| Type: | Package |
| Title: | Additive Heredity Model: Method for the Mixture-of-Mixtures Experiments |
| Version: | 1.0.1 |
| Maintainer: | Sumin Shen <sumin@vt.edu> |
| Description: | An implementation of the additive heredity model for the mixture-of-mixtures experiments of Shen et al. (2019) in Technometrics <doi:10.1080/00401706.2019.1630010>. The additive heredity model considers an additive structure to inherently connect the major components with the minor components. The additive heredity model has a meaningful interpretation for the estimated model because of the hierarchical and heredity principles applied and the nonnegative garrote technique used for variable selection. |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| LazyData: | true |
| Imports: | mixexp, plgp, devtools, dplyr, tibble, tidyr, Matrix |
| Depends: | R (≥ 2.10), quadprog, glmnet |
| Suggests: | knitr, rmarkdown, partitions |
| VignetteBuilder: | knitr |
| BuildVignettes: | yes |
| RoxygenNote: | 6.0.1 |
| NeedsCompilation: | no |
| Packaged: | 2019-07-25 12:10:43 UTC; shen |
| Author: | Sumin Shen [aut, cre], Lulu Kang [aut], Xinwei Deng [aut] |
| Repository: | CRAN |
| Date/Publication: | 2019-07-28 09:00:05 UTC |
This is one of the main functions. The function ahm computes the proposed additive heredity model.
Description
This is one of the main functions. The function ahm computes the proposed additive heredity model.
Usage
ahm(y, x, num_major = 3, dist_minor = c(2, 2, 1), type = "weak",
alpha = 0, lambda_seq = seq(0, 5, 0.01), nfolds = NULL,
mapping_type = c("power"), powerh = 0, rep_gcv = 100)
Arguments
y |
numeric vector |
x |
data.frame Note the column names of the x should be in the order of major components, minor components, and no interactions are needed. |
num_major |
number of major components |
dist_minor |
the allocation of number of minor components nested under major components |
type |
heredity type, weak heredity is the current support type |
alpha |
0 is for the ridge in glmnet https://web.stanford.edu/~hastie/glmnet/glmnet_alpha.html |
lambda_seq |
a numeric vector for the options of lambda used in ridge regression for estimating the initials |
nfolds |
used in cv.glmnet for initial value of parameters in the non-negative garrote method |
mapping_type |
the form of the coefficient function of major components in front of corresponding minor terms. Currently only support "power" |
powerh |
the power parameter used for the power function |
rep_gcv |
the number of choices of tuning parameter used in the GCV selection |
Value
Return a list
Examples
data("pringles_fat")
data_fat = pringles_fat
h_tmp = 1.3
x = data_fat[,c("c1","c2","c3","x11","x12","x21","x22")]
y = data_fat[,1]
out = ahm (y, x, num_major = 3, dist_minor = c(2,2,1),
type = "weak", alpha=0, lambda_seq=seq(0,5,0.01), nfold = NULL,
mapping_type = c("power"), powerh = h_tmp,
rep_gcv=100)
summary(out)
Check column correlations
Description
Check column correlations
Usage
check_col_correlation(dat)
Arguments
dat |
data.frame |
Examples
data("pringles_fat")
data_fat = pringles_fat
h_tmp = 1.3
x = data_fat[,c("c1","c2","c3","x11","x12","x21","x22")]
check_col_correlation (dat=x)
Photoresist-coating experiment data
Description
Photoresist-coating experiment data
Usage
data(coating)
Format
data.frame
References
Cornell, J.A. and Ramsey, P.J. (1998). A Generalized mixture model for categorized-components problems with an application to a photoresist-coating experiment. Technometrics, 40(1), 48-61. (tandfonline)
Examples
data(coating)
print(coating)
Coefficient method for the fitted ahm object
Description
Coefficient method for the fitted ahm object
Usage
## S3 method for class 'ahm'
coef(object, ...)
Arguments
object |
ahm object |
... |
not used |
Value
a numerical vector
Examples
data("pringles_fat")
data_fat = pringles_fat
h_tmp = 1.3
x = data_fat[,c("c1","c2","c3","x11","x12","x21","x22")]
y = data_fat[,1]
out = ahm (y, x, num_major = 3, dist_minor = c(2,2,1),
type = "weak", alpha=0, lambda_seq=seq(0,5,0.01), nfold = NULL,
mapping_type = c("power"), powerh = h_tmp,
rep_gcv=100)
coef(out)
Coefficient method for the fitted cv.ahm object
Description
Coefficient method for the fitted cv.ahm object
Usage
## S3 method for class 'cv.ahm'
coef(object, metric = "mse", ...)
Arguments
object |
cv.ahm object |
metric |
"mse" or "aicc" |
... |
not used |
Value
a numerical vector
Examples
data("pringles_fat")
data_fat = pringles_fat
h_tmp = 1.3
x = data_fat[,c("c1","c2","c3","x11","x12","x21","x22")]
y = data_fat[,1]
powerh_path = round(seq(0.001,2,length.out =15),3)
num_major = 3; dist_minor = c(2,2,1)
res = cv.ahm (y, x, powerh_path=powerh_path, metric = "mse", num_major, dist_minor, type = "weak"
, alpha=0, lambda_seq=seq(0,5,0.01), nfolds=NULL, mapping_type = c("power"), rep_gcv=100)
coefficients = coef(res)
compute AICc
Description
compute AICc
Usage
compute_aicc(rss, n, p, type = "AICc")
Arguments
rss |
residual sum of squares |
n |
number of observation |
p |
number of nonzero parameters |
type |
character "AICc" |
References
Calculating AIC “by hand” in R in Stack Overflow
Examples
compute_aicc (rss=10, n=30, p=6, type = "AICc")
This is one of the main functions. It perform the cross validation on ahm models to select the optimal setting of hyper parameter h
Description
This is one of the main functions. It perform the cross validation on ahm models to select the optimal setting of hyper parameter h
Usage
cv.ahm(y, x, powerh_path = NULL, metric = c("mse", "AICc"), num_major = 3,
dist_minor = c(2, 2, 1), type = "weak", alpha = 0, lambda_seq = seq(0,
5, 0.01), nfolds = NULL, mapping_type = c("power"), rep_gcv = 100)
Arguments
y |
numeric vector |
x |
data.frame Note the column names of the x should be in the order of major components, minor components, and no interactions between major or minor components are needed. |
powerh_path |
if NULL, then the default is the vector: round(seq(0.001,2,length.out =15),3) |
metric |
"mse" or "AICc" the metric used in cross validtion where the minimum is selected as the optimal |
num_major |
number of major components |
dist_minor |
the allocation of number of minor components nested under major components |
type |
heredity type, weak heredity is the current support type |
alpha |
0 is for the ridge in glmnet https://web.stanford.edu/~hastie/glmnet/glmnet_alpha.html |
lambda_seq |
a numeric vector for the options of lambda used in ridge regression for estimating the initials |
nfolds |
used in cv.glmnet for initial value of parameters in the non-negative garrote method |
mapping_type |
the form of the coefficient function of major components in front of corresponding minor terms. Currently only support "power" |
rep_gcv |
the number of choices of tuning parameter used in the GCV selection |
Value
Return a list
Examples
data("pringles_fat")
data_fat = pringles_fat
h_tmp = 1.3
x = data_fat[,c("c1","c2","c3","x11","x12","x21","x22")]
y = data_fat[,1]
powerh_path = round(seq(0.001,2,length.out =15),3)
num_major = 3; dist_minor = c(2,2,1)
res = cv.ahm (y, x, powerh_path=powerh_path, metric = "mse", num_major, dist_minor, type = "weak"
, alpha=0, lambda_seq=seq(0,5,0.01), nfolds=NULL, mapping_type = c("power"), rep_gcv=100)
object = res$metric_mse
Design points for the simplex centroid design with 3 components
Description
Design points for the simplex centroid design with 3 components
Usage
data(design_simplex_centroid_design_3_major_component)
Format
data.frame
Examples
data(design_simplex_centroid_design_3_major_component)
print(design_simplex_centroid_design_3_major_component)
Create a list
Description
Create a list
Usage
enlist(...)
Arguments
... |
object to be included as elements in the list |
Examples
item = c(1:10)
enlist(item)
Expand the interaction terms for each subset group, say x11, x12, or c1, c2, c3
Description
Expand the interaction terms for each subset group, say x11, x12, or c1, c2, c3
Usage
expand_interactions(dat, sel_names)
Arguments
dat |
data frame |
sel_names |
characters |
Examples
data("pringles_fat")
data_fat = pringles_fat
h_tmp = 1.3
x = data_fat[,c("c1","c2","c3","x11","x12","x21","x22")]
expand_interactions (dat=x, sel_names=c("c1", "c2", "c3"))
Compute the conditional number of design matrix
Description
Compute the conditional number of design matrix
Usage
find_condition_num(x)
Arguments
x |
matrix to be used in svd |
Examples
data("pringles_fat")
data_fat = pringles_fat
h_tmp = 1.3
x = data_fat[,c("c1","c2","c3","x11","x12","x21","x22")]
find_condition_num (x)
Mapping_function is a function to add the functional coefficients of major components in front of minor components terms
Description
Mapping_function is a function to add the functional coefficients of major components in front of minor components terms
Usage
mapping_function(x, num_major = 3, dist_minor = C(2, 2, 1),
mapping_type = c("power"), powerh = 0)
Arguments
x |
data.frame Note the column names of the x should be in the order of major components, minor components, and no interactions are needed. |
num_major |
number of major components |
dist_minor |
the allocation of number of minor components nested under major components |
mapping_type |
the form of the coefficient function of major components in front of corresponding minor terms. Currently only support "power" |
powerh |
the power parameter used for the power function |
Value
data frame
Examples
data("pringles_fat")
data_fat = pringles_fat
h_tmp = 1.3
x = data_fat[,c("c1","c2","c3","x11","x12","x21","x22")]
mapping_function(x=x, num_major=3, dist_minor=c(2,2,1), mapping_type = c("power"), powerh=0)
The mymaximin function generates the matrix of maximin design points. It uses the simplex centroid design as the base design, then in a stochastics way sample the candidate design points generated by the function partition.
Description
This method is modified based on Prof. Bobby Gramacy's Computer Experiment lecture at Virginia Tech. Prof. Gramacy's lecture website
Usage
mymaximin(pool, n = 50, m = 3, iter = 1e+05, Xorig = NULL)
Arguments
pool |
partition the base design points provided to the function |
n |
numeric, sample size |
m |
numeric, 3 stands for 3 components, i.e. c1, c2, and c3 |
iter |
numeric, iterations used in the stochastic sampling |
Xorig |
matrix, initial design points |
Value
Return a matrixt of the design points for the major components
Examples
# The case of unconstrainted experiments
library(mixexp)
num_size = 8 # num points in the design for the major component
Xorig = as.matrix(SCD(3))
# all possible combinations sum to 1
pool_3d =partitions::compositions(1000, 3,include.zero = TRUE)/1000
res_C = mymaximin(pool=pool_3d, n=num_size, m=3, iter=1e5, Xorig=Xorig)
DesignPoints(res_C,cornerlabs = c("c3","c2","c1"),axislabs=c("c1","c2","c3"))
# The case of constrainted experiments
library(mixexp)
num_size = 8 # num points in the design for the major component
# all possible combinations sum to 1
pool_3d =partitions::compositions(1000, 3,include.zero = TRUE)/1000
c1_min=0.2
c1_max=0.45
c2_min=0.4
c2_max=0.6
c3_min=0.1
c3_max=0.25
tmp = Xvert(nfac=3,lc=c(c1_min,c2_min,c3_min),uc =c(c1_max,c2_max,c3_max),ndm=1,pseudo=FALSE)
Xorig=tmp[c(1:6,13),c(1:3)]
colnames(Xorig)=c("V1","V2","V3")
pool_3d = t(dplyr::filter(as.data.frame(t(as.matrix(pool_3d))),t(pool_3d)[,1] > c1_min &
t(pool_3d)[,1] <= c1_max &
t(pool_3d)[,2] > c2_min &
t(pool_3d)[,2] <= c2_max &
t(pool_3d)[,3] > c3_min &
t(pool_3d)[,3] <= c3_max
)
)
res_C = mymaximin(pool=pool_3d, n=num_size, m=3, iter=1e5, Xorig=Xorig)
DesignPoints(res_C,cornerlabs = c("c3","c2","c1"),axislabs=c("c1","c2","c3")
,x1lower=c1_min,x2lower=c2_min,x3lower=c3_min
,x1upper=c1_max,x2upper=c2_max,x3upper=c3_max, pseudo=FALSE)
Predict method for the fitted ahm object
Description
Predict method for the fitted ahm object
Usage
## S3 method for class 'ahm'
predict(object, newx, ...)
Arguments
object |
ahm object |
newx |
Matrix of new values for x at which predictions are to be made. |
... |
not used |
Value
predicted value(s) at newx
Examples
data("pringles_fat")
data_fat = pringles_fat
h_tmp = 1.3
x = data_fat[,c("c1","c2","c3","x11","x12","x21","x22")]
y = data_fat[,1]
out = ahm (y, x, num_major = 3, dist_minor = c(2,2,1),
type = "weak", alpha=0, lambda_seq=seq(0,5,0.01), nfold = NULL,
mapping_type = c("power"), powerh = h_tmp,
rep_gcv=100)
predict(out)
Predict method for the fitted cv.ahm object
Description
Predict method for the fitted cv.ahm object
Usage
## S3 method for class 'cv.ahm'
predict(object, newx, metric = "mse", ...)
Arguments
object |
cv.ahm object |
newx |
Matrix of new values for x at which predictions are to be made. |
metric |
"mse" or "aicc" |
... |
not used |
Value
Return a list
Examples
data("pringles_fat")
data_fat = pringles_fat
h_tmp = 1.3
x = data_fat[,c("c1","c2","c3","x11","x12","x21","x22")]
y = data_fat[,1]
powerh_path = round(seq(0.001,2,length.out =15),3)
num_major = 3; dist_minor = c(2,2,1)
res = cv.ahm (y, x, powerh_path=powerh_path, metric = "mse", num_major, dist_minor, type = "weak"
, alpha=0, lambda_seq=seq(0,5,0.01), nfolds=NULL, mapping_type = c("power"), rep_gcv=100)
pred = predict(res)
The candidate search points in the nonlinear optimization for the optimal value in the Pringles experiment
Description
The candidate search points in the nonlinear optimization for the optimal value in the Pringles experiment
Usage
data(pringles_candidates2search)
Format
matrix
Examples
data(pringles_candidates2search)
print(pringles_candidates2search)
Pringles experiment data set with the percent of Fat as the response
Description
Pringles experiment data set with the percent of Fat as the response
Usage
data(pringles_fat)
Format
data.frame
References
Kang, L., Joseph, V.R. and Brenneman, W.A. (2011). Design and modeling strategies for mixture-of-mixtures experiments. Technometrics, 53(2), 125–36. (tandfonline)
Examples
data(pringles_fat)
print(pringles_fat)
Pringles experiment data set with the Hardness as the response
Description
Pringles experiment data set with the Hardness as the response
Usage
data(pringles_hardness)
Format
data.frame
References
Kang, L., Joseph, V.R. and Brenneman, W.A. (2011). Design and modeling strategies for mixture-of-mixtures experiments. Technometrics, 53(2), 125–36. (tandfonline)
Examples
data(pringles_hardness)
print(pringles_hardness)
Summary method for the fitted ahm object
Description
Summary method for the fitted ahm object
Usage
## S3 method for class 'ahm'
summary(object, ...)
Arguments
object |
fitted ahm object |
... |
not used |
Examples
data("pringles_fat")
data_fat = pringles_fat
h_tmp = 1.3
x = data_fat[,c("c1","c2","c3","x11","x12","x21","x22")]
y = data_fat[,1]
out = ahm (y, x, num_major = 3, dist_minor = c(2,2,1),
type = "weak", alpha=0, lambda_seq=seq(0,5,0.01), nfold = NULL,
mapping_type = c("power"), powerh = h_tmp,
rep_gcv=100)
summary(out)