![license](data:image/svg+xml;charset=utf-8;base64,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)
Import data
draft_unreal <- read.csv("C:/Users/GrandProf/Downloads/Repos_4cleanup/Repositories_AP7/On_GitHub/BinomReg/data/draft_unreal.csv")
Test for Correlation
draft_unreal$initial_prob <- ifelse(draft_unreal$draft==1,0.6,0.4)
draft_unreal$initial_logit <- ifelse(draft_unreal$draft==1,log(0.6/1.6),(1-log(0.6/1.6)))
draft_cormatrix <- cor(draft_unreal)
library(corrplot) # me preferably not ggcorrplot
## corrplot 0.92 loaded
corrplot(cor(draft_unreal))
![](data:image/png;base64,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)
Why Binomial Regression?
- Poor correlation between Bernoulli observations and predictors
- Poor Correlation between derived or calculated probabilities and
predictors
- Poor correlation between the log(OR) derived from initial
probabilities and predictors
- Unable to fit predictor variables to a commonly known models hence
making it difficult to make a judgement call as to IF the predictors
should be included in the binomial regression equation
- Unable to fit the response variable to commonly known models (normal
etc.) hence leading to difficulties in interpreting the results of the
binomial regression
Why the use of a Logit function?
- Constraints on using the probability directly (could lead to
negative values in the probability).
- Other mathematical constraints exists when taking the LN(prob) which
could lead to probability values out of range
- The solution is the Logit link which ensures that probability values
obtained are within range
Logit function
\[\frac{π_i}{1-π_i} = \frac{e^{β_o+β_1 x_i
}}{1 + e^{β_o+β_1 x_i}}\]
\[θ_{i}=β_o+β_1 x_i\]
Hypothesis
Mathematical
- NULL: \(Log(\frac{π_i}{1-π_i}) \neq
0\)
- ALTERNATE: \(Log(\frac{π_i}{1-π_i}) =
0\)
Procedure
- Guess initial coefficients (\(β_o\), \(β_1\) etc.) of \(θ_i\)
- Estimate \(θ_i\)
- Exponentiation of \(θ_i\)
- Calculate the probability of success \(π_i\) vs failure \(1 - π_i\)
- Logit = \(Log(π_i)\) for 1 vs \(Log(1-π_i)\) for 0
- Use a maximization function to determine the final coefficients
- Remember that the actual probability is \(θ_i\)
Procedure in R
m1 <- glm(draft ~ pts + rebs + ast, family = binomial, data = draft_unreal)
summary(m1)
##
## Call:
## glm(formula = draft ~ pts + rebs + ast, family = binomial, data = draft_unreal)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.10071 2.95905 -0.710 0.4777
## pts -0.01430 0.09372 -0.153 0.8788
## rebs 0.61073 0.34982 1.746 0.0808 .
## ast -0.12747 0.22178 -0.575 0.5654
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 26.920 on 19 degrees of freedom
## Residual deviance: 20.431 on 16 degrees of freedom
## AIC: 28.431
##
## Number of Fisher Scoring iterations: 4
coef(m1)[1] #just testing manipulation of the model
## (Intercept)
## -2.100706
significance for rebounds at the 0.1 level (Not real data so one
can assume that points and assist=making teammates better, will get one
into the NBA)
Test the model fit
Null: Model with p parameters fits well enough
Alternate: The model with p parameters does not fit well
Interpretation: p value > 0.05 indicates acceptance of the null hypothesis
plot(density(residuals(m1)))
![](data:image/png;base64,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)
pchisq(20.431, 16, lower = FALSE)
## [1] 0.2014327
Beta Binomial Practice
- This accounts for overdispersion
library(aod)
#m2 <- betabin( draft ~ pts + rebs + ast, ~ pts + rebs + ast, data=draft_unreal)
#summary(m2)
# Unable to run a beta binomial regression with bernoulli observations
Coefficient Determination
- Marginal PMF (a function \(π_i\),
and k=0,1,2…n)
- Joint PMF (a function of the binomial distribution)
- Likelihood function(\(L(β)\) - Like
the PMF but a function of \(β\))
- Log likelihood function (\(l(β)\))
- A non -linear function
- Maximize
- Log likelihood function:
\[\mathbf{l(β)}=\sum_{i=1}^{n} [{k_i}{n_i}
- {n_i}{log(1+e^{n_i})} + log{\binom{n_i}{k_i}}], n_i =
predictors \]
Interpretation
- Interpreted as a normal distribution because the PMF is shaped like
a normal distribution at certain p values
- The shape of the PMF will determine interpretations of the results.
This means it could be interpreted as a geometric distribution based on
the p value
- As a normal distribution, z values are calculated and compared to
standard values \[
z= \frac{β_j-0}{\sqrt{var(β_j)}}\]
Binomial vs Poisson
- Poisson best suited for an infinite number of trials
- Moreover, n should be large and p small when using a Poisson
distribution to approximate a binomial distribution
GLM Pitfalls
- Unable to maximize an already maximized coefficient (shows up when
analyzing groups that are skewed meaning all successes are confined to
one group vs failures in the adjacent group).
- A possible phenomenon in biological analysis (like methylation
coverage)
Conclusion
- This is witnessing the evolution of a Linear regression model to a
Binomial logistic regression model (Naive Bayes).
- The Primed Bayes is the next step in this evolution.