Logistic Regression and Categorical Inputs

btibert · September 2019

How is the Logistic Regression operator determine the category to be left-out from the regression model? In some tools, the first category is left out, but this does not appear to be the case, at least based on alpha-sorting. Any insight on the reference category is chosen? I also attempted to look at the docs for H20, but it's not jumping out to me from this page (though I could be missing something obvious):

http://docs.h2o.ai/h2o/latest-stable/h2o-docs/data-science/glm.html

YYH · September 2019

Hi @btibert,

Good catch! When we are talking about choosing reference (baseline) category of your categorical variable in logistic regression, there is no rule for that.

By default R uses the alpha-numerically first category as the reference category (e.g. “a” with letters, “0” with numbers). We can set a specific reference category by explicitly placing one of the levels first when specifying the levels.

According to the behavior of H2o logistic regression in RapidMiner, I can confirm that the default reference category is chosen by the first appearance in data. The example below gives you the testing process with shuffled data.

Spoiler

<?xml version="1.0" encoding="UTF-8"?><process version="9.4.000-BETA">
  <context>
    <input/>
    <output/>
    <macros/>
  </context>
  <operator activated="true" class="process" compatibility="9.4.000-BETA" expanded="true" name="Process" origin="GENERATED_TUTORIAL">
    <parameter key="logverbosity" value="init"/>
    <parameter key="random_seed" value="2001"/>
    <parameter key="send_mail" value="never"/>
    <parameter key="notification_email" value=""/>
    <parameter key="process_duration_for_mail" value="30"/>
    <parameter key="encoding" value="SYSTEM"/>
    <process expanded="true">
      <operator activated="true" class="retrieve" compatibility="9.4.000-BETA" expanded="true" height="68" name="Retrieve Deals" origin="GENERATED_TUTORIAL" width="90" x="45" y="34">
        <parameter key="repository_entry" value="//Samples/data/Deals"/>
      </operator>
      <operator activated="true" class="h2o:logistic_regression" compatibility="9.3.001" expanded="true" height="124" name="Logistic Regression" origin="GENERATED_TUTORIAL" width="90" x="179" y="34">
        <parameter key="solver" value="AUTO"/>
        <parameter key="reproducible" value="true"/>
        <parameter key="maximum_number_of_threads" value="4"/>
        <parameter key="use_regularization" value="false"/>
        <parameter key="lambda_search" value="false"/>
        <parameter key="number_of_lambdas" value="0"/>
        <parameter key="lambda_min_ratio" value="0.0"/>
        <parameter key="early_stopping" value="true"/>
        <parameter key="stopping_rounds" value="3"/>
        <parameter key="stopping_tolerance" value="0.001"/>
        <parameter key="standardize" value="true"/>
        <parameter key="non-negative_coefficients" value="false"/>
        <parameter key="add_intercept" value="true"/>
        <parameter key="compute_p-values" value="true"/>
        <parameter key="remove_collinear_columns" value="true"/>
        <parameter key="missing_values_handling" value="MeanImputation"/>
        <parameter key="max_iterations" value="0"/>
        <parameter key="max_runtime_seconds" value="0"/>
      </operator>
      <operator activated="true" class="generate_macro" compatibility="9.4.000-BETA" expanded="true" height="82" name="Generate Macro" width="90" x="313" y="136">
        <list key="function_descriptions">
          <parameter key="seed" value="date_millis(date_now())%1000"/>
        </list>
        <description align="center" color="transparent" colored="false" width="126">a &amp;quot;random&amp;quot; seed</description>
      </operator>
      <operator activated="true" class="shuffle" compatibility="9.4.000-BETA" expanded="true" height="82" name="Shuffle" width="90" x="447" y="238">
        <parameter key="use_local_random_seed" value="true"/>
        <parameter key="local_random_seed" value="%{seed}"/>
      </operator>
      <operator activated="true" class="write_csv" compatibility="9.4.000-BETA" expanded="true" height="82" name="Write CSV" width="90" x="581" y="136">
        <parameter key="column_separator" value=";"/>
        <parameter key="write_attribute_names" value="true"/>
        <parameter key="quote_nominal_values" value="true"/>
        <parameter key="format_date_attributes" value="true"/>
        <parameter key="append_to_file" value="false"/>
        <parameter key="encoding" value="SYSTEM"/>
      </operator>
      <operator activated="true" class="read_csv" compatibility="9.4.000-BETA" expanded="true" height="68" name="Read CSV" width="90" x="715" y="136">
        <parameter key="column_separators" value=";"/>
        <parameter key="trim_lines" value="false"/>
        <parameter key="use_quotes" value="true"/>
        <parameter key="quotes_character" value="&quot;"/>
        <parameter key="escape_character" value="\"/>
        <parameter key="skip_comments" value="false"/>
        <parameter key="comment_characters" value="#"/>
        <parameter key="starting_row" value="1"/>
        <parameter key="parse_numbers" value="true"/>
        <parameter key="decimal_character" value="."/>
        <parameter key="grouped_digits" value="false"/>
        <parameter key="grouping_character" value=","/>
        <parameter key="infinity_representation" value=""/>
        <parameter key="date_format" value=""/>
        <parameter key="first_row_as_names" value="true"/>
        <list key="annotations"/>
        <parameter key="time_zone" value="SYSTEM"/>
        <parameter key="locale" value="English (United States)"/>
        <parameter key="encoding" value="SYSTEM"/>
        <parameter key="read_all_values_as_polynominal" value="false"/>
        <list key="data_set_meta_data_information"/>
        <parameter key="read_not_matching_values_as_missings" value="true"/>
        <parameter key="datamanagement" value="double_array"/>
        <parameter key="data_management" value="auto"/>
      </operator>
      <operator activated="true" class="set_role" compatibility="9.4.000-BETA" expanded="true" height="82" name="shuffled data" width="90" x="849" y="136">
        <parameter key="attribute_name" value="Future Customer"/>
        <parameter key="target_role" value="label"/>
        <list key="set_additional_roles"/>
      </operator>
      <operator activated="true" class="h2o:logistic_regression" compatibility="9.3.001" expanded="true" height="124" name="Logistic Regression shuffled" origin="GENERATED_TUTORIAL" width="90" x="983" y="136">
        <parameter key="solver" value="AUTO"/>
        <parameter key="reproducible" value="true"/>
        <parameter key="maximum_number_of_threads" value="4"/>
        <parameter key="use_regularization" value="false"/>
        <parameter key="lambda_search" value="false"/>
        <parameter key="number_of_lambdas" value="0"/>
        <parameter key="lambda_min_ratio" value="0.0"/>
        <parameter key="early_stopping" value="true"/>
        <parameter key="stopping_rounds" value="3"/>
        <parameter key="stopping_tolerance" value="0.001"/>
        <parameter key="standardize" value="true"/>
        <parameter key="non-negative_coefficients" value="false"/>
        <parameter key="add_intercept" value="true"/>
        <parameter key="compute_p-values" value="true"/>
        <parameter key="remove_collinear_columns" value="true"/>
        <parameter key="missing_values_handling" value="MeanImputation"/>
        <parameter key="max_iterations" value="0"/>
        <parameter key="max_runtime_seconds" value="0"/>
      </operator>
      <connect from_op="Retrieve Deals" from_port="output" to_op="Logistic Regression" to_port="training set"/>
      <connect from_op="Logistic Regression" from_port="model" to_port="result 1"/>
      <connect from_op="Logistic Regression" from_port="exampleSet" to_op="Generate Macro" to_port="through 1"/>
      <connect from_op="Generate Macro" from_port="through 1" to_op="Shuffle" to_port="example set input"/>
      <connect from_op="Shuffle" from_port="example set output" to_op="Write CSV" to_port="input"/>
      <connect from_op="Shuffle" from_port="original" to_port="result 4"/>
      <connect from_op="Write CSV" from_port="file" to_op="Read CSV" to_port="file"/>
      <connect from_op="Read CSV" from_port="output" to_op="shuffled data" to_port="example set input"/>
      <connect from_op="shuffled data" from_port="example set output" to_op="Logistic Regression shuffled" to_port="training set"/>
      <connect from_op="Logistic Regression shuffled" from_port="model" to_port="result 2"/>
      <connect from_op="Logistic Regression shuffled" from_port="exampleSet" to_port="result 3"/>
      <portSpacing port="source_input 1" spacing="0"/>
      <portSpacing port="sink_result 1" spacing="0"/>
      <portSpacing port="sink_result 2" spacing="63"/>
      <portSpacing port="sink_result 3" spacing="21"/>
      <portSpacing port="sink_result 4" spacing="84"/>
      <portSpacing port="sink_result 5" spacing="21"/>
    </process>
  </operator>
</process>

Cheers,
YY

YYH · September 2019

Hi @btibert,

Good catch! When we are talking about choosing reference (baseline) category of your categorical variable in logistic regression, there is no rule for that.

By default R uses the alpha-numerically first category as the reference category (e.g. “a” with letters, “0” with numbers). We can set a specific reference category by explicitly placing one of the levels first when specifying the levels.

According to the behavior of H2o logistic regression in RapidMiner, I can confirm that the default reference category is chosen by the first appearance in data. The example below gives you the testing process with shuffled data.

Spoiler

<?xml version="1.0" encoding="UTF-8"?><process version="9.4.000-BETA">
  <context>
    <input/>
    <output/>
    <macros/>
  </context>
  <operator activated="true" class="process" compatibility="9.4.000-BETA" expanded="true" name="Process" origin="GENERATED_TUTORIAL">
    <parameter key="logverbosity" value="init"/>
    <parameter key="random_seed" value="2001"/>
    <parameter key="send_mail" value="never"/>
    <parameter key="notification_email" value=""/>
    <parameter key="process_duration_for_mail" value="30"/>
    <parameter key="encoding" value="SYSTEM"/>
    <process expanded="true">
      <operator activated="true" class="retrieve" compatibility="9.4.000-BETA" expanded="true" height="68" name="Retrieve Deals" origin="GENERATED_TUTORIAL" width="90" x="45" y="34">
        <parameter key="repository_entry" value="//Samples/data/Deals"/>
      </operator>
      <operator activated="true" class="h2o:logistic_regression" compatibility="9.3.001" expanded="true" height="124" name="Logistic Regression" origin="GENERATED_TUTORIAL" width="90" x="179" y="34">
        <parameter key="solver" value="AUTO"/>
        <parameter key="reproducible" value="true"/>
        <parameter key="maximum_number_of_threads" value="4"/>
        <parameter key="use_regularization" value="false"/>
        <parameter key="lambda_search" value="false"/>
        <parameter key="number_of_lambdas" value="0"/>
        <parameter key="lambda_min_ratio" value="0.0"/>
        <parameter key="early_stopping" value="true"/>
        <parameter key="stopping_rounds" value="3"/>
        <parameter key="stopping_tolerance" value="0.001"/>
        <parameter key="standardize" value="true"/>
        <parameter key="non-negative_coefficients" value="false"/>
        <parameter key="add_intercept" value="true"/>
        <parameter key="compute_p-values" value="true"/>
        <parameter key="remove_collinear_columns" value="true"/>
        <parameter key="missing_values_handling" value="MeanImputation"/>
        <parameter key="max_iterations" value="0"/>
        <parameter key="max_runtime_seconds" value="0"/>
      </operator>
      <operator activated="true" class="generate_macro" compatibility="9.4.000-BETA" expanded="true" height="82" name="Generate Macro" width="90" x="313" y="136">
        <list key="function_descriptions">
          <parameter key="seed" value="date_millis(date_now())%1000"/>
        </list>
        <description align="center" color="transparent" colored="false" width="126">a &amp;quot;random&amp;quot; seed</description>
      </operator>
      <operator activated="true" class="shuffle" compatibility="9.4.000-BETA" expanded="true" height="82" name="Shuffle" width="90" x="447" y="238">
        <parameter key="use_local_random_seed" value="true"/>
        <parameter key="local_random_seed" value="%{seed}"/>
      </operator>
      <operator activated="true" class="write_csv" compatibility="9.4.000-BETA" expanded="true" height="82" name="Write CSV" width="90" x="581" y="136">
        <parameter key="column_separator" value=";"/>
        <parameter key="write_attribute_names" value="true"/>
        <parameter key="quote_nominal_values" value="true"/>
        <parameter key="format_date_attributes" value="true"/>
        <parameter key="append_to_file" value="false"/>
        <parameter key="encoding" value="SYSTEM"/>
      </operator>
      <operator activated="true" class="read_csv" compatibility="9.4.000-BETA" expanded="true" height="68" name="Read CSV" width="90" x="715" y="136">
        <parameter key="column_separators" value=";"/>
        <parameter key="trim_lines" value="false"/>
        <parameter key="use_quotes" value="true"/>
        <parameter key="quotes_character" value="&quot;"/>
        <parameter key="escape_character" value="\"/>
        <parameter key="skip_comments" value="false"/>
        <parameter key="comment_characters" value="#"/>
        <parameter key="starting_row" value="1"/>
        <parameter key="parse_numbers" value="true"/>
        <parameter key="decimal_character" value="."/>
        <parameter key="grouped_digits" value="false"/>
        <parameter key="grouping_character" value=","/>
        <parameter key="infinity_representation" value=""/>
        <parameter key="date_format" value=""/>
        <parameter key="first_row_as_names" value="true"/>
        <list key="annotations"/>
        <parameter key="time_zone" value="SYSTEM"/>
        <parameter key="locale" value="English (United States)"/>
        <parameter key="encoding" value="SYSTEM"/>
        <parameter key="read_all_values_as_polynominal" value="false"/>
        <list key="data_set_meta_data_information"/>
        <parameter key="read_not_matching_values_as_missings" value="true"/>
        <parameter key="datamanagement" value="double_array"/>
        <parameter key="data_management" value="auto"/>
      </operator>
      <operator activated="true" class="set_role" compatibility="9.4.000-BETA" expanded="true" height="82" name="shuffled data" width="90" x="849" y="136">
        <parameter key="attribute_name" value="Future Customer"/>
        <parameter key="target_role" value="label"/>
        <list key="set_additional_roles"/>
      </operator>
      <operator activated="true" class="h2o:logistic_regression" compatibility="9.3.001" expanded="true" height="124" name="Logistic Regression shuffled" origin="GENERATED_TUTORIAL" width="90" x="983" y="136">
        <parameter key="solver" value="AUTO"/>
        <parameter key="reproducible" value="true"/>
        <parameter key="maximum_number_of_threads" value="4"/>
        <parameter key="use_regularization" value="false"/>
        <parameter key="lambda_search" value="false"/>
        <parameter key="number_of_lambdas" value="0"/>
        <parameter key="lambda_min_ratio" value="0.0"/>
        <parameter key="early_stopping" value="true"/>
        <parameter key="stopping_rounds" value="3"/>
        <parameter key="stopping_tolerance" value="0.001"/>
        <parameter key="standardize" value="true"/>
        <parameter key="non-negative_coefficients" value="false"/>
        <parameter key="add_intercept" value="true"/>
        <parameter key="compute_p-values" value="true"/>
        <parameter key="remove_collinear_columns" value="true"/>
        <parameter key="missing_values_handling" value="MeanImputation"/>
        <parameter key="max_iterations" value="0"/>
        <parameter key="max_runtime_seconds" value="0"/>
      </operator>
      <connect from_op="Retrieve Deals" from_port="output" to_op="Logistic Regression" to_port="training set"/>
      <connect from_op="Logistic Regression" from_port="model" to_port="result 1"/>
      <connect from_op="Logistic Regression" from_port="exampleSet" to_op="Generate Macro" to_port="through 1"/>
      <connect from_op="Generate Macro" from_port="through 1" to_op="Shuffle" to_port="example set input"/>
      <connect from_op="Shuffle" from_port="example set output" to_op="Write CSV" to_port="input"/>
      <connect from_op="Shuffle" from_port="original" to_port="result 4"/>
      <connect from_op="Write CSV" from_port="file" to_op="Read CSV" to_port="file"/>
      <connect from_op="Read CSV" from_port="output" to_op="shuffled data" to_port="example set input"/>
      <connect from_op="shuffled data" from_port="example set output" to_op="Logistic Regression shuffled" to_port="training set"/>
      <connect from_op="Logistic Regression shuffled" from_port="model" to_port="result 2"/>
      <connect from_op="Logistic Regression shuffled" from_port="exampleSet" to_port="result 3"/>
      <portSpacing port="source_input 1" spacing="0"/>
      <portSpacing port="sink_result 1" spacing="0"/>
      <portSpacing port="sink_result 2" spacing="63"/>
      <portSpacing port="sink_result 3" spacing="21"/>
      <portSpacing port="sink_result 4" spacing="84"/>
      <portSpacing port="sink_result 5" spacing="21"/>
    </process>
  </operator>
</process>

Cheers,
YY

btibert · September 2019

Got it, thank you.

YYH · September 2019

Always welcome!

Logistic Regression and Categorical Inputs

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