[讨论]Data Matrix for PROC MDS?

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I am wondering if there might be someone in this platform that might be kind enough to let me know how to translate a square raw data matrix to ANY sort of distance (diagonal) matrix suitable for input to PROC MDS in SAS ?

[此贴子已经被作者于2005-5-25 11:12:33编辑过]

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关键词：matrix Data For Mat MDS 讨论 proc matrix Data MDS

Question 1: Why The MDS and ALSCAL procedures in SAS may sometimes produce different results?

The MDS and ALSCAL procedures may sometimes produce different results for the following reasons:

• With the LEVEL=INTERVAL option, PROC MDS fits a regression model while PROC ALSCAL fits a measurement model. These models are not equivalent if there is more than one partition, although the differences in the parameter estimates are usually minor.
• PROC MDS and PROC ALSCAL use different algorithms for initialization and optimization. Hence, different local optima may be found by PROC MDS and PROC ALSCAL for some data sets with poor fit. Using the INAV=SSCP option causes the initial estimates from PROC MDS to be more like those from PROC ALSCAL.
• The default convergence criteria in PROC MDS are more strict than those in PROC ALSCAL. The convergence measure in PROC ALSCAL may cause PROC ALSCAL to stop iterating because progress is slow rather than because a local optimum has been reached. Even if you run PROC ALSCAL with a very small convergence criterion and a very large iteration limit, PROC ALSCAL may never achieve the same degree of precision as PROC MDS. For most applications, this problem is of no practical consequence since two- or three-digit precision is sufficient. If the model does not fit well, obtaining higher precision may require hundreds of iterations.

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SAS Proc Autoreg takes care of the serial correlation in the error term. PA computes predicted values based on the structural model and the full model. The structural piece uses only the parameter estimates of the independent variables (no error terms). The full model adds back the AR1 error term to the model. I'm having trouble reconciling the computation of the 1st predicted value for the full model. SAS uses a Kalman filter to do this, and the calculation appears complex. Can anyone explain how the calculation is done for a simple (y regressed on time w/AR1 error term) regression, and refer me to a good reference source.

There are a lot of references for Kalman filters. The best source certainly are

1. Peter S. Maybeck. Stochastic Models, Estimation, and Control, volume 1. Academic Press, New York, 1979.

2. Applied Optimal Estimation by Arthur Gelb

3. A.H. Jazwinski, Stochastic Processes and Filtering Theory, Academic Press, New York, 1970

data raw; input Y1 Y2 Y3 Y4 Y5; cards; 5.7 4.3 4.8 4.8 5.7 9.7 5.4 3.1 2.9 2.9 6.2 4.0 5.6 4.3 5.7 13.5 10.1 9.7 8.8 10.6 2.4 2.3 2.8 2.7 3.1 ;

proc print data=raw; %inc '/usr/courses/RS718/distnew.sas'; %distance (data=raw, var=y1-y5, out=rawdist, method=euclid); proc print data=rawdist;

PROC MDS data=rawdist alternate=none coef=identity condition=matrix decimals=3 dim=1 to 2 fit=distance formula=1 inav=data level=absolute out=rawout outres=rawres over=1 pfinal pineigval shape=triangle;

PROC PLOT data=rawout; plot dim2*dim1; PROC PLOT data=rawres; plot fitdata*fitdist;

data corl; /*similarity matrix*/ input V1 V2 V3 V4 V5; cards; 1.000 0.330 0.846 0.666 0.430; 0.330 1.000 0.380 0.902 -0.700; 0.846 0.380 1.000 0.697 0.336; 0.666 0.902 0.697 1.000 -0.338; 0.430 -0.700 0.336 -0.338 1.000 ;

PROC PRINT data=corl; PROC CORR data=raw; /*this his how to get the correlation matrix*/ PROC MDS data=corl alternate=none coef=identity condition=matrix decimals=3 dim=1 to 2 fit=distance formula=1 inav=data level=absolute out=corlout outres=corlres over=1 pfinal pineigval; PROC PLOT data=corlout; plot dim2*dim1; PROC PLOT data=corlres; plot fitdata*fitdist;

/* PART II*/

DATA ELECT; set ssd.elect96; educ=0; if v960610 le 2 then educ=1; if v960610 eq 3 then educ=2; if v960610 eq 4 then educ=3; if v960610 eq 5 then educ=4; if v960610 eq 6 then educ=5; if v960610 eq 7 then educ=6; income=0; if v960701 le 10 then income=1; if v960701 in (11, 12, 13, 14, 15) then income=2; if v960701 in (16, 17, 18) then income=3; if v960701 in (19, 20) then income=4; if v960701 eq 21 then income=5; if v960701 eq 22 then income=6; if v960701 eq 23 then income=7; if v960701 eq 24 then income=8;

PROC CORR; var educ income; DATA CORRELEC; input v1 v2; cards; 1.00000 0.40746 0.40746 1.00000 ; proc print data=correlec; /* Correlation (similarity matrix), metric solution*/

PROC MDS data=correlec alternate=none coef=identity condition=matrix decimals=3 dim=1 to 2 fit=distance formula=1 inav=data level=absolute out=celecout outres=celecres over=1 pfinal pineigval shape=triangle;

PROC PLOT data=celecout; plot dim2*dim1; PROC PLOT data=celecres; plot fitdata*fitdist;

DATA DISTELEC; set elect;

PROC TRANSPOSE out=tranelec; var educ income;

%inc '/usr/courses/RS718/distnew.sas'; %distance (data=tranelec, out=elecdist, method=euclid); PROC PRINT data=elecdist;

/*Dissimilarity matrix (raw data), metric solution*/ PROC MDS data=elecdist alternate=none coef=identity condition=matrix decimals=3 dim=1 to 2 fit=distance formula=1 inav=data level=absolute out=delecout outres=delecres over=1 pfinal pineigval shape=triangle;

PROC PLOT data=delecout; plot dim2*dim1; PROC PLOT data=delecres; plot fitdata*fitdist;

/*Dissimilarity matrix (raw data), nonmetric solution*/ PROC MDS data=elecdist alternate=none coef=identity condition=matrix decimals=3 dim=1 to 2 fit=distance formula=1 inav=data level=ordinal out=nmetout outres=nmetres over=1 pfinal pineigval shape=triangle;

PROC PLOT data=nmetout; plot dim2*dim1; PROC PLOT data=nmetres; plot fitdata*fitdist;

run;

例子

Dear all,

I'm trying to figure out how to estimate prediction intervals of a function using proc ARIMA. For example, there a time series Y_{n}, n=1... N, after modelling with proc ARIMA, how could I obtain the prediction interval for sum of Y_{N+1}, ...,Y_{N+16}?