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Marco Oesting
2023-10-09 16:14:00 +02:00
parent 08951f610d
commit 39892ad1c1
1 changed files with 32 additions and 30 deletions
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material/3_wed/regression/MultipleRegressionBasics.qmd
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@@ -232,31 +232,33 @@ $$
For the models above, these are: For the models above, these are:
+--------------+---------------------+--------------------+ +---------------+-------------------+------------------+
| Type of Data | Distribution Family | Link Function | | Type of Data | Distribution | Link Function |
+==============+=====================+====================+ | | Family | |
| continuous | Normal | identity: | +===============+===================+==================+
| | | | | continuous | Normal | identity: |
| | | $$ | | | | |
| | | g(x)=x | | | | $$ |
| | | $$ | | | | g(x)=x |
+--------------+---------------------+--------------------+ | | | $$ |
| count | Poisson | log: | +---------------+-------------------+------------------+
| | | | | count | Poisson | log: |
| | | $$ | | | | |
| | | g(x) = \log(x) | | | | $$ |
| | | $$ | | | | g(x) = \log(x) |
+--------------+---------------------+--------------------+ | | | $$ |
| binary | Bernoulli | logit: | +---------------+-------------------+------------------+
| | | | | binary | Bernoulli | logit: |
| | | $$ | | | | |
| | | g(x) = \log\left | | | | $$ |
| | | ( | | | | g(x) = \log\left |
| | | \ | | | | ( |
| | | f | | | | \ |
| | | rac{x}{1-x}\right) | | | | f |
| | | $$ | | | | ra |
+--------------+---------------------+--------------------+ | | | c{x}{1-x}\right) |
| | | $$ |
+---------------+-------------------+------------------+
In general, the parameter vector $\beta$ is estimated via maximizing the In general, the parameter vector $\beta$ is estimated via maximizing the
likelihood, i.e., likelihood, i.e.,