# Shared Statistical Concepts

## Levelization of Classification Variables

A classification variable enters the statistical analysis or model not through its values but through its levels. The process of associating values of a variable with levels is termed levelization.

During the process of levelization, observations that share the same value are assigned to the same level. The manner in which values are grouped can be affected by the inclusion of formats. The sort order of the levels can be determined by specifying the ORDER= option in the procedure statement. In high-performance statistical procedures, you can also control the sorting order separately for each variable in the CLASS statement.

Consider the data on nine observations in Table 4.2. The variable `A` is integer-valued, and the variable `X` is a continuous variable that has a missing value for the fourth observation. The fourth and fifth columns of Table 4.2 apply two different formats to the variable `X`.

Table 4.2: Example Data for Levelization

Obs

A

x

FORMAT x 3.0

FORMAT x 3.1

1

2

1.09

1

1.1

2

2

1.13

1

1.1

3

2

1.27

1

1.3

4

3

.

.

.

5

3

2.26

2

2.3

6

3

2.48

2

2.5

7

4

3.34

3

3.3

8

4

3.34

3

3.3

9

4

3.14

3

3.1

By default, levelization of the variables groups the observations by the formatted value of the variable, except for numerical variables for which no explicit format is provided. Numerical variables for which no explicit format is provided are sorted by their internal value. The levelization of the four columns in Table 4.2 leads to the level assignment in Table 4.3.

Table 4.3: Values and Levels

A

X

FORMAT x 3.0

FORMAT x 3.1

Obs

Value

Level

Value

Level

Value

Level

Value

Level

1

2

1

1.09

1

1

1

1.1

1

2

2

1

1.13

2

1

1

1.1

1

3

2

1

1.27

3

1

1

1.3

2

4

3

2

.

.

.

.

.

.

5

3

2

2.26

4

2

2

2.3

3

6

3

2

2.48

5

2

2

2.5

4

7

4

3

3.34

7

3

3

3.3

6

8

4

3

3.34

7

3

3

3.3

6

9

4

3

3.14

6

3

3

3.1

5

The sort order for the levels of CLASS variables can be specified in the ORDER= option in the CLASS statement.

When ORDER=FORMATTED (which is the default) is in effect for numeric variables for which you have supplied no explicit format, the levels are ordered by their internal values. To order numeric class levels that have no explicit format by their BEST12. formatted values, you can specify the BEST12. format explicitly for the CLASS variables.

Table 4.4 shows how values of the ORDER= option are interpreted.

Table 4.4: Interpretation of Values of ORDER= Option

Value of ORDER=

Levels Sorted By

DATA

Order of appearance in the input data set

FORMATTED

External formatted value, except for numeric variables that have no explicit format, which are sorted by their unformatted (internal) value

FREQ

Descending frequency count (levels that have the most observations come first in the order)

INTERNAL

Unformatted value

FREQDATA

Order of descending frequency count, and within counts by order of appearance in the input data set when counts are tied

FREQFORMATTED

Order of descending frequency count, and within counts by formatted value when counts are tied

FREQINTERNAL

Order of descending frequency count, and within counts by unformatted (internal) value when counts are tied

For FORMATTED, FREQFORMATTED, FREQINTERNAL, and INTERNAL values, the sort order is machine-dependent. For more information about sort order, see the chapter about the SORT procedure in the Base SAS Procedures Guide and the discussion of BY-group processing in SAS Language Reference: Concepts.

When the MISSING option is specified in the CLASS statement, the missing values ('.' for a numeric variable and blanks for a character variable) are included in the levelization and are assigned a level. Table 4.5 displays the results of levelizing the values in Table 4.2 when the MISSING option is in effect.

Table 4.5: Values and Levels with the MISSING Option

A

X

FORMAT x 3.0

FORMAT x 3.1

Obs

Value

Level

Value

Level

Value

Level

Value

Level

1

2

1

1.09

2

1

2

1.1

2

2

2

1

1.13

3

1

2

1.1

2

3

2

1

1.27

4

1

2

1.3

3

4

3

2

.

1

.

1

.

1

5

3

2

2.26

5

2

3

2.3

4

6

3

2

2.48

6

2

3

2.5

5

7

4

3

3.34

8

3

4

3.3

7

8

4

3

3.34

8

3

4

3.3

7

9

4

3

3.14

7

3

4

3.1

6

When the MISSING option is not specified, it is important to understand the implications of missing values for your statistical analysis. When a high-performance statistical procedure levelizes the CLASS variables, an observation for which any CLASS variable has a missing value is excluded from the analysis. This is true regardless of whether the variable is used to form the statistical model. For example, consider the case in which some observations contain missing values for variable `A` but the records for these observations are otherwise complete with respect to all other variables in the statistical models. The analysis results from the following statements do not include any observations for which variable `A` contains missing values, even though `A` is not specified in the MODEL statement:

```
class A B;
model y = B x B*x;
```

High-performance statistical procedures print a "Number of Observations" table that shows the number of observations that are read from the data set and the number of observations that are used in the analysis. Pay careful attention to this table—especially when your data set contains missing values—to ensure that no observations are unintentionally excluded from the analysis.