As McFadden (1978) showed, if the number of alternatives in a multinomial logit model is so large that computation becomes impossible, it is still feasible to obtain consistent estimates by randomly subsetting the alternatives, so that the estimated probabilities for each individual are based on the chosen alternative and C other randomly selected alternatives. In this case, the size of the subset of alternatives is C+1 for each individual.
My question is about the implementation of this algorithm in R. Is it already embedded in any multinomial logit package? If not - which seems likely based on what I know so far - how would one go about including the procedure in pre-existing packages without recoding extensively?
Not sure whether the question is more about doing the sampling of alternatives or the estimation of MNL models after sampling of alternatives. To my knowledge, there are no R packages that do sampling of alternatives (the former) so far, but the latter is possible with existing packages such as mlogit. I believe the reason is that the sampling process varies depending on how your data is organized, but it is relatively easy to do with a bit of your own code. Below is code adapted from what I used for this paper.
library(tidyverse)
# create artificial data
set.seed(6)
# data frame of choser id and chosen alt_id
id_alt <- data.frame(
id = 1:1000,
alt_chosen = sample(1:30, 1)
)
# data frame for universal choice set, with an alt-specific attributes (alt_x2)
alts <- data.frame(
alt_id = 1:30,
alt_x2 = runif(30)
)
# conduct sampling of 9 non-chosen alternatives
id_alt <- id_alt %>%
mutate(.alts_all =list(alts$alt_id),
# use weights to avoid including chosen alternative in sample
.alts_wtg = map2(.alts_all, alt_chosen, ~ifelse(.x==.y, 0, 1)),
.alts_nonch = map2(.alts_all, .alts_wtg, ~sample(.x, size=9, prob=.y)),
# combine chosen & sampled non-chosen alts
alt_id = map2(alt_chosen, .alts_nonch, c)
)
# unnest above data.frame to create a long format data frame
# with rows varying by choser id and alt_id
id_alt_lf <- id_alt %>%
select(-starts_with(".")) %>%
unnest(alt_id)
# join long format df with alts to get alt-specific attributes
id_alt_lf <- id_alt_lf %>%
left_join(alts, by="alt_id") %>%
mutate(chosen=ifelse(alt_chosen==alt_id, 1, 0))
require(mlogit)
# convert to mlogit data frame before estimating
id_alt_mldf <- mlogit.data(id_alt_lf,
choice="chosen",
chid.var="id",
alt.var="alt_id", shape="long")
mlogit( chosen ~ 0 + alt_x2, id_alt_mldf) %>%
summary()
It is, of course, possible without using the purrr::map functions, by using apply variants or looping through each row of id_alt.
Sampling of alternatives is not currently implemented in the mlogit package. As stated previously, the solution is to generate a data.frame with a subset of alternatives and then using mlogit (and importantly to use a formula with no intercepts). Note that mlogit can deal with unbalanced data, ie the number of alternatives doesn't have to be the same for all the choice situations.
My recommendation would be to review the mlogit package.
Vignette:
https://cran.r-project.org/web/packages/mlogit/vignettes/mlogit2.pdf
the package has a set of example exercises that (in my opinion) are worth looking at:
https://cran.r-project.org/web/packages/mlogit/vignettes/Exercises.pdf
You may also want to take a look at the gmnl package (I have not used it)
https://cran.r-project.org/web/packages/gmnl/index.html
Multinomial Logit Models with Continuous and Discrete Individual Heterogeneity in R: The gmnl Package
Mauricio Sarrias' (Author) gmnl Web page
Question: What specific problem(s) are you trying to apply a multinomial logit model too? Suitably intrigued.
Aside from the above question, I hope the above points you in the right direction.
Related
I have a panel dataset (countries and years) with a lot of missing data so I've decided to use multiple imputation. The goal is to see the relationship between the proportion of women in management (managerial_value) and total fatal workplace injuries (total_fatal)
From what I've read online, Amelia is the best option for panel data so I used that like so:
amelia_data <- amelia(spdata, ts = "year", cs = "country", polytime = 1,
intercs = FALSE)
where spdata is my original dataset.
This imputation process worked, but I'm unsure of how to proceed with forming decision trees using the imputed data (an object of class 'amelia').
I originally tried creating a function (amelia2df) to turn each of the 5 imputed datasets into a data frame:
amelia2df <- function(amelia_data, which_imp = 1) {
stopifnot(inherits(amelia_data, "amelia"), is.numeric(which_imp))
imps <- amelia_data$imputations[[which_imp]]
as.data.frame(imps)
}
one_amelia <- amelia2df(amelia_data, which_imp = 1)
two_amelia <- amelia2df(amelia_data, which_imp = 2)
three_amelia <- amelia2df(amelia_data, which_imp = 3)
four_amelia <- amelia2df(amelia_data, which_imp = 4)
five_amelia <- amelia2df(amelia_data, which_imp = 5)
where one_amelia is the data frame for the first imputed dataset, two_amelia is the second, and so on.
I then combined them using rbind():
total_amelia <- rbind(one_amelia, two_amelia, three_amelia, four_amelia, five_amelia)
And used the new combined dataset total_amelia to construct a decision tree:
set.seed(300)
tree_data <- total_amelia
I_index <- sample(1:nrow(tree_data), size = 0.75*nrow(tree_data), replace=FALSE)
I_train <- tree_data[I_index,]
I_test <- tree_data[-I_index,]
fatal_tree <- rpart(total_fatal ~ managerial_value, I_train)
rpart.plot(fatal_tree)
fatal_tree
This "works" as in it doesn't produce an error, but I'm not sure that it is appropriately using the imputed data.
I found a couple resources explaining how to apply least squares, logit, etc., but nothing about decision trees. I'm under the impression I'd need the 5 imputed datasets to be combined into one data frame, but I have not been able to find a way to do that.
I've also looked into Zelig and bind_rows but haven't found anything that returns one data frame that I can then use to form a decision tree.
Any help would be appreciated!
As already indicated by #Noah, you would set up the multiple imputation workflow different than you currently do.
Multiple imputation is not really a tool to improve your results or to make them more correct.
It is a method to enable you to quantify the uncertainty caused by the missing data, that comes along with your analysis.
All the different datasets created by multiple imputation are plausible imputations, because of the uncertainty, you don't know, which one is correct.
You would therefore use multiple imputation the following way:
Create your m imputed datasets
Build your trees on each imputed dataset separately
Do you analysis on each tree separately
In your final paper, you can now state how much uncertainty is caused trough the missing values/imputation
This means you get e.g. 5 different analysis results for m = 5 imputed datasets. First this looks confusing, but this enables you to give bounds, between the correct result probably lies. Or if you get completely different results for each imputed dataset, you know, there is too much uncertainty caused by the missing values to give reliable results.
Long story short:
I need to run a multinomial logit regression with both individual and time fixed effects in R.
I thought I could use the packages mlogit and survival to this purpose, but I am cannot find a way to include fixed effects.
Now the long story:
I have found many questions on this topic on various stack-related websites, none of them were able to provide an answer. Also, I have noticed a lot of confusion regarding what a multinomial logit regression with fixed effects is (people use different names) and about the R packages implementing this function.
So I think it would be beneficial to provide some background before getting to the point.
Consider the following.
In a multiple choice question, each respondent take one choice.
Respondents are asked the same question every year. There is no apriori on the extent to which choice at time t is affected by the choice at t-1.
Now imagine to have a panel data recording these choices. The data, would look like this:
set.seed(123)
# number of observations
n <- 100
# number of possible choice
possible_choice <- letters[1:4]
# number of years
years <- 3
# individual characteristics
x1 <- runif(n * 3, 5.0, 70.5)
x2 <- sample(1:n^2, n * 3, replace = F)
# actual choice at time 1
actual_choice_year_1 <- possible_choice[sample(1:4, n, replace = T, prob = rep(1/4, 4))]
actual_choice_year_2 <- possible_choice[sample(1:4, n, replace = T, prob = c(0.4, 0.3, 0.2, 0.1))]
actual_choice_year_3 <- possible_choice[sample(1:4, n, replace = T, prob = c(0.2, 0.5, 0.2, 0.1))]
# create long dataset
df <- data.frame(choice = c(actual_choice_year_1, actual_choice_year_2, actual_choice_year_3),
x1 = x1, x2 = x2,
individual_fixed_effect = as.character(rep(1:n, years)),
time_fixed_effect = as.character(rep(1:years, each = n)),
stringsAsFactors = F)
I am new to this kind of analysis. But if I understand correctly, if I want to estimate the effects of respondents' characteristics on their choice, I may use a multinomial logit regression.
In order to take advantage of the longitudinal structure of the data, I want to include in my specification individual and time fixed effects.
To the best of my knowledge, the multinomial logit regression with fixed effects was first proposed by Chamberlain (1980, Review of Economic Studies 47: 225–238). Recently, Stata users have been provided with the routines to implement this model (femlogit).
In the vignette of the femlogit package, the author refers to the R function clogit, in the survival package.
According to the help page, clogit requires data to be rearranged in a different format:
library(mlogit)
# create wide dataset
data_mlogit <- mlogit.data(df, id.var = "individual_fixed_effect",
group.var = "time_fixed_effect",
choice = "choice",
shape = "wide")
Now, if I understand correctly how clogit works, fixed effects can be passed through the function strata (see for additional details this tutorial). However, I am afraid that it is not clear to me how to use this function, as no coefficient values are returned for the individual characteristic variables (i.e. I get only NAs).
library(survival)
fit <- clogit(formula("choice ~ alt + x1 + x2 + strata(individual_fixed_effect, time_fixed_effect)"), as.data.frame(data_mlogit))
summary(fit)
Since I was not able to find a reason for this (there must be something that I am missing on the way these functions are estimated), I have looked for a solution using other packages in R: e.g., glmnet, VGAM, nnet, globaltest, and mlogit.
Only the latter seems to be able to explicitly deal with panel structures using appropriate estimation strategy. For this reason, I have decided to give it a try. However, I was only able to run a multinomial logit regression without fixed effects.
# state formula
formula_mlogit <- formula("choice ~ 1| x1 + x2")
# run multinomial regression
fit <- mlogit(formula_mlogit, data_mlogit)
summary(fit)
If I understand correctly how mlogit works, here's what I have done.
By using the function mlogit.data, I have created a dataset compatible with the function mlogit. Here, I have also specified the id of each individual (id.var = individual_fixed_effect) and the group to which individuals belongs to (group.var = "time_fixed_effect"). In my case, the group represents the observations registered in the same year.
My formula specifies that there are no variables correlated with a specific choice, and which are randomly distributed among individuals (i.e., the variables before the |). By contrast, choices are only motivated by individual characteristics (i.e., x1 and x2).
In the help of the function mlogit, it is specified that one can use the argument panel to use panel techniques. To set panel = TRUE is what I am after here.
The problem is that panel can be set to TRUE only if another argument of mlogit, i.e. rpar, is not NULL.
The argument rpar is used to specify the distribution of the random variables: i.e. the variables before the |.
The problem is that, since these variables does not exist in my case, I can't use the argument rpar and then set panel = TRUE.
An interesting question related to this is here. A few suggestions were given, and one seems to go in my direction. Unfortunately, no examples that I can replicate are provided, and I do not understand how to follow this strategy to solve my problem.
Moreover, I am not particularly interested in using mlogit, any efficient way to perform this task would be fine for me (e.g., I am ok with survival or other packages).
Do you know any solution to this problem?
Two caveats for those interested in answering:
I am interested in fixed effects, not in random effects. However, if you believe there is no other way to take advantage of the longitudinal structure of my data in R (there is indeed in Stata but I don't want to use it), please feel free to share your code.
I am not interested in going Bayesian. So if possible, please do not suggest this approach.
I have this data set.
wbh
I wanted to use the R package glmnet to determine which predictors would be useful in predicting fertility. However, I have been unable to do so, most likely due to not having a full understanding of the package. The fertility variable is SP.DYN.TFRT.IN. I want to see which predictors in the data set give the most predictive power for fertility. I wanted to use LASSO or ridge regression to shrink the number of coefficients, and I know this package can do that. I'm just having some trouble implementing it.
I know there are no code snippets which I apologize for but I am rather lost on how I would code this out.
Any advice is appreciated.
Thank you for reading
Here is an example on how to run glmnet:
library(glmnet)
library(tidyverse)
df is the data set your provided.
select y variable:
y <- df$SP.DYN.TFRT.IN
select numerical variables:
df %>%
select(-SP.DYN.TFRT.IN, -region, -country.code) %>%
as.matrix() -> x
select factor variables and convert to dummy variables:
df %>%
select(region, country.code) %>%
model.matrix( ~ .-1, .) -> x_train
run model(s), several parameters here can be tweaked I suggest checking the documentation. Here I just run 5-fold cross validation to determine the best lambda
cv_fit <- cv.glmnet(x, y, nfolds = 5) #just with numeric variables
cv_fit_2 <- cv.glmnet(cbind(x ,x_train), y, nfolds = 5) #both factor and numeric variables
par(mfrow = c(2,1))
plot(cv_fit)
plot(cv_fit_2)
best lambda:
cv_fit$lambda[which.min(cv_fit$cvm)]
coefficients at best lambda
coef(cv_fit, s = cv_fit$lambda[which.min(cv_fit$cvm)])
equivalent to:
coef(cv_fit, s = "lambda.min")
after running coef(cv_fit, s = "lambda.min") all features with - in the resulting table are dropped from the model. This situation corresponds to the left lambda depicted with the left vertical dashed line on the plots.
I suggest reading the linked documentation - elastic nets are quite easy to grasp if you know a bit of linear regression and the package is quite intuitive. I also suggest reading ISLR, at least the part with L1 / L2 regularization. and these videos: 1, 2, 3 4, 5, 6, first three are about estimating model performance via test error and the last three are about the question at hand. This one is how to implement these models in R. By the way these guys on the videos invented LASSO and made glment.
Also check the glmnetUtils library which provides a formula interface and other nice things like in built mixing parameter (alpha) selection. Here is the vignette.
This is complete reEdit of my orignal question
Let's assume I'm working on RT data gathered in a repeated measure experiment. As part of my usual routine I always transform RT to natural logarytms and then compute a Z score for each RT within each partipant adjusting for trial number. This is typically done with a simple regression in SPSS syntax:
split file by subject.
REGRESSION
/MISSING LISTWISE
/STATISTICS COEFF OUTS R ANOVA
/CRITERIA=PIN(.05) POUT(.10)
/NOORIGIN
/DEPENDENT rtLN
/METHOD=ENTER trial
/SAVE ZRESID.
split file off.
To reproduce same procedure in R generate data:
#load libraries
library(dplyr); library(magrittr)
#generate data
ob<-c(1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3)
ob<-factor(ob)
trial<-c(1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6)
rt<-c(300,305,290,315,320,320,350,355,330,365,370,370,560,565,570,575,560,570)
cond<-c("first","first","first","snd","snd","snd","first","first","first","snd","snd","snd","first","first","first","snd","snd","snd")
#Following variable is what I would get after using SPSS code
ZreSPSS<-c(0.4207,0.44871,-1.7779,0.47787,0.47958,-0.04897,0.45954,0.45487,-1.7962,0.43034,0.41075,0.0407,-0.6037,0.0113,0.61928,1.22038,-1.32533,0.07806)
sym<-data.frame(ob, trial, rt, cond, ZreSPSS)
I could apply a formula (blend of Mark's and Daniel's solution) to compute residuals from a lm(log(rt)~trial) regression but for some reason group_by is not working here
sym %<>%
group_by (ob) %>%
mutate(z=residuals(lm(log(rt)~trial)),
obM=mean(rt), obSd=sd(rt), zRev=z*obSd+obM)
Resulting values clearly show that grouping hasn't kicked in.
Any idea why it didn't work out?
Using dplyr and magrittr, you should be able to calculate z-scores within individual with this code (it breaks things into the groups you tell it to, then calculates within that group).
experiment %<>%
group_by(subject) %>%
mutate(rtLN = log(rt)
, ZRE1 = scale(rtLN))
You should then be able to do use that in your model. However, one thing that may help your shift to R thinking is that you can likely build your model directly, instead of having to make all of these columns ahead of time. For example, using lme4 to treat subject as a random variable:
withRandVar <-
lmer(log(rt) ~ cond + (1|as.factor(subject))
, data = experiment)
Then, the residuals should already be on the correct scale. Further, if you use the z-scores, you probably should be plotting on that scale. I am not actually sure what running with the z-scores as the response gains you -- it seems like you would lose information about the degree of difference between the groups.
That is, if the groups are tight, but the difference between them varies by subject, a z-score may always show them as a similar number of z-scores away. Imagine, for example, that you have two subjects, one scores (1,1,1) on condition A and (3,3,3) on condition B, and a second subject that scores (1,1,1) and (5,5,5) -- both will give z-scores of (-.9,-.9,-.9) vs (.9,.9,.9) -- losing the information that the difference between A and B is larger in subject 2.
If, however, you really want to convert back, you can probably use this to store the subject means and sds, then multiply the residuals by subjSD and add subjMean.
experiment %<>%
group_by(subject) %>%
mutate(rtLN = log(rt)
, ZRE1 = scale(rtLN)
, subjMean = mean(rtLN)
, subjSD = sd(rtLN))
mylm <- lm(x~y)
rstandard(mylm)
This returns the standardized residuals of the function. To bind these to a variable you can do:
zresid <- rstandard(mylm)
EXAMPLE:
a<-rnorm(1:10,10)
b<-rnorm(1:10,10)
mylm <- lm(a~b)
mylm.zresid<-rstandard(mylm)
See also:
summary(mylm)
and
mylm$coefficients
mylm$fitted.values
mylm$xlevels
mylm$residuals
mylm$assign
mylm$call
mylm$effects
mylm$qr
mylm$terms
mylm$rank
mylm$df.residual
mylm$model
I have built a multilayer perceptron neural network in SPSS 22. I try the same using "neuralnet" package in R, but the results are not desirable.
SPSS standardises data before performing training and I am wondering:
Does "neuralnet" package perform any sort of standardization? I could not find in its guide.
According to SPSS guide here, standardised process is done as below:
Subtract the mean and divide by the standard deviation, (x−mean)/s.
Is there an optimal function that can do this in R? Since the method is quite simple, I can implement the scaling by my own, but it might not be efficient since number of data elements and records are very large.
Or maybe should I use another neural network package like "monmlp"? that standardize data automatically?
Many thanks
This might be useful if you need to standardize multiple columns in a data frame (call it foo):
# Index of columns to standardize
cols <- c(1,2,3,4)
# Standardize
library(plyr)
standardize <- function(x) as.numeric((x - mean(x)) / sd(x))
foo[cols] <- plyr::colwise(standardize)(foo[cols])