# Logistic (3.6) (legacy)

Class for building and using a multinomial logistic regression model with a ridge estimator. There are some modifications, however, compared to the paper of leCessie and van Houwelingen(1992): If there are k classes for n instances with m attributes, the parameter matrix B to be calculated will be an m*(k-1) matrix. The probability for class j with the exception of the last class is Pj(Xi) = exp(XiBj)/((sum[j=1..(k-1)]exp(Xi*Bj))+1) The last class has probability 1-(sum[j=1..(k-1)]Pj(Xi)) = 1/((sum[j=1..(k-1)]exp(Xi*Bj))+1) The (negative) multinomial log-likelihood is thus: L = -sum[i=1..n]{ sum[j=1..(k-1)](Yij * ln(Pj(Xi))) +(1 - (sum[j=1..(k-1)]Yij)) * ln(1 - sum[j=1..(k-1)]Pj(Xi)) } + ridge * (B^2) In order to find the matrix B for which L is minimised, a Quasi-Newton Method is used to search for the optimized values of the m*(k-1) variables. Note that before we use the optimization procedure, we 'squeeze' the matrix B into a m*(k-1) vector. For details of the optimization procedure, please check weka.core.Optimization class. Although original Logistic Regression does not deal with instance weights, we modify the algorithm a little bit to handle the instance weights. For more information see: le Cessie, S., van Houwelingen, J.C. (1992). Ridge Estimators in Logistic Regression. Applied Statistics. 41(1):191-201. Note: Missing values are replaced using a ReplaceMissingValuesFilter, and nominal attributes are transformed into numeric attributes using a NominalToBinaryFilter.

(based on WEKA 3.6)

For further options, click the 'More' - button in the dialog.

All weka dialogs have a panel where you can specify classifier-specific parameters.

## Options

Class column
Choose the column that contains the target variable.
Preliminary Attribute Check

The Preliminary Attribute Check tests the underlying classifier against the DataTable specification at the inport of the node. Columns that are compatible with the classifier are marked with a green 'ok'. Columns which are potentially not compatible are assigned a red error message.

Important: If a column is marked as 'incompatible', it does not necessarily mean that the classifier cannot be executed! Sometimes, the error message 'Cannot handle String class' simply means that no nominal values are available (yet). This may change during execution of the predecessor nodes.

Capabilities: [Nominal attributes, Binary attributes, Unary attributes, Empty nominal attributes, Numeric attributes, Date attributes, Missing values, Nominal class, Binary class, Missing class values] Dependencies: [] min # Instance: 1

Classifier Options

D: Turn on debugging output.

R: Set the ridge in the log-likelihood.

M: Set the maximum number of iterations (default -1, until convergence).

Training data

## Output Ports

Trained classifier

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## Views

Weka Node View
Each Weka node provides a summary view that provides information about the classification. If the test data contains a class column, an evaluation is generated.

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## Developers

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