Rank

Rank(x, i)

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.

Examples

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.

Rank(Years) →

	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 ▶
	2005	2006	2007	2008	2009
VW	1	1	1	1	1
Honda	2	2	2	2	2
BMW	3	3	3	3	3

Optional Parameters

Type

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.

	Years ▶
	2005	2006	2007	2008	2009
	1	2	3	4	5

Case Sensitivity

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 caseInsensitive:true:

 Rank(D,I, caseInsensitive:true)

Case sensitivity only impacts text values.

Descending rank

You can easily reverse the rank of numeric arrays, where the largest numbers receive the lowest ranks, by simply using:

 Rank(-X, i)

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.

Multi-key ranking

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 for ties by gender:

Index keyIndex := ['age','gender'];
Rank(Array(keyIndex,[age,gender]), i, keyIndex )

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.

By default, Rank assigns an arbitrary ranking to NaN values -- placing them between -INF and any finite numeric value. To pass NaNs, include the optional parameter: 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:

 Rank(x, i, passNulls:true).

When this is not specified, Null values are assigned a rank (with Null coming after all numeric values).

Optional Type Parameter Examples

This example shows how the Rank function handles duplicate values. For Type = -1, lowest rank for the duplicate value is returned. For Type = 0, mid rank value of the duplicates is returned. For Type = 1, highest rank for the duplicate value is returned. For Type = NULL, Unique rank value is returned.

Index RankType := [-1,0,1, Null]

Rank(NumRepairs,CarNum,Type:RankType →

	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	5

Multi-Key Example

Rank(NumMaintEvents,CarNum,KeyIndex:MaintType) →

	1	2	3	4	5	6	7
	7	4	6	2	3	1	5