO5 BIO6 BIO8 Mean Temperature of Wettest Quarter BIO9 Mean Temperature of Driest Quarter BIO10 Mean Temperature of Warmest Quarter BIO11 Mean Temperature of Coldest Quarter BIO12 Annual Precipitation BIO13 Precipitation of Wettest Month BIO14 Precipitation of Driest Month BIO15 Precipitation Seasonality Coefficient of Variation BIO16 Precipitation of Wettest Quarter BIO17 Precipitation of Driest Quarter BIO18 Precipitation of Warmest Quarter BIO19 Precipitation of Coldest Quarter Bioclimatic Variables Precipitation Group BIO1 Annual Mean Temperature BIO2 Mean Diurnal Range Mean of monthly max temp min temp BIO3 Isothermality BIO2 BIO7 100 BIO4 Temperature Seasonality standard deviation 100 BIO5 Max Temperature of Warmest Month BIO6 Min Temperature of Coldest Month BIO7 Temperature Annual Range BIO5 BIO6 BIO8 Mean Temperature of Wettest Quarter BIO9 Mean Temperature of Driest Quarter BIO10 Mean Temperature of Warmest Quarter BIO11 Mean Temperature of Coldest Quarter BIO12 Annual Precipitation BIO13 Precipitation of Wettest Month BIO14 Precipitation of Driest Month BIO15 Precipitation Seasonality Coefficient of Variation BIO16 Precipitation of Wettest Quarter BIO17 Precipitation of Driest Quarter BIO18 Precipitation of Warmest Quarter BIO19 Precipitation of Coldest Quarter Question With PCA the author said that sometimes we would like to perform a PCA on the evolutionary correlation matrix rather than the evolutionary variance covariance matrix When should we use one or another Note PCA on correlation matrix PCA on re scaled variables so that each one is centered and has variance 1 Principal Component Analysis in R 1st column atl 2nd precip 3d season 6th abslat head oxalis dat c 1 2 3 6 alt precip seasonality abslat OadenophyllaADEPH1 2081 785 72 40 1 ObrasiliensisBRAS2 79 1097 17 30 5 OperdicariaMV79 275 1262 63 30 7 OdebilisEE171 684 1613 62 20 4 OhispidulaMV44MV342 79 1211 31 28 2 ObipartitaMV59MV320 803 1510 28 27 0 pca ind prcomp oxalis dat c 1 2 3 6 scale T summary pca ind Importance of components Comp 1 Standard deviation 1 4248 Proportion of Variance 0 5075 Cumulative Proportion 0 5075 Comp 2 0 9770 0 2386 0 7461 Comp 3 Comp 4 0 8254 0 57803 0 1703 0 08353 0 9165 1 00000 plot variances explained by each axis plot pca ind How much is explained by the PC axes 0 0 0 5 Variances 1 0 1 5 2 0 pca ind Comp 1 Comp 2 Comp 3 Comp 4 We could keep 3 components for future multiple regression Not very useful here then 4 original variables with clear interpretation versus 3 PC variables with less clear interpretation Interpretation of PC axes pca ind roration loadings Loadings Comp 1 Comp 2 Comp 3 Comp 4 alt 0 603 0 008 0 374 0 704 precip 0 441 0 716 0 229 0 491 seasonality 0 487 0 011 0 872 0 047 abslat 0 452 0 698 0 217 0 511 Interpretation axis 1 contrast between average of altitude seasonality and average of precip abslat axis 2 contrast between abs latitude and precipitation axis 3 seasonality mostly axis 4 average of alt precip and abslat Interpretation of PC axes Axis 1 Axis 4 Comp 3 0 0 0 2 OpinguiculaceaWood22147 ObrasiliensisBRAS2 OtrolliiEE281 OalpinaSW976 OlatifoliaEE756C ObipartitaMV59MV320 OhispidulaMV44MV342 alt OcaeruleaAG47 OlatifoliaAG70 OlasiandraAG69 OadenophyllaADEPH1 precip abslat OnelsoniiAG66 OdebilisEE171 OmorelosiiEPEREZ4856 OhernandesiiAG56 OdivergensAG62 OdecaphyllaAR2610A OperdicariaMV79 OdiscolorAG35 OmacrocarpaAG49 OtetraphyllaTETRA2 OprimaveraAG50 0 4 3 0 4 3 2 1 0 0 0 2 0 4 Comp 4 1 1 2 3 OoreocharisEE583 OtriangularisssppapilionaceaREG OpinguiculaceaWood22147 ObrasiliensisBRAS2 OtrolliiEE281 OalpinaSW976 OlatifoliaEE756C ObipartitaMV59MV320 OhispidulaMV44MV342 seasonality 0 0 0 2 Comp 1 precip 0 4 4 Axis 3 OlatifoliaAG70 OdebilisEE171 OoreocharisEE583 0 4 OoreocharisEE583 OtriangularisssppapilionaceaREG 0 4 ObipartitaMV59MV320 OtetraphyllaTETRA2 0 0 0 2 0 4 Comp 1 2 0 2 4 4 0 4 4 seasonalityalt alt OcaeruleaAG47 OlatifoliaAG70
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