多层次传销从库（lme4）固定和随机效应设计矩阵(Design matrix for MLM fro

应用的上下文
我有一个随机的斜率和截距模型。还有的随机效应无数的水平。（待预测的），新的数据可以或者可以不具有所有这些级。

为了使这更具体，我在这张专辑的水平（与音乐收入的工作title ）。每张专辑可以多种类型进来format2 （CD，乙烯基，电子音频等）。我有收入，在每个类型的专辑每张专辑测量。该模型被指定为：

lmer(physical~ format2+ (0+format2|title))

问题是，未来的数据可能不具有任何的所有级别title或format2 。对于随机拦截，这是很容易解决与predict(..., allow.new.levels= TRUE) 但它是固定效应和随机斜坡问题。因此，我试图写一个函数来做到的灵活预测merMod对象，类似于lme4::predict.merMod ; 但将处理训练数据和预测数据之间的差异。这是常见的多是出于无知到的具体细节问题lme4::predict.merMod为别的。

问题描述
问题的关键是获得正确model.matrix()固定和随机效应计算两种预测和SE的。对于类的方法S3 merMod 只返回固定效应 。

基础stats::model.matrix()函数具有非常有限的文件。不幸的是，我没有自己要么在的统计模型或软件对数据进行分析，这似乎有这些功能背后的细节。

model.matrix()应该采取的模型公式和新的数据帧，并产生一个设计矩阵。但我发现了一个错误。您可以提供任何帮助将非常感激。

示例数据

dat1 <- structure(list(dt_scale = c(16, 16, 16, 16, 16, 16, 16, 16, 16, 
16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16), title = c("Bahia", 
"Jazz Moods: Brazilian Romance", "Quintessence", "Amadeus: The Complete Soundtrack Recording (Bicentennial Edition)", 
"Live In Europe", "We'll Play The Blues For You", "The Complete Village Vanguard Recordings, 1961", 
"The Isaac Hayes Movement", "Jazz Moods: Jazz At Week's End", 
"Blue In Green: The Concert In Canada", "The English Patient - Original Motion Picture Soundtrack", 
"The Unique Thelonious Monk", "Since We Met", "You're Gonna Hear From Me", 
"The Colors Of Latin Jazz: Cubop!", "The Colors Of Latin Jazz: Samba!", 
"Homecoming", "Consecration: The Final Recordings Part 2 - Live At Keystone Korner, September 1980", "More Creedence Gold", "The Stardust Session"), format2 = c("CD", "CD", 
"CD", "CD", "CD", "CD", "CD", "SuperAudio", "SuperAudio", "CD", "E Audio", "CD", 
"Vinyl", "CD", "E Audio", "CD", "CD", "CD", "CD", "CD"), mf_day = c(TRUE, 
TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, 
TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE), xmas = c(FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE), vday = c(FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, FALSE, 
FALSE, FALSE, FALSE, FALSE), yr_since_rel = c(16.9050969937038, 
8.41815617876864, 9.2991404674865, 25.0870296783559, 39.1267038232812, 
27.9156764326061, 9.11596751812513, 23.3052837112449, 14.3123922258974, 
30.5208152866414, 5.83025071417496, 21.3090003877291, 7.75022155568392, 
11.3601605287827, 0.849006673421519, 31.9918631305662, 13.8861905547041, 
12.8342695062012, 29.6916671402534, 13.5912612705038), physical = c(1327.17849171096, 
-110.2265302258, -795.37376268564, 355.06192702004, -1357.3492884345, 
-1254.93442612023, -816.713683621225, 881.201935773452, -3092.02845691036, 
-2268.6304275652, 907.347941142021, -699.130275178185, 377.867849132077, 
-1047.50531157311, 1460.25978951805, 1376.84579069304, 3619.03629114089, 
962.888173535704, 2514.77880599199, 2539.14958588771)), .Names = c("dt_scale", 
"title", "format2", "mf_day", "xmas", "vday", "yr_since_rel", 
"physical"), row.names = c(1L, 2L, 5L, 6L, 7L, 8L, 9L, 11L, 12L, 
13L, 14L, 15L, 20L, 22L, 23L, 25L, 27L, 32L, 35L, 36L), class = "data.frame")

公式：

f1 <- as.formula(~1 + dt_scale + yr_since_rel + format2 + (0 + format2 + mf_day + 
xmas + vday | title))

执行/错误

library(lme4)
model.matrix(f1, data= dat1)
Error in 0 + format2 : non-numeric argument to binary operator

请注意我也试图与该Orthodont数据; 但是，我得到一个不同的错误。

library(lme4)
data("Orthodont",package="MEMSS")
fm1 <- lmer(formula = distance ~ age*Sex + (1+age|Subject), data = Orthodont)
newdat <- expand.grid(
  age=c(8,10,12,14)
  , Sex=c("Male","Female")
  , distance = 0
  , Subject= c("F01", "F02")
)


f1 <- formula(fm1)[-2] # simpler code via Ben Bolker below
mm <- model.matrix(f1, newdat) # attempt to use model.matrix
Warning message
In Ops.factor(1 + age, Subject) : | not meaningful for factors

# use lme4:::mkNewReTrms as suggested in comments
mm <- lme4:::mkNewReTrms(f1, newdat) 
Error in lme4:::mkNewReTrms(f1, newdat) : object 'ReTrms' not found
In addition: Warning message:
In Ops.factor(1 + age, Subject) : | not meaningful for factors

# check if different syntax would fix this
mm <- lme4::mkNewReTrms(f1, newdat)
Error: 'mkNewReTrms' is not an exported object from 'namespace:lme4'
mm <- mkNewReTrms(f1, newdat)
Error: could not find function "mkNewReTrms"

Editted 15年8月12日 ：看在Github上的变化和GitHub库

Editted，2014年10：这个答案还不是很完善。还有与错误（请参阅下面的评论链）一对夫妇的使用情况。但它在大多数情况下。我会找一些点定稿。

我相信这个功能将解决更重要的问题，merMod对象准确的预测。 Bolker博士，还存在一些问题，在这里（如稀疏性和效率）; 但我相信该方法的工作原理：

data("Orthodont",package="MEMSS")
fm1 <- lmer(formula = distance ~ age*Sex + (1+age|Subject), data = Orthodont)
newdat <- expand.grid(
  age=c(8,10,12,14)
  , Sex=c("Male","Female")
  , distance = 0
  , Subject= c("F01", "F02")
)

predict.merMod2 <- function(object, newdat=NULL) {
# 01. get formula and build model matrix
  # current problem--model matrix is not sparse, as would be ideal
  f1 <- formula(object)[-2]
  z.fe <- model.matrix(terms(object), newdat)
  z.re <- t(lme4:::mkReTrms(findbars(f1), newdat)$Zt)
  mm <- cbind(z.fe, 
              matrix(z.re, nrow= dim(z.re)[1], ncol= dim(z.re)[2],
                     dimnames= dimnames(z.re)))

  # 02. extract random effect coefficients needed for the new data
  # (a) - determine number of coef
  len <- length(ranef(object)) 
  re.grp.len <- vector(mode= "integer", length= len) 
  for (i in 1:len) { # for each random group
    re.grp.len[i] <- dim(ranef(object)[[i]])[2] # number of columns (slope and intercept terms)
  }

  # (b) - create beta vector
  fe.names <- unique(colnames(mm)[1:length(fixef(object)) - 1])
  re.names <- unique(colnames(mm)[-c(1:length(fixef(object)) - 1)]) 
  beta.re <- as.vector(rep(NA, length= sum(re.grp.len) * length(re.names)), mode= "numeric")
  for (i in 1:len) {
    re.beta  <- ranef(object)[[i]][rownames(ranef(object)[[i]]) %in% re.names,] 
    ind.i <- sum(!is.na(beta.re)) + 1; ind.j <- length(as.vector(t(re.beta))) 
    beta.re[ind.i:ind.j]  <- as.vector(t(re.beta)) 
  }
  beta <- c(fixef(object)[names(fixef(object)) %in% fe.names], beta.re)
  # 03. execute prediction
  return(mm %*% beta)
}

predict.merMod2(fm1, newdat)