Replacing Missing Values
If there are any missing values in either the X or the Y datasets, these values may need to be estimated. To set settings for identifying missing values and the options for replacing them, use the Options ~ Data ~ Missing Values menu item. A window will be opened that allows you to set the missing value flags. If any of the input data are equal to the value of this flag, they will be treated as missing. In version 10 file formats, this missing value flag is defined in the file, and should not normally be reset. For multiple fields it is possible to have missing value flags specific to each field, but these have to be set in the file using the cpt:missing tag because the menu option will only request a missing value flag that applies to all fields. The program will attempt to replace these missing values unless there are too many missing values for that location or time. What constitutes "too many" missing values can be set using two options:
- Maximum % of missing values: sets the maximum percentage of missing values for that gridpoint/station/series to be included in the analysis. For example, if you have 30 years of station data, and the maximum % of missing values is 10, any station with more than 3 missing values will be excluded. If this maximum percentage is zero, the program will exclude all series with any missing values.
- Maximum % of missing gridpoints/stations/indices: sets the maximum percentage of missing values for that year to be included in the analysis. For example, if you have 50 stations, and the maximum % of missing values is 10, any year with more than 5 missing values will be excluded. If this maximum percentage is zero, the program will exclude all years with any missing values.
If the Y input data are monthly values, and CPT is being asked to calculate seasonal averages/totals, then if any of the individual months in the season are missing the entire month is defined as missing. The maximum %s defined above apply to the number of missing seasonal values rather than to the monthly values.
If the number of missing values is less than the defined maximum, these values will be replaced using the selected method. The mean or the median value can be used, and the program will set all missing values to the mean/median of the non-missing values over the full training period. Note that the missing values are replaced before the cross-validation and so the replacement is not performed using the cross-validated means/medians.
Alternatively, normally-distributed random numbers can be used. These numbers have the same mean and variance as the non-missing values. The random numbers are not currently repeatable (although there are plans to implement repeatable versions in future releases), and so each time the analysis is performed different results may be obtained. As with using the mean or median, the random numbers are assigned before the cross-validation.
Finally, regression estimates of missing values can be obtained using the grid/station/series with the strongest correlation. This "nearest neighbour" is used only if the correlation is greater than zero, otherwise the mean value of the current gridpoint/station/series will be used.
Missing values are normally indicated in the input files using a missing value flag that is specified using the cpt:missing tag, but it is possible to omit entire time steps if the data for all the variables are missing. However, CPT does not permit time steps to be missing indiscriminately. If there are lagged fields, for example, all the lagged fields for the first time step have to be included, even if all the values are set to missing for some of these. In addition, the second time step for the first field/lagged field has to be present so that CPT can determine the date sequencing in the file (except in the "forecast files" containing updated values of the predictors, in which it is possible to have only one time step). CPT assumes that the dates for a given variable will increment either annually or daily, but does not make any assumption about the sequencing between lagged fields.
Given these restrictions, the following examples of sequences of dates are valid:
2001-01 2001-02 2002-01 2003-01 2003-02
In the example above, CPT will identify February as a lagged field with February 2002 missing, as is true in the following example.
2001-03 2001-02 2002-03 2003-03 2003-02
However, the following sequencing is invalid because after identifying February as a lagged field, with January 2002 missing CPT is unable to identify the annual sequencing.
2001-01 2001-02 2002-02 2003-01 2003-02
If all twelve months are present in the file, CPT will read the data as if there were a total of 12 lagged fields, and so if one of the months is missing in the first year CPT will assume there are only 11 lagged fields and will not be able to identify the sequencing when the missing month appears later.