Notice how PROC GLMSELECT handles the missing value in the third observation: because the X1 value is missing, the procedure puts a missing value into all interaction effects. Next, we’ll use proc univariate to perform a Kolmogorov-Smirnov test to determine if the sample is normally distributed: /*perform Kolmogorov-Smirnov test*/ proc univariate data=my_data; histogram Values / normal(mu=est sigma=est); run; At the bottom of the output we can see the test statistic and corresponding p-value of the Kolmogorov. The procedure offers extensive capabilities for customizing the. This example shows how you can use model selection to perform scatter plot smoothing. D. 44. Example 1 for PROC GLMSELECT /**/ /* S A S S A M P L E L I B R A R Y */ /* */ /* NAME: glsdt */ /* TITLE: Details Section Examples for PROC. PROC GLMSELECT fits an ordinary regression model. The original data came from a weekly diary study of about 400 people. Random partition into training, validation, and testing dataFunda Gunes, in the Statistical Applications Department at SAS, presents LASSO Selection with PROC GLMSELECT. . Salary example in proc glm Model salary ($1000) as function of age in years, years post-high school education (educ), & political a liation (pol), pol = D for Democrat, pol = R for Republican, and pol = O for other. . Lasso variable selection is available for logistic regression in the latest version of the HPGENSELECT procedure (SAS/STAT 13. CVMETHOD=BLOCK < ( n )> CVMETHOD=RANDOM < ( n )> CVMETHOD=SPLIT < ( n )> CVMETHOD=INDEX ( variable) specifies how the training data are subdivided into parts. For example, the first term that enters the model after the intercept is. The example also uses k -fold external cross validation as a criterion in the CHOOSE= option to choose the best model based on the penalized regression fit. With the same VALDATA= data set named in the PROC GLMSELECT statement as in the LASSO example, the minimum of the validation ASE occurs at step 105, and hence the model at this step is selected, resulting in 54 selected effects. The GLMSELECT procedure uses the keyword 'L1' instead of 'lambda' . However, beginning with SAS 9. NOSEPARATE. In order to demonstrate the efficiency in screening model selection, this example. The PARMDISTRIBUTION request in the PLOTS= option in the PROC GLMSELECT. However, if I use: /selection=lasso(stop=none choose=sbc). PROC GLMSELECT creates a SAS item store that is called YourModel. This may not be a realistic example for comparison purposes. Documentation Example 2 for PROC CLUSTER. The MODEL statement in PROC GLMSELECT includes 18 independent variables, but the final LASSO model contains only seven variables. Figure 2 SAS® Datastep and NPAR1WAY Procedure Code. Here's sample code for PROC GLMSELECT: proc glmselect data=input; model y = x1-x5 / selection=forward(select=sl) stats=bic details=all; run; The sub-option SELECT=SL specifies that variable selection is based on the significance level of the F statistic (similar to PROC REG, the default would be different: SBC). One example can be seen in the boxplot below, where different bluebook distributions by car type can. 1 Answer. It illustrates how you can use the experimental EFFECT statement to generate a large collection of B-spline basis functions from which a subset is selected to fit. . We will introduce a numeric ROW variable that we can later use to merge the design matrix back with the input data. See the section Macro Variables Containing Selected Models for details. Elastic Net Coefficient. . Model_Fit "Parameter Estimates" =. The HPMIXED Procedure. For more information on permanent SAS data sets, refer to the section "SAS Files" in SAS Language Reference: Concepts. PROC GLMSELECT provides a variety of selection and stopping criteria. 05. . 2 Using Validation and Cross Validation. . You can use a SAS autocall macro, %Marginal, to display marginal model plots. GENMOD fits the "generalized linear model" which allows for any response distribution in a family of distributions and it models a function (the "link" function) of the response mean. For example, the BP_Optimal column is redundant because that column contains a 1 only when the BP_High and. It is worth noting that the label for the MODEL statement in PROC REG is used by PROC SCORE to name the predicted variable. Say your input effect list consists of x1-x10. Example: How to Use PROC GLMSELECT in SAS for Model Selection. 1-15 of 17. (Although, in this example, the item store is saved to your Work library, you can use a LIBNAME statement to save these item stores to permanent locations. In traditional implementations of backward elimination, the contribution of an effect to. This example shows how you can use PROC GLMSELECT as a starting point for such an analysis. The GLMSELECT Procedure. Here’s an example: logit ˇ(x) = 0 + 1x 1 + 2x 2 + 3(x 1 3x 2):. This article demonstrates four SAS procedures that create design matrices: GLMMOD, LOGISTIC, TRANSREG, and GLIMMIX. 1 Modeling Baseball Salaries Using Performance Statistics. Consider a model with one classification variable A with four levels, 1, 2, 5, and 7. Both the REG and GLMSELECT procedures provide extensive options for model selection in ordinary linear regression models. , the CVMETHOD= options in PROC GLMSELECT [25]), none appear to be available for bootstrap estimation of optimism as of SAS version 9. For example, consider the data shown inFigure 2, where the variance of Y increases with X. PROC GLMSELECT Statement. This example uses data from Cole and Grizzle to illustrate a commonly occurring repeated measures ANOVA design. Then &_GLSIND would be set to x1 x3 x4 x10 if, for example, the first, third, fourth, and tenth effects were selected for the model. As discussed by Agresti (2013), one such situation occurs when there is a large number of covariates, of which only a small subset are strongly. Example 42. Then &_GLSIND would be set to x1 x3 x4 x10 if, for example, the first, third, fourth, and tenth effects were selected for the model. documentation. For example, specifying. PROC GLMSELECT deals with this issue automatically. This paper describes the GLMSELECT procedure, a new procedure in SAS/STAT software that performs model selection in the framework of general linear models. proc format; value proga 1="academic" 2="general" 3="vocational"; run; data tobit; set tobit; format prog proga. GLMMOD or GLIMMIX: For models using GLM parameterization (also called indicator or dummy coding) of CLASS variables, you can use an ODS OUTPUT statement with PROC GLMMOD to save the design matrix to a data set. comThe two models specified are the same. This question already has an answer here : Lasso features selection through Crossvalidation (1 answer) Closed 5 years ago. It also demonstrates the use of split classification variables. 1 documentation, with changes. The simulated data for this example describe a two-week summer tennis camp. For. Example 42. PROC GLMSELECT combines features from these two procedures to create a useful new model selection tool. b: Slope or Coefficient. 3 Scatter Plot Smoothing by Selecting Spline Functions This example shows how you can use model selection to perform scatter plot smoothing. RANDOM FOREST – THE HIGH-PERFORMANCE PROCEDURE The SAS® code below calls the High-Performance Random Forest procedure, PROC HPFOREST. which are available in SAS through PROC GLMSELECT. At each step, the variable that is added is the one that most improves the fit. You can write the group LASSO method in the equivalent Lagrangian form, which is an example. The GLMSELECT procedure is the best way to create a. For this example, PROC GLMSELECT runs only slightly faster when SCREEN=SIS than it does when SCREEN=SASVI, although it runs about twice as fast as it does when SCREEN=NONE. One example can be seen in the boxplot below, where different bluebook distributions by car type can be. GENMOD fits the "generalized linear model" which allows for any response distribution in a family of distributions and it models a function (the "link" function) of the response mean. . LASSO. The HPGENSELECT procedure implements the group LASSO method, which is described in the section Group LASSO Selection. Learn more at GLMSELECT supports several criteria that you can use for this purpose. This algorithm for SELECTION=LASSO is used in PROC GLMSELECT. . PROC GLMSELECT saves the list of selected effects in a macro variable, &_GLSIND. Getting Started: GLMSELECT Procedure. Elastic Net Coefficient. If you a fitting a. The MODEL statement in PROC GLMSELECT includes 18 independent variables, but the final LASSO model contains only seven variables. . carvalue(obs=10); var SequenceID policyno bluebook car_type car_use Car_Age_Months travtime; run; The Basic Idea of the Analysis . The %Marginal macro takes as input an output SAS data set. Simple Linear Regression. 4 Multimember Effects and the Design Matrix. 3789 Example 47. These criteria fall into two groups—information criteria and criteria based on out-of-sample prediction performance. 02 <. A SAS programmer recently mentioned that some open-source software uses the QR algorithm to solve least-squares regression problems and asked how that compares with SAS. 5. Examples. Afraid you'll need to loop through using the SAS macro language for proc logistic though. is minimized, where is the value of the variable specified in the WEIGHT statement, is the observed value of the response variable, and is the predicted value of the response variable. Note that many procedures (for example, PROC GLM, PROC MIXED, PROC GLIMMIX, and PROC LIFEREG) do not allow different parameterizations of. This algorithm for SELECTION= LASSO is used in PROC GLMSELECT. , the CVMETHOD= options in PROC GLMSELECT [25]), none appear to be available for bootstrap estimation of optimism as of SAS version 9. For example, if you have a binary response you can use the EFFECT statement in PROC LOGISTIC. After settling on a final model, it is often desirable to assess of the relative importance of the predictors in the model. The following sections describe the ODS graphical displays produced by PROC GLMSELECT. If you specify a VALDATA= data set in the PROC GLMSELECT statement, then you cannot also specify the VALIDATE= suboption in the PARTITION statement. . For this example, I am using restricted cubic splines and four evenly spaced internal knots, but the same ideas apply to any choice of spline effects. This example shows how you can use both test set and cross validation to monitor and control variable selection. An example is PROC REG, which does not support the CLASS statement, although for most regression analyses you can use PROC GLM or PROC GLMSELECT. Getting Started;. The PRINQUAL Procedure. The second call writes the design matrix for. Documentation Examples for Clustering Introduction. carvalue(obs=10); var SequenceID policyno bluebook car_type car_use Car_Age_Months travtime; run; The Basic Idea of the Analysis . ALPHA=number. The results of the two examples are shown in Table 3 to Table 6 in below. Since the variation of salaries is much greater for the higher salaries, it is appropriate to apply a log transformation to the salaries before doing the model selection. Re: Lasso Logistic Regression using GLMSELECT procedure. 15 SLS=0. 2 Using Validation and Cross Validation. 1 SLS=0. The horizontal direct product between matrices A and B is formed by the elementwise multiplication of their columns. This selection method is available in the GLMSELECT, LOGISTIC, PHREG, QUANTSELECT, and REG procedures. The simulated data for this example describe a two-week summer tennis camp. Usage Note 60240: Regularization, regression penalties, LASSO, ridging, and elastic net. First and last five observations from PROC CONTENTS in the order of variables in the dataset. Examples: GLMSELECT Procedure. The model statement has the main effects of female and prog, as well as their interaction; the interaction is specified by taking the product of the two main effect terms. This process results in valid statistical inferences that properly reflect the uncertainty due to missing values; for example, valid confidenceAs stated in the documentation, "PROC GLMSELECT provides results (displayed tables, output data sets, and macro variables) that make it easy to take the selected model and explore it in more detail in a subsequent procedure such as REG or GLM. The CPREFIX= applies only when you specify the PARMLABELSTYLE=INTERLACED option in the PROC GLMSELECT statement. . EXAMPLE USING PROC NPAR1WAY in SAS® Now that we have investigated the K-S two sample test manually, let us demonstrate how easily the example presented in (Table 1) [8] can be handled using the SAS® procedure NPAR1WAY. The PARMDISTRIBUTION request in the PLOTS= option in the PROC GLMSELECT. 1 Model selection Backward Elimination. g. This list can be used, for example, in the model statement of a. Options / Examples: GLMSELECT= Input optional CLASS. . The GLMSELECT procedure enables you to throw hundreds of candidate variables into a MODEL statement. 72. 2: Using Validation and Cross Validation. EFFECT MyPoly=POLYNOMIAL (x1 x2/degree=4 MDEGREE=2); generates the terms , , , , ,, and . 4 and SAS® Viya® 3. Suppose we want to fit a multiple linear regression model that uses (1) number of hours spent studying, (2) number of prep exams taken and (3) gender to predict the final exam score of students. 0001 where Probt is a parameter's p-value. In that example, the default stepwise selection method based on the SBC criterion was used to select a model. . References. . In the examples, both entry model (&SLENTRY) and depart model (&SLSTAY) significant level are 0. This. The documentation for the PLM procedure includes more information and examples. You can find further discussion and formula for these criteria in the PROC GLMSELECT documentation. Use ODS TRACE get the names of output tables. PROC GLMSELECT performs advanced model selection in the framework of. CLASS and EFFECT statements, if present, must precede the MODEL statement. 1: Modeling Baseball Salaries Using Performance Statistics. PROC GLM does not have an option, like the STB option in PROC REG, to compute standardized parameter estimates. This macro application, ALLMIXED2 will complement the Model Selection option currently available in the SAS PROC REG for multiple linearregressions and the experimental SAS procedure GLMSELECT that focuses on the standardindependently and identically distributed general linear Model for univariate responses. junkmail maxtrees=1000 vars_to_try=10. The following call to PROC GLMSELECT displays the standardized regression coefficients. + fp(x)*θp SAS provides several methods for packaging. The output is organized into various tables, which are discussed in the order of appearance. sas. 2 Using Validation and Cross Validation. The procedure also provides graphical summaries of the selection process. 15; run; proc glmselect data=data; class c1 c2 c3; model y = x1 x2 x3 c1 c2 c3 x1*x2 x1*c1 /selection=stepwise(select=SL SLE=0. The following call to PROC GLMSELECT includes an EFFECT statement that generates a natural cubic spline basis using internal knots placed at specified percentiles of the data. Thanks. The following statements are available in the GLMSELECT procedure: All statements other than the MODEL statement are optional and multiple SCORE statements can be used. Dennis Fisher Dennis G. uses a forward-selection algorithm to select variables. First, I ran: proc glmselect data=sashelp. where is the residual and is the leverage of the ith observation. Then &_QRSIND would be set to x1 x3 x4 x10 if the first, third, fourth, and tenth effects were selected for the model. 02 <. The procedure offers options for customizing the selection with a wide variety of selection and stopping criteria. D. I was reminded of this fact recently when I wrote an article about model building with PROC GLMSELECT in SAS. • Proc REG – Ridge regression • Proc GLMSelect – LASSO – Elastic Net • Proc HPreg – High Performance for linear regression with variable selection (lots of options, including LAR, LASSO, adaptive LASSO) – Hybrid versions: Use LAR and LASSO to select the model, but then estimate the regression coefficients by ordinary For example, if the number of observations in the data set is 100, then the following two PROC GLMSELECT steps are mathematically equivalent, but the second step is computed much more efficiently: proc glmselect; model y=x1-x10/selection=forward(stop=CV) cvMethod=split(100); run; proc glmselect; model y=x1-x10/selection=forward(stop=PRESS); run; Many SAS regression procedures support the EFFECT statement, the CLASS statement, and enable you to specify interactions on the MODEL statement. However, the following example uses PROC GLMSELECT (without variable selection) because you can simultaneously use the OUTDESIGN= option to write the design matrix to a SAS data set. First in proc glmselect, I'm going to select the plots equal to option to all. The GLMSELECT procedure supports a variety of model selection methods for general linear models. . 05 results in 95% intervals. Perform search. For example, you might decide to use an information criterion to decide what effects to include and when to terminate the selection process. For this example, PROC GLMSELECT runs only slightly faster when SCREEN=SIS than it does when SCREEN=SASVI, although it runs about twice as fast as it does when SCREEN=NONE. The following statements provide. PROC GLMSELECT with SELECTION = LASSO (CHOOSE=SBC) The use of PROC GLMSELECT (method #4) may seem inappropriate when discussing logistic regression. The MODELAVERAGE. . IMPORT; class gender(ref='female') pepper discipline; model quality = gender numYears pepper discipline easiness raterInterest / selection=none; run; Note that you can also do this with prox mixed. The HPGENSELECT Procedure. Many of these options and syntax are shared with other procedures, such as proc glmselect and proc reg. 05 in SAS PROC LOGISTIC). If you specify the WEIGHT statement, it must appear before the first RUN statement or it is. 35: 53. 49. 2. The idea is to calculate stratified values for the bluebook that base on these variables. as option for proc glmselect I get: Effect Parameter DF Estimate StandardizedEst StdErr tValue Probt Intercept Intercept 1 9. Proc Glmselect under three scenarios: forward, backward, stepwise. The GLMSELECT procedure performs effect selection in the framework of general linear models. The first call writes the design matrix that PROC GLM uses (internally) for the default reference levels. Getting Started. It also demonstrates several features of the OUTDESIGN= option in the PROC GLMSELECT statement. If you have requested -fold cross validation by requesting CHOOSE= CV, SELECT= CV, or STOP= CV in the MODEL statement, then a variable _CVINDEX_ is included in the output data set. . . In this example, model selection that uses other information criteria and out-of-sample prediction. To use PROC PLM you must first use the STORE statement in a regression procedure to create an item store that summarizes the model. ” With the same VALDATA= data set named in the PROC GLMSELECT statement as in the LASSO example, the minimum of the validation ASE occurs at step 105, and hence the model at this step is selected, resulting in 54 selected effects. Other approaches for performing model averaging are presented in Burnham and Anderson , and. ; run; Let’s look at the data. The tennis ability of each camper was assessed and ratings were assigned at the. The GLMSELECT Procedure. 25 validate=0. e. Unfortunately, it doesn’t do “all subsets selection”, but it does forward, backward, and stepwise selection. Example: How to Use PROC GLMSELECT in SAS for Model Selection Examples: GLMSELECT Procedure. Since the variation of salaries is much greater for the higher salaries, it is appropriate to apply a log transformation to the. CLASS Variable Parameterization. A variety of model selection methods are available, including forward, backward, stepwise, the LASSO method of Tibshirani (), and the related least angle regression method of Efron et al. com. For example, if you compute the skewness of a univariate sample, you get an estimate for the skewness of the population. This example shows how you can use multimember effects to build predictive models. Examples of tobit analysis. 08. Graphics Programming. The _GLSInd macro contains the name of the selected variables. You might want to know the range of skewness values that you might observe from a second sample (of the same size) from the population. For more information, see Chapter 5, Introduction to Analysis of Variance Procedures, and Chapter 52, The GLM Procedure. Choose PROC GLMSELECT for “large p” problems and choose PROC REG for smaller numbers of predictors, e. . brfss2;. The HPLOGISTIC Procedure. This selection method is available in the GLMSELECT, LOGISTIC, PHREG, QUANTSELECT, and REG procedures. PROC GLMSELECT Statement. How can salary be predicted from performance? data baseball; set sashelp. 5. 4M63. The following procedures support the STORE statement: GEE, GENMOD, GLIMMIX, GLM, GLMSELECT,. 12 weeks of observation. Learn more about TeamsPROC GLMSELECT saves the list of selected effects in a macro variable, &_GLSIND. The definitions now used in PROC GLMSELECT yield the same final models as before, but PROC GLMSELECT makes the connection between the AIC statistic and the AICC statistic more transparent. 4). Training TESTDATA = WORK. Unlike the GLMSELECT procedure, the REGSELECT procedure does not perform model selection by default. As discussed by Agresti (2013), one such situation occurs when there is a large number of covariates, of which only a small subset are strongly. You can use this macro to display plots from output data sets after running procedures such as REG, GLM, GLMSELECT, TRANSREG, and so on. This option applies only when. It also demonstrates several features of the OUTDESIGN= option in the PROC GLMSELECT statement. The GLM procedure supports a CLASS statement but does not include effect selection methods. The following statements show how you can use PROC GLMSELECT to implement this strategy: proc glmselect data=dojoBumps; effect spl = spline(x / knotmethod=multiscale(endscale=8) split details); model bumpsWithNoise=spl; output out=out1 p=pBumps; run; proc sgplot data=out1; yaxis display=(nolabel); series x=x. You can name the fractions of the data that you want to reserve as test data and validation data. The tennis ability of. selection=stepwise (select=SL SLE=0. proc glmselect data=ex7Data; class c:; model y = x: c:/ selection=lasso; run; Output 49. Table 45. CLASS variables (like PROC GLM) and model selection (like PROC REG). If we define the angle theta as 2*pi* (DAY/365), then we convert from polar coordinates (assuming that radius = 1) to. . SAS will perform forward selection with a very large number of variables GLMSELECT fits the "general linear model" that assumes that the response distribution is normal and it directly models the response mean. 4 and SAS® Viya® 3. The HPCANDISC Procedure. Features. Base SAS Procedures . . . Examples Modeling Baseball Salaries Using Performance Statistics Using Validation and Cross Validation Scatter Plot Smoothing by Selecting Spline Functions Multimember Effects and the Design Matrix Model Averaging. ODS Graph Names. For example, the following statements create and run a macro that uses PROC GLM to perform LSMeans analyses. In conclusion, we saw different procedures used in SAS predictive modeling: PROC ADAPTIVEREG, PROC GLMSELECT, PROC HPGENSELECT, PROC TRANSREG, and PROC PLS with example & syntax. The example also uses k-fold external cross validation as a criterion in the CHOOSE= option to choose the best model based on the penalized regression fit. "However, to get inferential statistics and hypotheses tests, you should select a. The PRINQUAL Procedure. Proc Logistic, and %StepSvyreg vs. First let's make a sample dataset with a long character ID variable. Elastic net isn't supported quite yet. Proc Glmselect under three scenarios: forward, backward, stepwise. This value is used as the default confidence level for limits computed by the. The following sections describe the ODS graphical displays produced by PROC GLMSELECT. Random partition into training, validation, and testing data Funda Gunes, in the Statistical Applications Department at SAS, presents LASSO Selection with PROC GLMSELECT. TPHREG PROC PHREG is used for proportional hazard modeling in SAS. The Power and Sample Size Application. 3 Scatter Plot. But sometimes there are problems. Provides detailed reference material for using SAS/STAT software to perform statistical analyses, including analysis of variance, regression, categorical data analysis, multivariate analysis, survival analysis, psychometric analysis, cluster analysis, nonparametric analysis, mixed-models analysis, and survey data analysis, with numerous examples in addition to syntax and usage information. Both PROC GLMSELECT and PROC REG can do stepwise regression. specifies the criterion that PROC GLMSELECT uses to determine the order in which effects enter and/or leave at each step of the specified selection method. This example continues the investigation of the baseball data set introduced in the section Getting Started: GLMSELECT Procedure. Examples focus on logistic regression using the LOGISTIC procedure, but these techniques can be readily extended to other procedures and statistical models. If you have requested n -fold cross validation by requesting CHOOSE= CV, SELECT= CV, or STOP= CV in the MODEL statement, then a variable _CVINDEX_ is. 1 sls=0. Then &_GLSIND would be set to x1 x3 x4 x10 if, for example, the first, third, fourth, and tenth effects were selected for the model. But running the PROC SGPLOT code as it is, results, on my computer, in a graph including not only four coloured curves but many and many. 05. Proc genmod use numerical methods to maximize the likelihood functions. For this example, PROC GLMSELECT runs only slightly faster when SCREEN=SIS than it does when SCREEN=SASVI, although it runs about twice as fast as it does when SCREEN=NONE. A variety of model selection methods are available, including the LASSO method of Tibshirani and the related LAR method of Efron et al. This includes the class of generalized linear models and generalized additive models based on distributions such as the binomial for logistic models, Poisson, gamma, and others. This example continues the investigation of the baseball data set introduced in the section Getting Started: GLMSELECT Procedure. A possible search term is "proc glmselect" outdesign site:. In addressing these examples, built-in facilities of the procedure to handle validation and test data are highlighted in addition to techniquesThe PROC GLMSELECT statement invokes the procedure. The HPLMIXED Procedure. selection=stepwise (select=SL SLE=0. The following sections describe the ODS graphical. . 2. The HPMIXED Procedure. comFor example, there are many ways to solve for the least-squares solution of a linear regression model. For a reference to this trick see Hastie Tibshirani Friedman-Elements of statistical learning 2nd ed -2009 page 661 "Lasso regression can be applied to a two-class classifcation problem by coding the outcome +-1, and applying a cutoff. Chapter 6 6. If you were to sample from the distribution of Y but discard values less than (greater than) C, the distribution of the remaining observations would be. This section provides an example of using splines in PROC GLMSELECT to fit a GLM regression model. where Probt is a parameter's p-value. This section provides an example of using splines in PROC GLMSELECT to fit a GLM regression model. (View the complete code for this example . Baseball data set contains salary and performance information for Major League Baseball players who played at least one game in both the 1986 and 1987 seasons, excluding pitchers. See Table 60. Information on the tables will be written to the log. This example shows how you can use the SCREEN= option to speed up model selection when you have a large number of regressors. This example shows how you can use PROC LIFEREG and the DATA step to compute two of the three types of predicted values discussed there. Sorry I am still a SAS newby. DATA Step Programming . , 1999 ), which is used in the paper by Zou and Hastie ( 2005 ) to demonstrate the performance of the. You can now leverage these macro variables and the output data set created by PROC GLMSELECT to perform postselection analyses that match the selected models with the appropriate BY-group observations. You use the CHOOSE= option of forward selection to specify the criterion for selecting one model from the sequence of models produced. The simulated data for this example describe a two-week summer tennis camp. For example, suppose your input effect list consists of x1–x10.