Quantile Regression - Data360_Analyze - Latest

Models data using quantile regression allowing identification of data trends for conditional quantiles of a response variable distribution.

This node uses the embedded R engine to model the relationship between a dependent (response) variable and one or more independent (explanatory) variables. The node fits the data using a quantile regression model.

Quantile regression provides a means to flexibly model data with heterogeneous conditional distributions. Typically these types of distributions occur in the study of ecology, life sciences and economics, where the relationship with the conditional mean of the dependent variable is different to the relationship across the quantiles of the dependent variable. Linear Regression uses Ordinary Least Squares (OLS) to model the relationship between the independent variables and the conditional mean of the dependent variable but may not provide an accurate model where there is a heterogeneous conditional distribution. Under these conditions Quantile regression can provide a more comprehensive picture of the effect of the independent variables across the spectrum of the dependent variable.

Quantile regression can also be used to model the effects at the median (i.e. the 0.50 quantile) which can be more robust to the impact of outliers on the regression.

The node accepts the data to be analyzed on its input pin. The ModelName can be specified. If it is not set, a default name "QuantileReg" is used for the generated model.

The model to be analyzed can be defined by configuring the DependentVariable property and IndependentVariables property. Alternatively, the model can be defined by specifying the ModelFormula property. The ModelFormula property can be a Literal value or obtained from a field on the node's optional second input pin.

If categorical independent variables are being used in the model, please ensure that there are a sufficient number of observations in each category of the variable. Otherwise the node may not be able to process the data correctly, resulting in an error.

By default, the following values apply to the model:

• Quantile level is 0.50.
• Estimation method is Barrowdale and Roberts.

The quantile levels to be used in the regression can be specified as a Literal value or obtained from a field on the node's optional second input pin.

The weights to be used in a weighted OLS model can be specified as a Literal value or obtained from a field on the node's optional second input pin.

The model constant can be included or omitted from the model.

The generated model can optionally be saved to a file. The configured ModelName is used as part of the filename of the file that contains the serialized model. The location where the saved model is to be written can also be specified. If not set, a default location is used. The node's exception behavior can be configured to specify whether an existing file will be overwritten.

Hypothesis statistics for the quantile coefficients can optionally be output.

There is a choice of estimation method to be used in the quantile regression. The choice of estimation method should take into consideration the size of the data set being analyzed as some methods are less efficient for large data sets.

You can specify the assumption to be made on variable distribution - i.e. whether or not the data are "independent and identically distributed" (iid).

The node can be configured to remove input data records where a record has a missing (NULL) value. By default, records with missing values are not excluded from the model and will generate an error.

When run, the node provides a summary of the model created at its Summary pin. The information provided depends on the number of quantiles (taus) that were analyzed in the model. By default, only one quantile level i.e. 0.50 is analyzed.

If one quantile (tau) was analyzed, the Summary pin includes information on:

• The call used to generate the model.
• The quantile level.
• The estimates for the coefficients of the independent variables used in the model and the estimate of the intercept.
• If the node was not configured to output the model test statistics, the upper and lower confidence bounds for the coefficients (for the 95% confidence interval).
• If the node was configured to output the model test statistics, the summary instead includes information on the Standard Error, the t-value and the p-value.
• The Degrees of Freedom (DF) together with the Log Likelihood (LogLik), the Akaike information criterion (AIC) and the value of objective function at the solution (rho).

If more than one quantile (tau) was analyzed, the Summary pin includes the following information for each quantile level (tau):

• The call used to generate the model.
• The quantile level.
• The estimates for the coefficients of the independent variables used in the model and the estimate of the intercept at the specified quantile level.
• If the node was not configured to output the model test statistics, the upper and lower confidence bounds for the 95% confidence interval at the specified quantile level.
• If the node was configured to output the model test statistics, the summary instead includes information on the Standard Error, the t-value and the p-value for each quantile level (tau).
• The Degrees of Freedom; together with the Log Likelihood (LogLik), the Akaike information criterion (AIC) and the value of objective function at the solution (rho) for each quantile level (tau).

If the node is configured to output the serialized model to a file, the Summary pin also includes the file path to the file that contains the serialized model.

The Residuals pin contains, for each observation and quantile level, the value of the residual (error) - i.e. the difference between each of the observations in the input data and the fitted values derived by the model at each quantile level. The pin also contains a record ID field where the ID aligns with the position of the record in the input data set (i.e. it will be non-contiguous where records have been omitted due to them containing NULL values).

The information provided on the Coefficients pin depends on the number of quantiles (taus) that were analyzed in the model and whether model hypothesis test statistics were to be output. By default, hypothesis test statistics are not output.

If one quantile (tau) was analyzed and test statistics are not output, the Coefficients pin contains multiple types of records. For the quantile level, the following records are output:

• The quantile regression coefficient value.
• The upper confidence bound for the quantile regression coefficient.
• The lower confidence bound for the quantile regression coefficient.
• The Ordinary Least Squares (OLS) coefficient from the corresponding Linear Regression model.
• The upper confidence bound for the OLS coefficient.
• The lower confidence bound for the OLS coefficient.

Each record contains the following fields: the quantile level, the record type, and the coefficient/bound value for each independent variable and the intercept.

If one quantile (tau) was analyzed and test statistics are output, the 'Coefficients' pin contains multiple types of records. For the quantile level, the following records are output:

• The quantile regression coefficient value.
• The standard error value.
• The t-test value.
• The p-value.

Each record contains the following fields: the quantile level, the record type, and the coefficient/test statistic value for each independent variable and the intercept.

If more than one quantile (tau) was analyzed and test statistics are not output, the "Coefficients" pin contains multiple types of records for each quantile level. For a particular quantile level, the following records are output:

• The quantile regression coefficient value.
• The upper confidence bound for the quantile regression coefficient.
• The lower confidence bound for the quantile regression coefficient.

Each record contains the following fields: the quantile level, the record type, and the coefficient/confidence bound value for each independent variable and the intercept.If more than one quantile (tau) was analyzed and test statistics are output, the 'Coefficients' pin contains multiple types of records for each quantile level. For a particular quantile level, the following records are output:

• The quantile regression coefficient value.
• The standard error value.
• The t-test value.
• The p-value.

Each record contains the following fields: the quantile level, the record type, and the coefficient/test statistic value for each independent variable and the intercept.

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