# modelAccuracy

Compute RMSE of predicted and observed PDs on grouped data

Since R2020b

`modelAccuracy` is renamed to `modelCalibration`. `modelAccuracy` is not recommended. Use `modelCalibration` instead.

## Syntax

``AccMeasure = modelAccuracy(pdModel,data,GroupBy)``
``[AccMeasure,AccData] = modelAccuracy(___,Name,Value)``

## Description

````AccMeasure = modelAccuracy(pdModel,data,GroupBy)` computes the root mean squared error (RMSE) of the observed compared to the predicted probabilities of default (PD). `GroupBy` is required and can be any column in the `data` input (not necessarily a model variable). The `modelAccuracy` function computes the observed PD as the default rate of each group and the predicted PD as the average PD for each group. `modelAccuracy` supports comparison against a reference model.```
````[AccMeasure,AccData] = modelAccuracy(___,Name,Value)` specifies options using one or more name-value pair arguments in addition to the input arguments in the previous syntax.```

## Input Arguments

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Probability of default model, specified as a previously created `Logistic`, `Probit`, or `Cox` object using `fitLifetimePDModel`. Alternatively, you can create a custom probability of default model using `customLifetimePDModel`.

Data Types: `object`

Data, specified as a `NumRows`-by-`NumCols` table with projected predictor values to make lifetime predictions. The predictor names and data types must be consistent with the underlying model.

Data Types: `table`

Name of column in the `data` input used to group the data, specified as a string or character vector. `GroupBy` does not have to be a model variable name. For each group designated by `GroupBy`, the `modelAccuracy` function computes the observed default rates and average predicted PDs are computed to measure the RMSE.

Data Types: `string` | `char`

### Name-Value Arguments

Specify optional pairs of arguments as `Name1=Value1,...,NameN=ValueN`, where `Name` is the argument name and `Value` is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose `Name` in quotes.

Example: ```[AccMeasure,AccData] = modelAccuracy(pdModel,data(Ind,:),'GroupBy',["YOB","ScoreGroup"],'DataID',"DataSetChoice")```

Data set identifier, specified as the comma-separated pair consisting of `'DataID'` and a character vector or string. `DataID` is included in the `modelAccuracy` output for reporting purposes.

Data Types: `char` | `string`

Conditional PD values predicted for `data` by the reference model, specified as the comma-separated pair consisting of `'ReferencePD'` and a `NumRows`-by-`1` numeric vector. The functions reports the `modelAccuracy` output information for both the `pdModel` object and the reference model.

Data Types: `double`

Identifier for the reference model, specified as the comma-separated pair consisting of `'ReferenceID'` and a character vector or string. `ReferenceID` is used in the `modelAccuracy` output for reporting purposes.

Data Types: `char` | `string`

## Output Arguments

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Accuracy measure, returned as a table.

RMSE values, returned as a single-column `'RMSE'` table. The table has one row if only the `pdModel` accuracy is measured and it has two rows if reference model information is given. The row names of `AccMeasure` report the model IDs, grouping variables, and data ID.

Note

The reported RMSE values depend on the grouping variable for the required `GroupBy` argument.

Accuracy data, returned as a table.

Observed and predicted PD values for each group, returned as a table. The reported observed PD values correspond to the observed default rate for each group. The reported predicted PD values are the average PD values predicted by the `pdModel` object for each group, and similarly for the reference model. The `modelAccuracy` function stacks the PD data, placing the observed values for all groups first, then the predicted PDs for the `pdModel`, and then the predicted PDs for the reference model, if given.

The column `'ModelID'` identifies which rows correspond to the observed PD, `pdModel`, or reference model. The table also has one column for each grouping variable showing the unique combinations of grouping values. The `'PD'` column of `AccData` is a the PD data. The last column of `AccData` is a `'GroupCount'` column with the group counts data.

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### Model Accuracy

Model accuracy measures the accuracy of the predicted probability of default (PD) values.

To measure model accuracy, also called model calibration, you must compare the predicted PD values to the observed default rates. For example, if a group of customers is predicted to have an average PD of 5%, then is the observed default rate for that group close to 5%?

The `modelAccuracy` function requires a grouping variable to compute average predicted PD values within each group and the average observed default rate also within each group. `modelAccuracy` uses the root mean squared error (RMSE) to measure the deviations between the observed and predicted values across groups. For example, the grouping variable could be the calendar year, so that rows corresponding to the same calendar year are grouped together. Then, for each year the software computes the observed default rate and the average predicted PD. The `modelAccuracy` function then applies the RMSE formula to obtain a single measure of the prediction error across all years in the sample.

Suppose there are N observations in the data set, and there are M groups G1,...,GM. The default rate for group Gi is

`$D{R}_{i}=\frac{{D}_{i}}{{N}_{i}}$`

where:

Di is the number of defaults observed in group Gi.

Ni is the number of observations in group Gi.

The average predicted probability of default PDi for group Gi is

`$P{D}_{i}=\frac{1}{{N}_{i}}{\sum }_{j\in {G}_{i}}PD\left(j\right)$`

where PD(j) is the probability of default for observation j. In other words, this is the average of the predicted PDs within group Gi.

Therefore, the RMSE is computed as

`$RMSE\text{​}=\sqrt{{\sum }_{i=1}^{M}\left(\frac{{N}_{i}}{N}\right){\left(D{R}_{i}-P{D}_{i}\right)}^{2}}$`

The RMSE, as defined, depends on the selected grouping variable. For example, grouping by calendar year and grouping by years-on-books might result in different RSME values.

Use `modelAccuracyPlot` to visualize observed default rates and predicted PD values on grouped data.

## References

[1] Baesens, Bart, Daniel Roesch, and Harald Scheule. Credit Risk Analytics: Measurement Techniques, Applications, and Examples in SAS. Wiley, 2016.

[2] Bellini, Tiziano. IFRS 9 and CECL Credit Risk Modelling and Validation: A Practical Guide with Examples Worked in R and SAS. San Diego, CA: Elsevier, 2019.

[3] Breeden, Joseph. Living with CECL: The Modeling Dictionary. Santa Fe, NM: Prescient Models LLC, 2018.

[4] Roesch, Daniel and Harald Scheule. Deep Credit Risk: Machine Learning with Python. Independently published, 2020.

## Version History

Introduced in R2020b

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