The FACTOR Procedure

PATHDIAGRAM Statement

  • PATHDIAGRAM <options>;

You can use the PATHDIAGRAM statement to specify and modify the layout algorithm, to control the formatting of estimates, and to fine-tune many graphical and nongraphical features of path diagrams. You can use multiple PATHDIAGRAM statements to produce path diagrams that have different styles and graphical features.

Specifying a PATHDIAGRAM statement without any options has the same effect as specifying the PLOTS= PATHDIAGRAM option in the PROC FACTOR statement. Both produce a default path diagram for the last factor solution in a PROC FACTOR run. The default path diagrams show the links between factors and variables, the factor correlations, and the error variances in the model. For more information about the default path diagram, see the PLOTS= PATHDIAGRAM option.

The options in the PATHDIAGRAM statement can be classified into three categories, which are summarized in Table 37.2 through Table 37.4. The following three tables summarize these options. An alphabetical listing of these options that includes more details follows the tables.

Table 37.2 shows the options that you can use to specify the path diagram layout algorithm, to set the criteria for displaying the directed paths between variables and factors, and to specify the size of factors relative to the observed variables.

Table 37.2: Options for Controlling the Layout

Option

Description

ALPHA=

Specifies the significance level of the loading estimate that is required in order to display the corresponding link between a variable and a factor

ARRANGE=

Specifies the algorithm for laying out variables in the path diagram

COVER=

Specifies the salience criterion on the loading estimate

FACTORSIZE=

Specifies the size of latent factors relative to observed variables

FUZZ=

Specifies the magnitude of the loading estimate that is required in order to display the corresponding link between a variable and a factor

SCALE=

Specifies the scale factor for the node size


Table 37.3 shows the options that you can use to control the display of parameter estimates in output path diagrams.

Table 37.3: Options for Displaying Parameter Estimates

Option

Description

DECP=

Specifies the number of decimal places in the estimates

NOESTIM

Disables the display of all numerical estimates

NOERRVAR

Disables the display of error variances

NOFACTORVAR

Disables the display of factor variances

NOVARIANCE

Disables the display of all variances


Table 37.4 shows the options that you can use to specify the title, the path diagram label, and the variable labels.

Table 37.4: Options for Specifying Titles and Labels

Option

Description

DESIGNHEIGHT=

Sets the height, in pixels, of the output path diagram

DESIGNWIDTH=

Sets the width, in pixels, of the output path diagram

DIAGRAMLABEL=

Specifies the label of the diagram in the ODS

LABEL=

Specifies labels of the nodes that are shown in the path diagram

NODELABEL=

Specifies whether the variable names or labels are used to label nodes

NOTITLE

Suppresses the display of the title

TITLE=

Specifies the title to display in the output path diagram


ALPHA=$\alpha $
ALPHALOAD=$\alpha $

specifies the significance level ($\alpha $-level) of the loading estimate that is required in order to display the corresponding directed link (path) between a variable and a factor. If $\alpha $ is greater than 1, it is interpreted as a percentage and divided by 100. If the p-value of a loading estimate is greater than $\alpha $, the loading estimate is insignificant and PROC FACTOR does not display the corresponding link in the path diagram. By default, $\alpha =0.05$.

The ALPHA= option applies only when you specify the METHOD= ML option in the PROC FACTOR statement and when standard errors are computed in the analysis (for example, by specifying the SE option in the PROC FACTOR statement).

If you specify the ALPHA= option in the PROC FACTOR statement, all PATHDIAGRAM statements use the same $\alpha $ value that is specified in the ALPHA= option in the PROC FACTOR statement unless you respecify the ALPHA= option in individual PATHDIAGRAM statements.

Note: The p-value of a loading estimate is computed by using a reference sampling distribution that has a specific mean value. This mean value reflects the criterion for determining the salience of loading estimates. You can use the COVER= option or the SALIENCE= option to specify the salience criterion. By default, COVER=0; so PROC FACTOR displays all directed links between variables and factors that are significantly greater than 0.

ARRANGE=name
ARRANGEMENT=name
METHOD=name

specifies the algorithm for laying out the variables in the path diagram. You can specify the following names:

FLOW

specifies the process-flow algorithm.

GRIP

specifies the GRIP (graph drawing with intelligent placement) algorithm.

GROUPEDFLOW

specifies the grouped-flow algorithm.

By default, ARRANGE=FLOW if the number of observed variables is less than 15; otherwise, the default is ARRANGE=GRIP. The reason for switching the default layout algorithm is that when the number of observed variables becomes large, the process-flow algorithm might run out of vertical space for aligning all observed variables in a vertical line. In that case, the GRIP algorithm might be a better choice because the observed variables tend to scatter around the space rather than being aligned vertically. See Example 37.5 for the use of the ARRANGE= option. For more information and for general uses of these layout algorithms, see the section The Process-Flow, Grouped-Flow, and GRIP Layout Algorithms in Chapter 29: The CALIS Procedure.

COVER=p
SALIENCE=p

specifies the salience criterion, p, for the loading estimate. In order to display a loading estimate and its corresponding link between a variable and a factor in the path diagram, the magnitude of the loading estimate must be significantly greater than p. By default, p = 0 and the significance level ($\alpha $-level) is 0.05. You can specify the significance level in the ALPHA= option.

The COVER= option applies only when you specify METHOD= ML in the PROC FACTOR statement and when standard errors are computed in the analysis (for example, by specifying the SE option in the PROC FACTOR statement).

If you specify the COVER= option in the PROC FACTOR statement, any PATHDIAGRAM statement that does not include a COVER= option uses the value that is specified in the PROC FACTOR statement.

DECP=i

sets the number of decimal places in the estimates that are displayed in the path diagram, where i is between 0 and 4. The displayed estimates are at most seven digits long, including the decimal point for the nonzero value of i. By default, DECP=2.

DESIGNHEIGHT | DH=i

sets the height of the path diagram, in number of pixels, where i is between 100 and 32,767. The default heights are 800, 500, and 600 for ARRANGE= FLOW, GROUPEDFLOW, and GRIP, respectively. Typically, you might want to set a larger design height and width when your path diagram contains more nodes or variables.

DESIGNWIDTH | DW=i

sets the width of the path diagram, in number of pixels, where i is between 100 and 32,767. The default widths are 450, 720, and 600 for ARRANGE= FLOW, GROUPEDFLOW, and GRIP, respectively. Typically, you might want to set a larger design width and height when your path diagram contains more nodes or variables.

DIAGRAMLABEL=name
DLABEL=name

specifies the label of the path diagram. You can use any valid SAS name or quoted string of up to 256 characters for name. However, only up to 40 characters of the label are used by ODS. The following statements show two example label specifications: 

pathdiagram diagramlabel=MyFactorModel;
pathdiagram diagramlabel="Varimax-Rotated Factor Solution";

If you do not specify this option, PROC FACTOR uses the name that is provided in the TITLE= option. If you specify neither the DIAGRAMLABEL= option nor the TITLE= option, PROC FACTOR uses "Path Diagram" for the label when there is only one path diagram. When there is more than one path diagram, a unique number is appended to the label of each path diagram. For example, "Path Diagram 3" is the third path diagram in the output.

FACTORSIZE=size
FACTSIZE=size

specifies the size of latent factors relative to the size of observed variables, where size is between 0.2 and 5. By default, FACTSIZE=1.5, which means that the size ratio of factors to observed variables is about 3 to 2.

FUZZ=p

specifies the magnitude, p $ > $ 0, of the factor loading estimate that is required in order to display the corresponding directed link between a variable and a factor. If the magnitude of a loading estimate is less than p, then PROC FACTOR does not display the corresponding directed link in the path diagram. By default, FUZZ=0.3.

If you specify the FUZZ= option in the PROC FACTOR statement, any PATHDIAGRAM statement that does not include a FUZZ= option uses the value that is specified in the PROC FACTOR statement.

If you specify METHOD= ML and standard errors are computed, PROC FACTOR displays only those directed links (paths) between variables and factors that are statistically significant in the path diagram. In this situation, only the criteria that are specified by the ALPHA= and COVER= options are used and the FUZZ= option is irrelevant. When METHOD=ML is not specified or standard errors are not computed, PROC FACTOR uses the criterion that is specified by the FUZZ= option.

LABEL= [varlabel <, varlabel …>]  |  {varlabel <, varlabel …>}

specifies the labels of variables to be displayed in path diagrams, where each varlabel has the following form:

  •     variable=label

You can use any valid SAS names or quoted strings of up to 256 characters for labels. The labels identify the corresponding variables or factors in output path diagrams. For example, instead of using original variable names such as x1 and Factor1 in the path diagram, the following statement specifies the use of more meaningful labels: 

pathdiagram label=[x1="Simple Math" Factor1="Math Ability"];

This option is not the only way that you can provide labels for variables. For example, you can also use the LABEL statement to specify labels for observed variables. PROC FACTOR uses the following rules to determine the label for a node (variable) in the path diagram:

  1. If you specify the label for a variable or a factor by using the LABEL= option in the PATHDIAGRAM statement, the associated node (variable) uses this label in the output path diagram. Proceed to the next rule if the label of a node is not resolved.

  2. If the NODELABEL=VARNAME option is specified, the associated node uses the original variable name as its label in the output path diagram. Otherwise, proceed to the next rule.

  3. If the label of a variable is specified in a LABEL statement, the associated node uses this label in the output path diagram. Otherwise, proceed to the next rule.

  4. The associated node uses the original variable name as its label in the output path diagram.

NODELABEL=VARNAME | VARLABEL

specifies whether the variables (nodes) in path diagrams are labeled by the original variable names (VARNAME) or their variable labels (VARLABEL), which are provided by specifying the LABEL statement. If you provide variable labels (applicable only to observed variables) in the LABEL statement, PROC FACTOR uses those provided labels unless you specify this option.

This option is not the only determinant of the final labels of nodes in the path diagram. The specifications in the LABEL= option of the PATHDIAGRAM statement are also considered. For the rules that PROC FACTOR uses to determine the node labels, see the LABEL= option.

NOERRVAR
NOERRORVARIANCE

suppresses the default display of error variances, which are represented as double-headed paths that are attached to observed variables.

NOESTIM
NOEST

suppresses the default display of all numerical estimates in path diagrams.

NOFACTORVAR
NOFACTORVARIANCE

suppresses the default display of factor variances, which are represented as double-headed paths that are attached to factors.

NOTITLE

suppresses the display of the default title. You can use the TITLE= option to provide your own title.

NOVARIANCE

suppresses the default display of all variances. This option has the same effect as specifying both the NOFACTORVAR and NOERRVAR options.

SCALE=n
DIAGRAMSCALE=n

specifies the scaling factor, n, for the node size relative to the dimensions of the path diagram. Valid values of n are between 0 and 6. This option applies to the ARRANGE= GRIP layout only.

PROC FACTOR uses certain default pixel dimensions for the nodes in path diagrams that have default design dimensions (see the DESIGNHEIGHT= and DESIGNWIDTH= options for the default design dimensions). The ratio of this node dimension to the design dimension defines the point at which SCALE=1. SCALE= option values greater than 1 enlarge the nodes (relative to the design dimensions). SCALE= option values less than 1 shrink the nodes (relative to the design dimensions). Hence, you can accommodate more nodes (variables) in your path diagram by setting smaller SCALE= option values.

If you use the GRIP layout algorithm, PROC FACTOR automatically adjusts the SCALE= value according to the number of nodes in the path diagram, as shown in the following table:

Number of Nodes

SCALE=

14 or less

1.00

15–19

0.95

20–24

0.90

25–29

0.85

30–34

0.80

35–39

0.75

40–44

0.70

45–49

0.65

50–59

0.60

60–69

0.55

70 or more

0.50

Although these values yield reasonable relative node sizes in different situations, you can always adjust the relative node size by setting the SCALE= option value manually. For example, if you have 33 nodes in your path diagram and some nodes appear to be overlapping, then you can consider setting a SCALE= option value that is less than 0.8. When you are satisfied with the SCALE= option value, you can then improve the resolution of the path diagram by using the DESIGNHEIGHT= and DESIGNWIDTH= options.

TITLE=name

specifies the title of the path diagram. You can use any valid SAS name or a quoted string of up to 256 characters for name. If you do not specify this option, PROC FACTOR uses "Path Diagram" for the title when there is only one path diagram. A unique number (for example, "Path Diagram 3") is appended to the title of each path diagram when there is more than one path diagram.