Thanks Steve. These are the codes I used for ANOVA without the fixed covariate effects. I tried four CVs (CS, CSH, AR(1), and UN), and CSH gives the best fit statistics. PROC Mixed DATA=WORK.NFldGrav_Final PLOTS(ONLY) = (ResidualPanel(Marginal)); CLASS Block Treat Point Year Time; MODEL NM = Treat|Year|Point Time(Year) Treat*Time(Year) Point*Time(Year) RANDOM Block Block*Treat Block*Treat*Point; REPEATED Time/SUBJECT=Point(Block*Treat*Year) TYPE = CSH; LSMEANS Treat*Year Treat*Year*Point Treat*Time(Year)/ADJUST=TUKEY SLICE=(Treat Year Point Time)CL; LSMEANS Treat*Point*Time(Year)/ADJUST=TUKEY SLICE=(Treat Year Point Time)CL; RUN; The approach you mentioned for analysis that includes the fixed covariate effects seems logical. I just would like to know if there's a way we could do to detect collinearity using this approach. While I was browsing for ideas to do the analysis with fixed covariates, I found that one solution is to do principal component analysis first then MLR, or MLR only with automatic selection and variance inflation factors to detect collinearity. However, I don't know how to do PCA in SAS, much more with RCBD. I had experienced doing MLR in SAS, but not with data from RCBD experiment. So, my approach will be to do MLR by treatment and point with both dependent variables and covariates averaged over three blocks. To illustrate: Treatment 1, Point 1 PROC REG DATA = WORK.NField PLOTS (ONLY) = (CP); STEPWISE: MODEL NM = BD TN TC CNR WC TMP/ SELECTION = STEPWISE; RUN; PROC REG DATA = WORK.NField PLOTS; FULL: MODEL NM = BD TN TC CNR WC TMP / VIF; RUN; . . . Treatment 3, Point 2 PROC REG DATA = WORK.NField PLOTS (ONLY) = (CP); STEPWISE: MODEL NM= BD TN TC CNR WC TMP/ SELECTION = STEPWISE; RUN; PROC REG DATA = WORK.NField PLOTS; FULL: MODEL NM = BD TN TC CNR WC TMP / VIF; RUN; I didn't proceed with this idea, because I am not sure how much information will be lost by averaging over 3 blocks, if ever doing the analysis per treatment is a correct approach, in addition to eliminating time out of the equation. The bottomline is, I just would like to know, if some (eliminate collinear var.) or all of the fixed covariate effects significantly explain the variation in the dependent variable for each treatment at each point within each treatment. Thanks.
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