Semi2: Oxide layer thicknesses on semiconductors

In SASmixed: Data sets from "SAS System for Mixed Models"

Description

The Semi2 data frame has 72 rows and 5 columns.

Format

This data frame contains the following columns:

Source

a factor with levels 1 and 2

Lot

a factor with levels 1 to 8

Wafer

a factor with levels 1 to 3

Site

a factor with levels 1 to 3

Thickness

a numeric vector

Source

Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, SAS Institute (Data Set 4.4).

Examples

str(Semi2)
xtabs(~Lot + Wafer, Semi2)
if (require("lme4", quietly = TRUE, character = TRUE)) {
  options(contrasts = c(unordered = "contr.SAS", ordered = "contr.poly"))
  ## compare with output 4.13, p. 156
  print(fm1Semi2 <- lmer(Thickness ~ 1 + (1|Lot/Wafer), Semi2))
  ## compare with output 4.15, p. 159
  print(fm2Semi2 <- lmer(Thickness ~ Source + (1|Lot/Wafer), Semi2))
  print(anova(fm2Semi2))
  ## compare with output 4.17, p. 163
  print(fm3Semi2 <- lmer(Thickness ~ Source + (1|Lot/Wafer) + (1|Lot:Source),
                         Semi2))
  ## This is not the same as the SAS model.
}

Example output

'data.frame':	72 obs. of  5 variables:
 $ Source   : Factor w/ 2 levels "1","2": 1 1 1 1 1 1 1 1 1 1 ...
 $ Lot      : Factor w/ 8 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 2 ...
 $ Wafer    : Factor w/ 3 levels "1","2","3": 1 1 1 2 2 2 3 3 3 1 ...
 $ Site     : Factor w/ 3 levels "1","2","3": 1 2 3 1 2 3 1 2 3 1 ...
 $ Thickness: num  2006 1999 2007 1980 1988 ...
 - attr(*, "ginfo")=List of 7
  ..$ formula     :Class 'formula'  language Thickness ~ 1 | Lot/Wafer
  .. .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv> 
  ..$ order.groups:List of 2
  .. ..$ Lot  : logi TRUE
  .. ..$ Wafer: logi TRUE
  ..$ FUN         :function (x)  
  ..$ outer       :Class 'formula'  language ~Source
  .. .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv> 
  ..$ inner       : NULL
  ..$ labels      :List of 1
  .. ..$ Thickness: chr "Thickness of oxide layer"
  ..$ units       : list()
   Wafer
Lot 1 2 3
  1 3 3 3
  2 3 3 3
  3 3 3 3
  4 3 3 3
  5 3 3 3
  6 3 3 3
  7 3 3 3
  8 3 3 3
Linear mixed model fit by REML ['lmerMod']
Formula: Thickness ~ 1 + (1 | Lot/Wafer)
   Data: Semi2
REML criterion at convergence: 454.0221
Random effects:
 Groups    Name        Std.Dev.
 Wafer:Lot (Intercept)  5.989  
 Lot       (Intercept) 11.396  
 Residual               3.545  
Number of obs: 72, groups:  Wafer:Lot, 24; Lot, 8
Fixed Effects:
(Intercept)  
       2000  
Linear mixed model fit by REML ['lmerMod']
Formula: Thickness ~ Source + (1 | Lot/Wafer)
   Data: Semi2
REML criterion at convergence: 446.4779
Random effects:
 Groups    Name        Std.Dev.
 Wafer:Lot (Intercept)  5.989  
 Lot       (Intercept) 10.950  
 Residual               3.545  
Number of obs: 72, groups:  Wafer:Lot, 24; Lot, 8
Fixed Effects:
(Intercept)      Source1  
    2005.19       -10.08  
Analysis of Variance Table
       Df Sum Sq Mean Sq F value
Source  1 19.179  19.179  1.5259
Linear mixed model fit by REML ['lmerMod']
Formula: Thickness ~ Source + (1 | Lot/Wafer) + (1 | Lot:Source)
   Data: Semi2
REML criterion at convergence: 446.4779
Random effects:
 Groups     Name        Std.Dev.
 Wafer:Lot  (Intercept) 5.989   
 Lot        (Intercept) 4.841   
 Lot:Source (Intercept) 9.808   
 Residual               3.546   
Number of obs: 72, groups:  Wafer:Lot, 24; Lot, 8; Lot:Source, 8
Fixed Effects:
(Intercept)      Source1  
    2005.19       -10.08  
convergence code 0; 2 optimizer warnings; 0 lme4 warnings 
Warning messages:
1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  unable to evaluate scaled gradient
2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv,  :
  Model failed to converge: degenerate  Hessian with 1 negative eigenvalues

SASmixed documentation built on May 1, 2019, 9:18 p.m.