From 2b8708a1b9a1c0aef306464fec1caaa83783e756 Mon Sep 17 00:00:00 2001 From: Jakub Adamski Date: Sun, 20 Jun 2021 11:57:11 +0200 Subject: [PATCH] lab10 --- podsumowanie/README.md | 87 +++++++++++++++++++++++++++- podsumowanie/lab10/logistyczna.png | Bin 0 -> 48477 bytes podsumowanie/lab10/logistyczna2.png | Bin 0 -> 45606 bytes podsumowanie/lab10/nieliniowa.png | Bin 0 -> 60863 bytes podsumowanie/lab10/poisson.png | Bin 0 -> 36654 bytes podsumowanie/lab10/roc.png | Bin 0 -> 156689 bytes podsumowanie/lab10/roc2.png | Bin 0 -> 150440 bytes testowe/pomocnicze.R | 62 ++++++++++---------- zajecia10/README.md | 4 +- 9 files changed, 118 insertions(+), 35 deletions(-) create mode 100644 podsumowanie/lab10/logistyczna.png create mode 100644 podsumowanie/lab10/logistyczna2.png create mode 100644 podsumowanie/lab10/nieliniowa.png create mode 100644 podsumowanie/lab10/poisson.png create mode 100644 podsumowanie/lab10/roc.png create mode 100644 podsumowanie/lab10/roc2.png diff --git a/podsumowanie/README.md b/podsumowanie/README.md index 4d4a4ac..388b069 100644 --- a/podsumowanie/README.md +++ b/podsumowanie/README.md @@ -702,11 +702,94 @@ summary(model_2)$adj.r.squared --- ## LAB 10 Zagadnienia: - - + - regresja logistyczna i Poissona + + - wykład 9 końcówka - ### R +### R +```r +# regresja logistyczna +model_1 <- glm(condition ~ bilirubin + ldh, data = liver_data, family = 'binomial') +summary(model_1) +step(model_1) + +# iloraz szans +exp(coef(model_1)[2]) +exp(coef(model_1)[3]) + +# krzywa ROC +install.packages("ROCR") +library(ROCR) +pred_1 <- prediction(model_1$fitted, liver_data$condition) +plot(performance(pred_1, 'tpr', 'fpr'), main = "Model 1") +performance(pred_1, 'auc')@y.values + +# predykcja z wykresem +liver_data_new <- data.frame(bilirubin = c(0.9, 2.1, 3.4), ldh = c(100, 200, 300)) +(predict_glm <- stats::predict(model_1, liver_data_new, type = 'response')) +model_1_hat <- coef(model_1)[1] + coef(model_1)[2] * liver_data$bilirubin + coef(model_1)[3] * liver_data$ldh +model_1_temp <- seq(min(model_1_hat) - 1, max(model_1_hat) + 2.5, length.out = 100) +condition_temp <- exp(model_1_temp) / (1 + exp(model_1_temp)) +plot(model_1_temp, condition_temp, type = "l", xlab = "X beta", ylab = "condition", xlim = c(-6, 9), ylim = c(-0.1, 1.1)) +points(model_1_hat, liver_data$condition, pch = 16) +points(coef(model_1)[1] + coef(model_1)[2] * liver_data_new$bilirubin + coef(model_1)[3] * liver_data_new$ldh, predict_glm, pch = 16, col = "red") + +# regresja Poissona +install.packages("DAAG") +library(DAAG) +head(moths) +model_1 <- glm(A ~ log(meters), data = moths, family = 'poisson') + +# predykcja +data_new <- data.frame(meters = c(3, 20, 100)) +(pred_1 <- stats::predict(model_1, data_new, type = "response")) +moths$A_hat <- stats::predict(model_1, type = "response") +moths <- moths[with(moths, order(meters)), ] +plot(log(moths$meters), moths$A_hat, + type = "l", col = "red", lwd = 2, + xlab = "log(moths$meters)", ylab = "A", + ylim = c(0, 40), main = "Model 1") +points(log(moths$meters), moths$A, pch = 16) +points(log(data_new$meters), pred_1, pch = 16, col = "blue", lwd = 4) +``` + + + +### Krzywa ROC +W statystyce matematycznej krzywa ROC jest graficzną reprezentacją efektywności modelu predykcyjnego poprzez wykreślenie charakterystyki jakościowej klasyfikatorów binarnych powstałych z modelu przy zastosowaniu wielu różnych punktów odcięcia. Mówiąc inaczej – każdy punkt krzywej ROC odpowiada innej macierzy błędu uzyskanej przez modyfikowanie „cut-off point”. W punkcie (0, 0) model klasyfikuje wszystko jako negative w punkcie (1, 1) model klasyfikuje wszystko jako positive. Pojęcia: +- TPR (True Positive Rate) – określa zdolność klasyfikatora do wykrywania klasy pozytywnej + +- Lepiej jest powyżej przekątnej, gorzej poniżej. Przekątna to klasyfikator losowy. Przekątna idzie od początku układu współrzędnych. + +- False positive rate = 1-specyficzność + +- Punkt równowagi to klasyfikator gdzie czułość = specyficzność. Jest to na przecięciu drugiej przekątnej z wykresem.
+![roc2](lab10/roc2.png) + +- AUC - Interpretacja AUROC (Area Under the ROC) to prawdopodobieństwo, że badany model predykcyjny oceni wyżej (wartość score) losowy element klasy pozytywnej od losowego elementu klasy negatywnej. Jest to dokłądność modelu - dla idealnego AUC=100%.
+![ROC](roc.png) ### Zagadnienia +- Regresja logistyczna – jedna z metod regresji używanych w statystyce w przypadku, gdy zmienna zależna jest na skali dychotomicznej (przyjmuje tylko dwie wartości). Zmienne niezależne w analizie regresji logistycznej mogą przyjmować charakter nominalny, porządkowy, przedziałowy lub ilorazowy. W przypadku zmiennych nominalnych oraz porządkowych następuje ich przekodowanie w liczbę zmiennych zero-jedynkowych taką samą lub o 1 mniejszą niż liczba kategorii w jej definicji. +

+Zwykle wartości zmiennej objaśnianej wskazują na wystąpienie, lub brak wystąpienia pewnego zdarzenia, które chcemy prognozować. Regresja logistyczna pozwala wówczas na obliczanie prawdopodobieństwa tego zdarzenia (tzw. prawdopodobieństwo sukcesu). Wykres krzywej to sigmoid function
+ +![logistyczna](lab10/logistyczna.png) +![logistyczna2](lab10/logistyczna2.png) + +- Rozkład Poissona – dyskretny rozkład prawdopodobieństwa, wyrażający prawdopodobieństwo szeregu wydarzeń mających miejsce w określonym czasie, gdy te wydarzenia występują ze znaną średnią częstotliwością i w sposób niezależny od czasu jaki upłynął od ostatniego zajścia takiego zdarzenia. + +- Regresja Poissona - ilość wydarzeń.
+![poisson](lab10/poisson.png) + +- Liczba stopni swobody – liczba niezależnych wyników obserwacji pomniejszona o liczbę związków, które łączą te wyniki ze sobą. Liczbę stopni swobody można utożsamiać z **liczbą niezależnych zmiennych losowych**, które wpływają na wynik. Inną interpretacją liczby stopni swobody może być: liczba obserwacji minus liczba parametrów estymowanych przy pomocy tych obserwacji. + +- Regresja nieliniowa
+![nieliniowa](lab10/nieliniowa.png) + +- Iloraz szans - w skrócie OR określa nam stosunek szansy wystąpienia danego zdarzenia w danej grupie do wystąpienia tego samego zdarzenia w innej porównywanej grupie. + + diff --git a/podsumowanie/lab10/logistyczna.png b/podsumowanie/lab10/logistyczna.png new file mode 100644 index 0000000000000000000000000000000000000000..50576eccb828a08dcdb810447c4091aa1bffcd32 GIT binary patch literal 48477 zcmeGDWmp|e(=H4n!QI{6Ex5Y{53q2D5ZocSyL)hl;J$Eo3+`^g-R)hu_p|rDuKW9b zzrWsf%p5cHbXRv*S9P6d%@D4vD2)V<4-W`l z^|lljSC$nQCslT|Gq1kuXFGdf&rvu(9pA}SMjPtD#U4WUHdcYbrFv!cx99%;x4{7OdI$G)Az*pOkdPWrRZ{^<1om3}XFCSgO zgG1aa1YpBRgZe_#8+oj@FktHEL}*x$VCIpN1SA->!D@zIaG;b>2PJiud|?chdiD8% zHW@>cQaFQeU~y^Lp5WjFOf-~z`DOf-Gl{) zgxGC&uwn;1Q5bq556bC(BpiK^Tz9+=)5O1iY-PFF;IMae{|Q4?-T9dQ{NV|Q6#iBz z4ptT9M@x}WdDq9~g-2-H8VtvpjdD|0vsT9$r3vBfdWsANL4s;!+SM0pcoVY_d)!x79z5QWq$#yIYJr0?SoJ;)kj6Cwi}#nu$ah7ncoRd8qH<}oP|yn1>p_W4Qj z==;SCNkV?po$V2RG*Z*zM)C(|_oBO|P(m7};UTPvK-AL?1QDa*m!Mh+=bFkR=2&f2 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