Rank(x, i) returns an array of the rank values of «x» across index «i». The lowest value in «x» has a rank value of 1, the next-lowest has a rank of 2, and so on. «i» is optional if «x» is one-dimensional. If «i» is omitted when «x» has more than one dimension, the innermost dimension is ranked. Since you, as a modeler, have little control over which dimension is the inner dimension, you should always specify «i» unless you can guarantee that «x» will always be one-dimensional.
In the example below, the rank of a list is evaluated. Thus, the second parameter «i» is unnecessary. A one-dimensional array is returned, indexed by
Years. This array has a value of 1 where
Year has the smallest value, a value of 2 where
Year has the second smallest value, and so on.
Years ▶ 2005 2006 2007 2008 2009 1 2 3 4 5
In the example below, the Rank function works with a multidimensional table. Each car type is given a rank for each year, with the cheapest car in that year given 1 and the most expensive car in that year given 3.
Rank(Car_prices, Car_type) →
Years ▶ Car_Type ▼ 2005 2006 2007 2008 2009 VW 1 1 1 1 1 Honda 2 2 2 2 2 BMW 3 3 3 3 3
If two (or n) values are equal, they receive the same rank and the next higher value receives a rank 2 (or n) higher. You can use an optional parameter, «Type», to control which rank is assigned to equal values. By default, the lowest rank is used, equivalent to
Rank(x, i, Type: -1) Alternatively,
Rank(x, i, Type: 0) uses the mid-rank and
Rank(x, i, Type:1) uses the upper-rank.
Rank(x, i, Type: Null) assigns a unique rank to every element (the numbers 1 thru n) in which tied elements may have different ranks.
The example below shows how the Rank function handles duplicate values.
Rank(NumRepairs, CarNum, Type: RankType) →
CarNum ▶ Rank Type ▼ 1 2 3 4 5 6 7 -1 7 2 6 2 2 1 2 0 7 3.5 6 3.5 3.5 1 3.5 1 7 5 6 5 5 1 5 Null 7 2 6 3 4 1 6
Type = -1, lowest rank for the duplicate value is returned.
Type = 0, mid rank value of the duplicates is returned.
Type = 1, highest rank for the duplicate value is returned.
Type = Null, unique rank value is returned.
When ranking text values, Rank treats text values as being case-sensitive with capital letters preceding lower case letters. So, for example,
Zebra gets a lower rank than
apply. In Analytica 4.2 or later, you can supply the optional parameter
Rank(x, i, caseInsensitive: true)
Case sensitivity only impacts text values.
You can easily reverse the rank of numeric arrays, where the largest numbers receive the lowest ranks, by simply using
For arrays containing text values, in Analytica 4.2 and later you can specify the optional
descending: true parameter
Rank(x, i, descending: true)
which uses the reverse rank order for text as well as numbers.
When two values are tied for the same rank, a second array can be used to break the tie. This is referred to as a multi-key sort (or multi-key rank). The first array is the primary key, the next is the secondary key, and so on. Analytica 4.2's Rank function support multi-key ranking. To use, your keys must all share a common index, «i». You must then introduce a new index, «keyIndex», to dimension your keys (any number of keys may be used), and bundle your keys into a 2-D array indexed by «i» and «keyIndex». For example, the following ranks by
age, then, in case of a tie, by
Index keyIndex := ['age', 'gender'];
Rank(Array(keyIndex, [age, gender]), i, keyIndex)
This example shows how multi-key rank can be calculated by passing the optional «keyIndex» parameter to the rank function. The rank of the cars by the number of maintenance events using index
maintType as the «keyIndex» is returned.
Rank(NumMaintEvents, CarNum, keyIndex: maintType: RankType) →
CarNum ▶ MaintType ▼ 1 2 3 4 5 6 7 Repair 10 4 9 4 4 1 4 Scheduled 0 2 0 1 2 0 5 Tires 0 2 0 0 1 0 0
Treatment of NaN and Null values
When a NaN value occurs in your data, Rank can either pass it through as a NaN or assign it a numeric rank. The optional «passNaNs» parameter controls this behavior. The special value NaN indicates an indeterminate real number, which in theory cannot be compared to other numbers, so the ordering of NaN by Rank doesn't actually make logical sense. By passing NaN values through without assigning an actual rank, you may catch errors in your model that lead to the introduction of the NaN value in the first place, since these errors continue to be propagated to your results. This is often a desirable property.
Rank(x, i, passNaNs: true).
Null values are sometimes used for missing data, and in these cases can also be passed using the
passNulls: true parameter. When this is not specified, null values are assigned a rank (with Null coming after all numeric values).