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39 Cards in this Set
- Front
- Back
- 3rd side (hint)
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What are the two modeling choices for GLM? |
Distribution and Link functions |
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Any distribution belonging to what family can be chosen? |
The linear exponential function |
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The mean u for any distribution belonging to the linear exponential function is embedded in its what? |
Probability function |
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What function establishes the relationship between u and the predictors (the function g where g(u) = x transpose times B |
Link function |
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What combo gives us MLR? |
Normal distribution + identity link |
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MLR assumes that the target follows what distribution? |
The Normal distribution |
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How does GLM relax some of MLR’s assumptions? |
We can choose from any member of the linear exponential family |
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5 example distributions that belong to the linear exponential family |
Binomial (fixed trials) Gaussian Gamma Inverse Gaussian Poisson |
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The distribution we choose relates to what? |
The random component |
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The link function we choose relates to what? |
The systematic component |
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If the target is continuous, it should be paired with one of what 3 distributions? |
Normal, gamma, or inverse Gaussian |
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A binary target should be paired with what distribution? |
Bernoulli |
Bernoulli is made of successes and failures- two options like binary has |
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A count target should be paired with what distribution? |
Poisson |
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What is a link function? |
It links the mean target with predictors |
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Identity link g(u) |
u |
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Log link g(u) |
ln(u) |
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Logit link g(u) |
ln(u/1-u) |
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The identity link is best for what values of u? |
Real-valued u |
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The log link is best for what values of u? |
Positive valued u |
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Logit link is best for what values of u |
Between 0 and 1 |
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How are the betas found for GLM? |
Maximum likelihood estimation (MLE) finds the b’s that maximize the log-likelihood |
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The first important GLM metric |
Maximized log-likelihoods |
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What is a maximized log-likelihood? |
The log-likelihood evaluated at the maximum likelihood estimates |
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What do we call the maximized log-likelihood with the least number of betas? |
l-null |
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What does we call the maximized log likelihood of the model with the most number of betas? |
l-sat |
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l-sat has the most what? |
Flexibility |
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What does the maximized log-likelihood measure? |
The likelihood that the model and its estimated parameters match the data |
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Another meaning of what the maximized log likelihood measures? |
How close the predicted target is to the target |
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So do we want a higher or lower maximized log-likelihood? |
Higher |
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But we don’t want the maximized log likelihood to be too high to avoid what? |
Overfitting |
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What is a second metric for GLM? |
Deviance |
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Generally, a good fit has a big or small deviance? |
small |
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What is the estimated variance of the target for observation I called? |
Pearson chi-square statistic |
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Do we prefer higher or lower values for deviance? |
lower |
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As p increases, what happens to the training RMSE? |
Decreases |
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As p increases, what happens to the training deviance? |
Decreases |
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What happens to the Pearson chi-square statistic as p increases? |
Decreases |
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What happens to the maximized log likelihood as p increases? |
Increases |
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To test the value of a beta parameter in GLM, we perform one of what two tests? |
A z or t test |
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