Package 'SASmixed'

Animal breeding experiment

Description

The Animal data frame has 20 rows and 3 columns giving the average daily weight gains for animals with different genetic backgrounds.

Format

This data frame contains the following columns:

Sire

a factor denoting the sire. (5 levels)

Dam

a factor denoting the dam. (2 levels)

AvgDailyGain

a numeric vector of average daily weight gains

Details

This appears to be a constructed data set.

Source

Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, SAS Institute (Data Set 6.4).

Examples

str(Animal)

---

Average daily weight gain of steers on different diets

Description

The AvgDailyGain data frame has 32 rows and 6 columns.

Format

This data frame contains the following columns:

Id

the animal number

Block

an ordered factor indicating the barn in which the steer was housed.

Treatment

an ordered factor with levels 0 < 10 < 20 < 30 indicating the amount of medicated feed additive added to the base ration.

adg

a numeric vector of average daily weight gains over a period of 160 days.

InitWt

a numeric vector giving the initial weight of the animal

Trt

the Treatment as a numeric variable

Source

Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, SAS Institute (Data Set 5.3).

Examples

str(AvgDailyGain)
if (require("lattice", quietly = TRUE, character = TRUE)) {
  ## plot of adg versus Treatment by Block
  xyplot(adg ~ Treatment | Block, AvgDailyGain, type = c("g", "p", "r"),
         xlab = "Treatment (amount of feed additive)",
         ylab = "Average daily weight gain (lb.)", aspect = "xy",
         index.cond = function(x, y) coef(lm(y ~ x))[1])
}
if (require("lme4", quietly = TRUE, character = TRUE)) {
  options(contrasts = c(unordered = "contr.SAS", ordered = "contr.poly"))
  ## compare with output 5.1, p. 178
  print(fm1Adg <- lmer(adg ~ InitWt * Treatment - 1 + (1 | Block),
                         AvgDailyGain))
  print(anova(fm1Adg))   # checking significance of terms
  print(fm2Adg <- lmer(adg ~ InitWt + Treatment + (1 | Block),
                         AvgDailyGain))
  print(anova(fm2Adg))
  print(lmer(adg ~ InitWt + Treatment - 1 + (1 | Block), AvgDailyGain))
}

---

Data from a balanced incomplete block design

Description

The BIB data frame has 24 rows and 5 columns.

Format

This data frame contains the following columns:

Block

an ordered factor with levels 1 < 2 < 3 < 8 < 5 < 4 < 6 < 7

Treatment

a treatment factor with levels 1 to 4.

y

a numeric vector representing the response

x

a numeric vector representing the covariate

Grp

a factor with levels 13 and 24

Details

These appear to be constructed data.

Source

Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, SAS Institute (Data Set 5.4).

Examples

str(BIB)
if (require("lattice", quietly = TRUE, character = TRUE)) {
  xyplot(y ~ x | Block, BIB, groups = Treatment, type = c("g", "p"),
         aspect = "xy", auto.key = list(points = TRUE, space = "right",
         lines = FALSE))
}
if (require("lme4", quietly = TRUE, character = TRUE)) {
  options(contrasts = c(unordered = "contr.SAS", ordered = "contr.poly"))
  ## compare with Output 5.7, p. 188
  print(fm1BIB <- lmer(y ~ Treatment * x + (1 | Block), BIB))
  print(anova(fm1BIB))     # strong evidence of different slopes
  ## compare with Output 5.9, p. 193
  print(fm2BIB <- lmer(y ~ Treatment + x : Grp + (1 | Block), BIB))
  print(anova(fm2BIB))
}

---

Strengths of metal bonds

Description

The Bond data frame has 21 rows and 3 columns of data on the strength required to break metal bonds according to the metal and the ingot.

Format

This data frame contains the following columns:

pressure

a numeric vector of pressures required to break the bond

Metal

a factor with levels c, i and n indicating the metal involved (copper, iron or nickel).

Ingot

an ordered factor indicating the ingot of the composition material.

Source

Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, SAS Institute (Data Set 1.2.4).

Mendenhall, M., Wackerly, D. D. and Schaeffer, R. L. (1990), Mathematical Statistics, Wadsworth (Exercise 13.36).

Examples

str(Bond)
options(contrasts = c(unordered = "contr.SAS", ordered = "contr.poly"))
if (require("lme4", quietly = TRUE, character = TRUE)) {
  ## compare with output 1.1 on p. 6
  print(fm1Bond <- lmer(pressure ~ Metal + (1|Ingot), Bond))
  print(anova(fm1Bond))
}

---

Bacterial innoculation applied to grass cultivars

Description

The Cultivation data frame has 24 rows and 4 columns of data from an experiment on the effect on dry weight yield of three bacterial inoculation treatments applied to two grass cultivars.

Format

This data frame contains the following columns:

Block

a factor with levels 1 to 4

Cult

the cultivar factor with levels a and b

Inoc

the innoculant factor with levels con, dea and liv

drywt

a numeric vector of dry weight yields

Source

Littell, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, SAS Institute (Data Set 2.2(a)).

Littel, R. C., Freund, R. J., and Spector, P. C. (1991), SAS System for Linear Models, Third Ed., SAS Institute.

Examples

str(Cultivation)
xtabs(~Block+Cult, Cultivation)
if (require("lme4", quietly = TRUE, character = TRUE)) {
  options(contrasts = c(unordered = "contr.SAS", ordered = "contr.poly"))
  ## compare with Output 2.10, page 58
  print(fm1Cult <- lmer(drywt ~ Inoc * Cult + (1|Block) + (1|Cult),
                          Cultivation))
  print(anova(fm1Cult))
  print(fm2Cult <- lmer(drywt ~ Inoc + Cult + (1|Block) + (1|Cult),
                          Cultivation))
  print(anova(fm2Cult))
  print(fm3Cult <- lmer(drywt ~ Inoc + (1|Block) + (1|Cult), Cultivation))
  print(anova(fm3Cult))
}

---

Per-capita demand deposits by state and year

Description

The Demand data frame has 77 rows and 8 columns of data on per-capita demand deposits by state and year.

Format

This data frame contains the following columns:

State

an ordered factor with levels WA < FL < CA < TX < IL < DC < NY

Year

an ordered factor with levels 1949 < ... < 1959

d

a numeric vector of per-capita demand deposits

y

a numeric vector of permanent per-capita personal income

rd

a numeric vector of service charges on demand deposits

rt

a numeric vector of interest rates on time deposits

rs

a numeric vector of interest rates on savings and loan association shares.

Source

Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, SAS Institute (Data Set 1.2.4).

Feige, E. L. (1964), The Demand for Liquid Assets: A Temporal Cross-Sectional Analysis., Prentice Hall.

Examples

str(Demand)
if (require("lme4", quietly = TRUE, character = TRUE)) {
  ## compare to output 3.13, p. 132
  summary(fm1Demand <-
      lmer(log(d) ~ log(y) + log(rd) + log(rt) + log(rs) + (1|State) + (1|Year),
         Demand))
}

---

Heritability data

Description

The Genetics data frame has 60 rows and 4 columns.

Format

This data frame contains the following columns:

Location

a factor with levels 1 to 4

Block

a factor with levels 1 to 3

Family

a factor with levels 1 to 5

Yield

a numeric vector of crop yields

Source

Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, SAS Institute (Data Set 4.5).

Examples

str(Genetics)
if (require("lme4", quietly = TRUE, character = TRUE)) {
  options(contrasts = c(unordered = "contr.SAS", ordered = "contr.poly"))
  summary(fm1Gen <- lmer(Yield ~ Family + (1|Location/Block), Genetics))
}

---

Heart rates of patients on different drug treatments

Description

The HR data frame has 120 rows and 5 columns of the heart rates of patients under one of three possible drug treatments.

Format

This data frame contains the following columns:

Patient

an ordered factor indicating the patient.

Drug

the drug treatment - a factor with levels a, b and p where p represents the placebo.

baseHR

the patient's base heart rate

HR

the observed heart rate at different times in the experiment

Time

the time of the observation

Source

Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, SAS Institute (Data Set 3.5).

Examples

str(HR)
if (require("lattice", quietly = TRUE, character = TRUE)) {
  xyplot(HR ~ Time | Patient, HR, type = c("g", "p", "r"), aspect = "xy",
         index.cond = function(x, y) coef(lm(y ~ x))[1],
         ylab = "Heart rate (beats/min)")
}
if (require("lme4", quietly = TRUE, character = TRUE)) {
  options(contrasts = c(unordered = "contr.SAS", ordered = "contr.poly"))
  ## linear trend in time
  print(fm1HR <- lmer(HR ~ Time * Drug + baseHR + (Time|Patient), HR))  
  print(anova(fm1HR))
## Not run: 
fm2HR <- update(fm1HR, weights = varPower(0.5)) # use power-of-mean variance
summary(fm2HR)
intervals(fm2HR)             # variance function does not seem significant
anova(fm1HR, fm2HR)         # confirm with likelihood ratio

## End(Not run)
 print(fm3HR <- lmer(HR ~ Time + Drug + baseHR + (Time|Patient), HR))
 print(anova(fm3HR))
 ## remove Drug term
 print(fm4HR <- lmer(HR ~ Time + baseHR + (Time|Patient), HR))
 print(anova(fm4HR))
}

---

An unbalanced incomplete block experiment

Description

The IncBlk data frame has 24 rows and 4 columns.

Format

This data frame contains the following columns:

Block

an ordered factor giving the block

Treatment

a factor with levels 1 to 4

y

a numeric vector

x

a numeric vector

Details

These data are probably constructed data.

Source

Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, SAS Institute (Data Set 5.5).

Examples

str(IncBlk)

---

Nitrogen concentrations in the Mississippi River

Description

The Mississippi data frame has 37 rows and 3 columns.

Format

This data frame contains the following columns:

influent

an ordered factor with levels 3 < 5 < 2 < 1 < 4 < 6

y

a numeric vector

Type

a factor with levels 1 2 3

Source

Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, SAS Institute (Data Set 4.2).

Examples

str(Mississippi)
if (require("lattice", quietly = TRUE, character = TRUE)) {
  dotplot(drop(influent:Type) ~ y, groups = Type, Mississippi)
} 
if (require("lme4", quietly = TRUE, character = TRUE)) {
  options(contrasts = c(unordered = "contr.SAS", ordered = "contr.poly"))
  ## compare with output 4.1, p. 142
  print(fm1Miss <- lmer(y ~ 1 + (1|influent), Mississippi))
  ## compare with output 4.2, p. 143
  print(fm1MLMiss <- update(fm1Miss, REML=FALSE))
  ## BLUP's of random effects on p. 142
  ranef(fm1Miss)            
  ## BLUP's of random effects on p. 144
  print(ranef(fm1MLMiss))
#intervals(fm1Miss)       # interval estimates of variance components
  ## compare to output 4.8 and 4.9, pp. 150-152
  print(fm2Miss <- lmer(y ~ Type+(1|influent), Mississippi, REML=TRUE))
  print(anova(fm2Miss))
}

---

A multilocation trial

Description

The Multilocation data frame has 108 rows and 7 columns.

Format

This data frame contains the following columns:

obs

a numeric vector

Location

an ordered factor with levels B < D < E < I < G < A < C < F < H

Block

a factor with levels 1 to 3

Trt

a factor with levels 1 to 4

Adj

a numeric vector

Fe

a numeric vector

Grp

an ordered factor with levels B/1 < B/2 < B/3 < D/1 < D/2 < D/3 < E/1 < E/2 < E/3 < I/1 < I/2 < I/3 < G/1 < G/2 < G/3 < A/1 < A/2 < A/3 < C/1 < C/2 < C/3 < F/1 < F/2 < F/3 < H/1 < H/2 < H/3

Source

Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, SAS Institute (Data Set 2.8.1).

Examples

str(Multilocation)
if (require("lme4", quietly = TRUE, character = TRUE)) {
  options(contrasts = c(unordered = "contr.SAS", ordered = "contr.poly"))
  ### Create a Block %in% Location factor
  Multilocation$Grp <- with(Multilocation, Block:Location)
  print(fm1Mult <- lmer(Adj ~ Location * Trt + (1|Grp), Multilocation))
  print(anova(fm1Mult))
  print(fm2Mult <- lmer(Adj ~ Location + Trt + (1|Grp), Multilocation), corr=FALSE)
  print(fm3Mult <- lmer(Adj ~ Location + (1|Grp), Multilocation), corr=FALSE)
  print(fm4Mult <- lmer(Adj ~ Trt + (1|Grp), Multilocation))
  print(fm5Mult <- lmer(Adj ~ 1 + (1|Grp), Multilocation))
  print(anova(fm2Mult))
  print(anova(fm1Mult, fm2Mult, fm3Mult, fm4Mult, fm5Mult))
  ### Treating the location as a random effect
  print(fm1MultR <- lmer(Adj ~ Trt + (1|Location/Trt) + (1|Grp), Multilocation))
  print(anova(fm1MultR))
  fm2MultR <- lmer(Adj ~ Trt + (Trt - 1|Location) + (1|Block), Multilocation)
  ## Warning (not error ?!): Convergence failure in 10000 iter %% __FIXME__
  print(fm2MultR)# does not mention previous conv.failure %% FIXME ??
  print(anova(fm1MultR, fm2MultR))
 ## Not run: 
  confint(fm1MultR)
 
## End(Not run)
}

---

A partially balanced incomplete block experiment

Description

The PBIB data frame has 60 rows and 3 columns.

Format

This data frame contains the following columns:

response

a numeric vector

Treatment

a factor with levels 1 to 15

Block

an ordered factor with levels 1 to 15

Source

Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, SAS Institute (Data Set 1.5.1).

Examples

str(PBIB)
if (require("lme4", quietly = TRUE, character = TRUE)) {
  options(contrasts = c(unordered = "contr.SAS", ordered = "contr.poly"))
  ## compare with output 1.7  pp. 24-25
  print(fm1PBIB <- lmer(response ~ Treatment + (1|Block), PBIB))
  print(anova(fm1PBIB))
}

---

Oxide layer thicknesses on semiconductors

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.
}

---

Semiconductor split-plot experiment

Description

The Semiconductor data frame has 48 rows and 5 columns.

Format

This data frame contains the following columns:

resistance

a numeric vector

ET

a factor with levels 1 to 4 representing etch time.

Wafer

a factor with levels 1 to 3

position

a factor with levels 1 to 4

Grp

an ordered factor with levels 1/1 < 1/2 < 1/3 < 2/1 < 2/2 < 2/3 < 3/1 < 3/2 < 3/3 < 4/1 < 4/2 < 4/3

Source

Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, SAS Institute (Data Set 2.2(b)).

Examples

str(Semiconductor)
if (require("lme4", quietly = TRUE, character = TRUE)) {
  options(contrasts = c(unordered = "contr.SAS", ordered = "contr.poly"))
  print(fm1Semi <- lmer(resistance ~ ET * position + (1|Grp), Semiconductor))
  print(anova(fm1Semi))
  print((fm2Semi <- lmer(resistance ~ ET + position + (1|Grp), Semiconductor)))
  print(anova(fm2Semi))
}

---

Second International Mathematics Study data

Description

The SIMS data frame has 3691 rows and 3 columns.

Format

This data frame contains the following columns:

Pretot

a numeric vector giving the student's pre-test total score

Gain

a numeric vector giving gains from pre-test to the final test

Class

an ordered factor giving the student's class

Source

Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, SAS Institute (section 7.2.2)

Kreft, I. G. G., De Leeuw, J. and Var Der Leeden, R. (1994), “Review of five multilevel analysis programs: BMDP-5V, GENMOD, HLM, ML3, and VARCL”, American Statistician, 48, 324–335.

Examples

str(SIMS)
if (require("lme4", quietly = TRUE, character = TRUE)) {
  options(contrasts = c(unordered = "contr.SAS", ordered = "contr.poly"))
  ## compare to output 7.4, p. 262
  print(fm1SIMS <- lmer(Gain ~ Pretot + (Pretot | Class), data = SIMS))
  print(anova(fm1SIMS))
}

---

Teaching Methods I

Description

The TeachingI data frame has 96 rows and 7 columns.

Format

This data frame contains the following columns:

Method

a factor with levels 1 to 3

Teacher

a factor with levels 1 to 4

Gender

a factor with levels f and m

Student

a factor with levels 1 to 4

score

a numeric vector

Experience

a numeric vector

uTeacher

an ordered factor with levels

Source

Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, SAS Institute (Data Set 5.6).

Examples

str(TeachingI)

---

Teaching Methods II

Description

The TeachingII data frame has 96 rows and 6 columns.

Format

This data frame contains the following columns:

Method

a factor with levels 1 to 3

Teacher

a factor with levels 1 to 4

Gender

a factor with levels f and m

IQ

a numeric vector

score

a numeric vector

uTeacher

an ordered factor with levels

Source

Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, SAS Institute (Data Set 5.7).

Examples

str(TeachingII)

---

Data on different types of silicon wafers

Description

The WaferTypes data frame has 144 rows and 8 columns.

Format

This data frame contains the following columns:

Group

a factor with levels 1 to 4

Temperature

an ordered factor with levels 900 < 1000 < 1100

Type

a factor with levels A and B

Wafer

a numeric vector

Site

a numeric vector

delta

a numeric vector

Thick

a numeric vector

uWafer

an ordered factor giving a unique code to each group, temperature, type and wafer combination.

Source

Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, SAS Institute (Data Set 5.8).

Examples

str(WaferTypes)

---

Data from a weight-lifting program

Description

The Weights data frame has 399 rows and 5 columns.

Format

This data frame contains the following columns:

strength

a numeric vector

Subject

a factor with levels 1 to 21

Program

a factor with levels CONT (continuous repetitions and weights), RI (repetitions increasing) and WI (weights increasing)

Subj

an ordered factor indicating the subject on which the measurement is made

Time

a numeric vector indicating the time of the measurement

Source

Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, SAS Institute (Data Set 3.2(a)).

Examples

str(Weights)
if (require("lme4", quietly = TRUE, character = TRUE)) {
  options(contrasts = c(unordered = "contr.SAS", ordered = "contr.poly"))
  ## compare with output 3.1, p. 91
  print(fm1Weight <- lmer(strength ~ Program * Time + (1|Subj), Weights))
  print(anova(fm1Weight))
  print(fm2Weight <- lmer(strength ~ Program * Time + (Time|Subj), Weights))
  print(anova(fm1Weight, fm2Weight))
## Not run: 
intervals(fm2Weight)
fm3Weight <- update(fm2Weight, correlation = corAR1())
anova(fm2Weight, fm3Weight)
fm4Weight <- update(fm3Weight, strength ~ Program * (Time + I(Time^2)),
                    random = ~Time|Subj)
summary(fm4Weight)
anova(fm4Weight)
intervals(fm4Weight)

## End(Not run)
}

---

Winter wheat

Description

The WWheat data frame has 60 rows and 3 columns.

Format

This data frame contains the following columns:

Variety

an ordered factor with 10 levels

Yield

a numeric vector of yields

Moisture

a numeric vector of soil moisture contents

Source

Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, SAS Institute (Data Set 7.2).

Examples

str(WWheat)

---