Tātai Whakamuri Whakatakotoranga
Ko te whakatauira arorau tētahi o ngā tikanga rongonui i roto i ngā tatauranga me te pūtaiao raraunga mō te whakatauira i te whanaungatanga i waenga i te maha o ngā taurangi motuhake (ngā matapae) me te taurangi whakawhirinaki kāwai, inā koa ko te rua (hei tauira, āe/kāo, angitu/kore, mate/hauora). Kāore i rite ki te whakatauira rārangi, e whakaputa ana i ngā uara tonu, kua hangaia te whakatauira arorau hei whakatau tata i te tūponotanga o tētahi huihuinga, nō reira ko te hua whakamutunga kei roto i te awhe o te 0 ki te 1. I roto i tēnei tuhinga, ka matapakihia e mātou te tātai whakatauira arorau, te tikanga o ia wāhanga, me pēhea te whakamaori.
He aha i hiahiatia ai te Whakamuritanga Logistic?
Mena ka whakamahia e tātou te whakatauira rārangi hei matapae i ngā tūponotanga, ka taea e te tauira te whakaputa uara i raro i te 0, i runga ake rānei i te 1, he mea tino koretake tēnei mō te tūponotanga. Ka arohia tēnei raruraru e te whakatauira arorau mā te whakamahi i tētahi mahi kore-rārangi e mahere ana i te hua kua tatauhia (tērā pea he uara) ki tētahi uara tūponotanga i waenga i te 0 me te 1. Ko te mahi e whakamahia whānuitia ana ko te mahi arorau, te mahi sigmoid rānei.
Hei tauira, me kī tātou e hiahia ana ki te matapae mēnā ka huri te kiritaki i runga i tōna tau, te roa o te ohaurunga, me te auau o te whakamahinga. E rua noa ngā mea ka taea te puta i te putanga kua matapaetia: te huri (1) te kore rānei o te huri (0). He pai te whakatauira logistic mō tēnei momo āhuatanga.
Te Tātai Taketake mō te Whakamuritanga Rautaki
Ko te kaupapa matua o te whakatauira whakahāngaitanga ko te whakatauira i te tūponotanga \( p \) ka puta te kaupapa \( Y = 1 \)), i runga i te uara o te taurangi matapae \( X \).
Ko ngā tauira whakatauira logistic e tuhia ana i roto i ngā āhua nui e rua:
1) Puka Tūponotanga (Sigmoid)
\[
p = P(Y=1 \mid X) = \frac{1}{1 + e^{-z}}
\]
dengan
\[
z = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \cdots + \beta_k X_k
\]
Ngā Mōhiohio:
– Ko te tūponotanga o te takahanga ko \( p \) (hei tauira: churn = 1).
– Ko te tau a Euler ko \( e \) (tata ki te 2,71828).
– Ko te \( z \) he huinga rārangi o ngā matapae.
– Ko \( \beta_0 \) te pūmau (taurangi).
– Ko \( \beta_1, \beta_2, \ldots, \beta_k \) ngā taunga whakatauira.
– He taurangi motuhake a \( X_1, X_2, \ldots, X_k \).
Mā te mahi sigmoid ka noho tonu te uara o \( z \) i waenga i te 0 me te 1 ahakoa te uara o \( p \).
2) Puka Takiuru (Ngā Tūponotanga Takiuru)
Ko tētahi atu āhua tino hira ko te āhua logit, arā, ko te logarithm o ngā tūponotanga:
\[
\text{logit}(p) = \ln\left(\frac{p}{1-p}\right) = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \cdots + \beta_k X_k
\]
Ngā Mōhiohio:
– Ko te \( \frac{p}{1-p} \) e kiia ana ko ngā tūponotanga (te tūponotanga whanaunga).
– Ko te logarithm tūturu te \( \ln \).
E whakamārama ana te puka logit ko te whakatauira o te whakatauira logistic i ngā tūponotanga log hei mahi rārangi o ngā matapae. Mā tēnei ka mārama ake te whakamārama i ngā tauwehenga, inā koa i roto i te horopaki o ngā ōwehenga tūponotanga.
Te Mārama ki ngā Tūponotanga me ngā Tauwehenga Tūponotanga
Hei tino mārama ki te tātai whakatauira logistic, me wehewehe tātou i waenga i te tūponotanga me te ōritetanga.
– Tūponotanga \( p \): te tūponotanga o te puta o tētahi kaupapa (0 ki te 1).
– Ngā Tūponotanga: te whakataurite i te tūponotanga o tētahi mea ka tupu me te kore e tupu:
\[
\text{taurangi} = \frac{p}{1-p}
\]
Tauira: mēnā ko \( p = 0{,}8 \), kātahi:
\[
\text{taurangi} = \frac{0{,}8}{0{,}2} = 4
\]
Ko te tikanga tēnei, e whā ngā wā ka nui ake te tūponotanga o te tupu o tēnei huihuinga i tō te korenga.
I roto i te whakatauira logistic, ka whakamāramahia te tauwehenga \( \beta \) mā te ōwehenga tūponotanga:
\[
\text{OR} = e^{\beta}
\]
– Mēnā ko \( \beta > 0 \), kāti ko \( e^{\beta} > 1 \): ka whakanuia e te matapae te tūponotanga o te kaupapa.
– Mena \( \beta < 0 \), kātahi \( e^{\beta} < 1 \): ka whakaitihia e te matapae te tūponotanga o te kaupapa. - Mena \( \beta = 0 \), kātahi \( e^{\beta} = 1 \): kāore he pānga ki ngā tūponotanga. Hei tauira, mena \( \beta_1 = 0{,}7 \), kātahi: \[ e^{0{,}7} \approx 2{,}01 \] Ko te tikanga o tēnei ko ia pikinga 1 waeine i roto i te \( X_1 \) ka whakareatia te tūponotanga o te kaupapa mā te 2,01 ngā wā pea (me te whakaaro kei te noho pūmau tonu ētahi atu taurangi). Tauira o te Tauira Whakamuri Rautaki Māmā Me kī kotahi noa te taurangi matapae \( X \), hei tauira ko te maha o ngā hāora ako ia wiki, hei matapae i te angitu i tētahi whakamātautau (paahi = 1, rahua = 0). Ko te tauira:
