This means we’ve pretty much seen it all, whether it’s something super common or a problem that’s more rare.īasically, whatever problem you’re facing, we’re confident we know how to tackle it. Well, to start, we’ve been in the business since 1979, and we’ve maintained a solid reputation throughout this time for successfully solving a number of chimney and fireplace problems. For other references, see the end of my previous article about the SWEEP operator.We can talk a big game about our quality services all we want, but we’re guessing you want an inside look on just what we’ve done to ensure we’re up to date and well informed on everything chimney. (1979), "A Tutorial on the SWEEP Operator," The American Statistician. This useful property of the SWEEP operator is among the many features discussed in Goodnight, J. (This is most of the work!) You can then quickly compute any model that uses the columns of the design matrix in any order. From a design matrix, you can compute the SSCP matrix. The SWEEP operator enables you to specify the order in which you want to add effects to the model. But the current article shows that you do not need to permute the elements of an SSCP matrix if you use the SWEEP operator. The output matches the "PARTIAL" model from PROC REG.Īn efficient way to permute the order of rows and columns of a matrix. S = sweep (SSCP, v ) /* sweeps in the variables in the order of v */ī = S /* get the parameter estimates */ PVarNames = varNames /* effect names for this model */ No need to form a newĭesign matrix or to extract a portion of the SCCP. Following Goodnight (1979), the last column contains the response variable, but this is merely a convenience. The following SAS/IML statements read the data and compute the SSCP matrix. You can use the SAS/IML language to illuminate how PROC REG can compute one SSCP matrix and re-use it for all subsequent models. There is no need to physically permute the rows and columns of the SSCP matrix. The next section shows that how the SWEEP operator can quickly compute the parameter estimates for any model and for any order of the variables. As I have previously shown, computing the SSCP matrix is often 90% of the work of computing regression estimates, which means that the second and third models are computed very quickly. It simply re-uses the original SSCP matrix. PROC REG estimates the second and third models without re-reading the data. The output for the "PERMUTE" model is not shown, because the estimates are the same as for the "FULL" model, but in a different order. PERMUTE: model MSRP = Horsepower Weight EngineSize MPG_Highway It uses that SSCP matrix to compute the parameter estimates: The following call to PROC REG computes the SSCP matrix for five variables and the intercept effect. In other words, PROC REG re-uses that SSCP matrix for every MODEL statement. As stated in the documentation, for each subsequent model, "the procedure selects the appropriate crossproducts from the matrix." Why? Because when PROC REG encounters the RUN statement it builds the SSCP matrix for the variables that you have specified. However, if you are going to explore several different models, you must use the VAR statement to specify all variables that you might conceivably want to use BEFORE the first RUN statement. The REG procedure is interactive, which means that you can interactively add or delete effects from a model as part of the model-building process. But if you use the SWEEP operator, you do not need to permute the SSCP matrix at all!īefore discussing the SWEEP operator, let's review a little-used feature of PROC REG in SAS. Being able to permute the rows and columns of the SSCP matrix efficiently means that you can solve the linear regression problem very quickly for any ordering of the columns of the design matrix. You never need to use a permutation matrix to rearrange the order of rows and columns of a matrix.Īs an application, I used the sum of squares and crossproducts (SSCP) matrix, which is used to estimate the regression coefficients in a least-squares regression model. This post relates to a previous post, in which I showed that This article shows that if you use the SWEEP operator, you can compute a SSCP matrix and use it repeatedly to estimate any linear regression model that uses those effects. One of the benefits of using the SWEEP operator is that it enables you to "sweep in" columns (add effects to a model) in any order.
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