SAS/STAT 9.1 Users Guide, Volumes 1-7
Missing Values
Observations with missing values are omitted from the analysis and are given missing values for canonical variable scores in the OUT= data set.
Output Data Sets
OUT= Data Set
The OUT= data set contains all the variables in the original data set plus new variables containing the canonical variable scores. The N= option determines the number of new variables . The OUT= data set is not created if N=0. The names of the new variables are formed by concatenating the value given by the PREFIX= option (or the prefix CAN if the PREFIX= option is not specified) and the numbers 1, 2, 3, and so on. The OUT= data set can be used as input to PROC CLUSTER or PROC FASTCLUS. The cluster analysis should be performed on the canonical variables, not on the original variables.
OUTSTAT= Data Set
The OUTSTAT= data set is a TYPE=ACE data set containing the following variables.
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the BY variables, if any
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the two new character variables, _TYPE_ and _NAME_
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the variables analyzed , that is, those in the VAR statement, or, if there is no VAR statement, all numeric variables not listed in any other statement
Each observation in the new data set contains some type of statistic as indicated by the _TYPE_ variable. The values of the _TYPE_ variable are as follows :
| _TYPE_ | |
|---|---|
| MEAN | mean of each variable |
| STD | standard deviation of each variable |
| N | number of observations on which the analysis is based. This value is the same for each variable. |
| SUMWGT | sum of the weights if a WEIGHT statement is used. This value is the same for each variable. |
| COV | covariances between each variable and the variable named by the _NAME_ variable. The number of observations with _TYPE_ =COV is equal to the number of variables being analyzed. |
| ACE | estimated within-cluster covariances between each variable and the variable named by the _NAME_ variable. The number of observations with _TYPE_ =ACE is equal to the number of variables being analyzed. |
| EIGENVAL | eigenvalues of INV(ACE)*(COV ˆ’ ACE). If the N= option requests fewer than the maximum number of canonical variables, only the specified number of eigenvalues are produced, with missing values filling out the observation. |
| RAWSCORE | raw canonical coefficients. To obtain the canonical variable scores, these coefficients should be multiplied by the raw data centered by means obtained from the observation with _TYPE_ = MEAN . |
| SCORE | standardized canonical coefficients. The _NAME_ variable contains the name of the corresponding canonical variable as constructed from the PREFIX= option. The number of observations with _TYPE_ =SCORE equals the number of canonical variables computed. To obtain the canonical variable scores, these coefficients should be multiplied by the standardized data using means obtained from the observation with _TYPE_ = MEAN and standard deviations obtained from the observation with _TYPE_ = STD . |
The OUTSTAT= data set can be used
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to initialize another execution of PROC ACECLUS
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to compute canonical variable scores with the SCORE procedure
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as input to the FACTOR procedure, specifying METHOD=SCORE, to rotate the canonical variables
Computational Resources
Let
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n = number of observations
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v = number of variables
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i = number of iterations
Memory
The memory in bytes required by PROC ACECLUS is approximately
bytes. If you request the PP or QQ option, an additional 4 n ( n ˆ’ 1) bytes are needed.
Time
The time required by PROC ACECLUS is roughly proportional to
Displayed Output
Unless the SHORT option is specified, the ACECLUS procedure displays the following items:
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Means and Standard Deviations of the input variables
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the S matrix, labeled COV: Total Sample Covariances
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the name or value of the matrix used for the Initial Within-Cluster Covariance Estimate
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the Threshold value if the PROPORTION= option is specified
For each iteration, PROC ACECLUS displays
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the Iteration number
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RMS Distance, the root mean square distance between all pairs of observations
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the Distance Cutoff ( u ) for including pairs of observations in the estimate of the within-cluster covariances, which equals the RMS distance times the threshold
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the number of Pairs Within Cutoff
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the Convergence Measure ( e i ) as specified by the METRIC= option
If the SHORT option is not specified, PROC ACECLUS also displays the A matrix, labeled ACE: Approximate Covariance Estimate Within Clusters.
The ACECLUS procedure displays a table of eigenvalues from the canonical analysis containing the following items:
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Eigenvalues of Inv(ACE)*(COV ˆ’ ACE)
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the Difference between successive eigenvalues
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the Proportion of variance explained by each eigenvalue
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the Cumulative proportion of variance explained
If the SHORT option is not specified, PROC ACECLUS displays
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the Eigenvectors or raw canonical coefficients
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the standardized eigenvectors or standard canonical coefficients
ODS Table Names
PROC ACECLUS assigns a name to each table it creates. You can use these names to reference the table when using the Output Delivery System (ODS) to select tables and create output data sets. These names are listed in the following table. For more information on ODS, see Chapter 14, Using the Output Delivery System.
| ODS Table Name | Description | Statement | Option |
|---|---|---|---|
| ConvergenceStatus | Convergence status | PROC | default |
| DataOptionInfo | Data and option information | PROC | default |
| Eigenvalues | Eigenvalues of Inv(ACE)*(COV-ACE) | PROC | default |
| Eigenvectors | Eigenvectors (raw canonical coefficients) | PROC | default |
| InitWithin | Initial within-cluster covariance estimate | PROC | INITIAL=INPUT |
| IterHistory | Iteration history | PROC | default |
| SimpleStatistics | Simple statistics | PROC | default |
| StdCanCoef | Standardized canonical coefficients | PROC | default |
| Threshold | Threshold value | PROC | PROPORTION= |
| TotSampleCov | Total sample covariances | PROC | default |
| Within | Approximate covariance estimate within clusters | PROC | default |