I have a logistic regression model using glm that looks something like this:
glm(formula = output ~ cut(X1,c(1,2,3,4,5,6,7)) + X2 + X3 + X4 + X5 + X1:term + term:X5 - 1, family="binomial", data=mydata)
When I use summary(glm) I get parameter outputs for each cut of X1. Suppose I wanted to implement / deploy this model. How do I handle each of the 'cut' derived parameters? For example, if the value is between 1 and 2 do I simply use the parameter associated with 2 multiplied by the value and set all others (since the value is not in their range) to 0? Any insight is appreciated.
Categorical variables, such as those you produced with cut, become indicators (AKA dummy variables) in regression. If your value is somewhere between 1 and 2, it's precise value doesn't matter - you have chosen to discard that information for your model. You simply add the parameter associated with the 1-to-2 range (times 1, if you want to think of it that way) and ignore all the others (or times 0, if you want to think of it that way).
This isn't really a programming or R-specific question - it's incidental that you're using R to bin your variable and fit your model. Any tutorial on regression with categorical variables should cover this. This one looks all right, or maybe this one (pdf link).
Related
How to run Latent Class Growth Modelling (LCGM) with a multinomial response variable in R (using the flexmix package)?
And how to stratify each class by a binary/categorical dependent variable?
The idea is to let gender shape the growth curve by cluster (cf. Mikolai and Lyons-Amos (2017, p. 194/3) where the stratification is done by education. They used Mplus)
I think I might have come close with the following syntax:
lcgm_formula <- as.formula(rel_stat~age + I(age^2) + gender + gender:age)
lcgm <- flexmix::stepFlexmix(.~ .| id,
data=d,
k=nr_of_classes, # would be 1:12 in real analysis
nrep=1, # would be 50 in real analysis to avoid local maxima
control = list(iter.max = 500, minprior = 0),
model = flexmix::FLXMRmultinom(lcgm_formula,varFix=T,fixed = ~0))
,which is close to what Wardenaar (2020,p. 10) suggests in his methodological paper for a continuous outcome:
stepFlexmix(.~ .|ID, k = 1:4,nrep = 50, model = FLXMRglmfix(y~ time, varFix=TRUE), data = mydata, control = list(iter.max = 500, minprior = 0))
The only difference is that the FLXMRmultinom probably does not support varFix and fixed parameters, altough adding them do produce different results. The binomial equivalent for FLXMRmultinom in flexmix might be FLXMRglm (with family="binomial") as opposed FLXMRglmfix so I suspect that the restrictions of the LCGM (eg. fixed slope & intercept per class) are not specified they way it should.
The results are otherwise sensible, but model fails to put men and women with similar trajectories in the same classes (below are the fitted probabilities for each relationship status in each class by gender):
We should have the following matches by cluster and gender...
1<->1
2<->2
3<->3
...but instead we have
1<->3
2<->1
3<->2
That is, if for example men in class one and women in class three would be forced in the same group, the created group would be more similar than the current first row of the plot grid.
Here is the full MVE to reproduce the code.
Got similar results with another dataset with diffent number of classes and up to 50 iterations/class. Have tried two alternative ways to predict the probabilities, with identical results. I conclude that the problem is most likely in the model specification (stepflexmix(...,model=FLXMRmultinom(...) or this is some sort of label switch issue.
If the model would be specified correctly and the issue is that similar trajectories for men/women end up in different classes, is there a way to fix that? By for example restricting the parameters?
Any assistance will be highly appreciated.
This seems to be a an identifiability issue apparently common in mixture modelling. In other words the labels are switched so that while there might not be a problem with the modelling as such, men and women end up in different groups and that will have to be dealt with one way or another
In the the new linked code, I have swapped the order manually and calculated the predictions with by hand.
Will be happy to hear, should someone has an alternative approach to deal with the label swithcing issue (like restricting parameters or switching labels algorithmically). Also curious if the model could/should be specified in some other way.
A few remarks:
I believe that this is indeed performing a LCGM as we do not specify random effects for the slopes or intercepts. Therefore I assume that intercepts and slopes are fixed within classes for both sexes. That would mean that the model performs LCGM as intended. By the same token, it seems that running GMM with random intercept, slope or both is not possible.
Since we are calculating the predictions by hand, we need to be able to separate parameters between the sexes. Therefore I also added an interaction term gender x age^2. The calculations seems to slow down somewhat, but the estimates are similar to the original. It also makes conceptually sense to include the interaction for age^2 if we have it for age already.
varFix=T,fixed = ~0 seem to be reduntant: specifying them do not change anything. The subsampling procedure (of my real data) was unaffected by the set.seed() command for some reason.
The new model specification becomes:
lcgm_formula <- as.formula(rel_stat~ age + I(age^2) +gender + age:gender + I(age^2):gender)
lcgm <- flexmix::flexmix(.~ .| id,
data=d,
k=nr_of_classes, # would be 1:12 in real analysis
#nrep=1, # would be 50 in real analysis to avoid local maxima (and we would use the stepFlexmix function instead)
control = list(iter.max = 500, minprior = 0),
model = flexmix::FLXMRmultinom(lcgm_formula))
And the plots:
For my class we have to create a model to predict the credit balance of each individuals. Based on observations, many results are zero where the lm tries to calculate them.
To overcome this I created a new variable that results in zero if X and Y are true.
CB$Balzero = ifelse(CB$Rating<=230 & CB$Income<90,0,1)
This resulted in getting 90% of the zero results right. The problem is:
How can I place this variable in the lm so it correctly results in zeros when the proposition is true and the calculation when it is false?
Something like: lm=Balzero*(Balance~.)
I think that
y ~ -1 + Balzero:Balance
might work (you haven't given us a reproducible example to try).
-1 tells R to omit the intercept
: specifies an interaction. If both variables are numeric, then A:B includes the product of A and B as a term in the model.
The second term could also be specified as I(Balzero*Balance) (I means "as is", i.e. interpret * in the usual numerical sense, not in its formula-construction context.)
These specifications should fit the model
Y = beta1*Balzero*Balance + eps
where eps is an error term.
If Balzero == 0, the predicted value will be zero. If Balzero==1 the predicted value will be beta1*Balance.
You might want to look into random forest models, which naturally incorporate the kind of qualitative splitting that you're doing by hand in your example.
I saw quite a few examples of how to do regression (linear, multiple... etc.) but on every example I saw, you had to define every single feature in the formula...
linearMod <- lm(Y ~ x1 + x2 + x3 + ..., data=myData)
Well, we used TSFresh to generate more features. Around 100. So how am I supposed to do this now? I don't really want to type in x1 .. all the way to .. x100.
In Phyton scikit-learn I could just put in all the data:
lm = linear_model.LinearRegression()
model = lm.fit(X,y)
And then repeat this for each 'feature group' to create a multiple linear regression.
Is there a way to do this in R? Or am I doing it wrong? Maybe another approach?
Originally we had 8 features/properties per Row. And with TSFresh we gernerated more of those. (Mean, STD and so on)
And every one of those features has a pretty linear influence on the Y result. So how can I now define something like a multiple linear model that just uses all extended features? Ideally without me having to tell it by hand each time.
So for example (one formulare would probably be feature 1-12 for Y) the next one (13-24 for Y) and so on. Is there a easy way to do this?
If you want to regress on all variables except Y you can do
lm(Y ~ ., data = myData)
This question already has an answer here:
Set one or more of coefficients to a specific integer
(1 answer)
Closed 6 years ago.
In R, how can I set weights for particular variables and not observations in lm() function?
Context is as follows. I'm trying to build personal ranking system for particular products, say, for phones. I can build linear model based on price as dependent variable and other features such as screen size, memory, OS and so on as independent variables. I can then use it to predict phone real cost (as opposed to declared price), thus finding best price/goodness coefficient. This is what I have already done.
Now I want to "highlight" some features that are important for me only. For example, I may need a phone with large memory, thus I want to give it higher weight so that linear model is optimized for memory variable.
lm() function in R has weights parameter, but these are weights for observations and not variables (correct me if this is wrong). I also tried to play around with formula, but got only interpreter errors. Is there a way to incorporate weights for variables in lm()?
Of course, lm() function is not the only option. If you know how to do it with other similar solutions (e.g. glm()), this is pretty fine too.
UPD. After few comments I understood that the way I was thinking about the problem is wrong. Linear model, obtained by call to lm(), gives optimal coefficients for training examples, and there's no way (and no need) to change weights of variables, sorry for confusion I made. What I'm actually looking for is the way to change coefficients in existing linear model to manually make some parameters more important than others. Continuing previous example, let's say we've got following formula for price:
price = 300 + 30 * memory + 56 * screen_size + 12 * os_android + 9 * os_win8
This formula describes best possible linear model for dependence between price and phone parameters. However, now I want to manually change number 30 in front of memory variable to, say, 60, so it becomes:
price = 300 + 60 * memory + 56 * screen_size + 12 * os_android + 9 * os_win8
Of course, this formula doesn't reflect optimal relationship between price and phone parameters any more. Also dependent variable doesn't show actual price, just some value of goodness, taking into account that memory is twice more important for me than for average person (based on coefficients from first formula). But this value of goodness (or, more precisely, value of fraction goodness/price) is just what I need - having this I can find best (in my opinion) phone with best price.
Hope all of this makes sense. Now I have one (probably very simple) question. How can I manually set coefficients in existing linear model, obtained with lm()? That is, I'm looking for something like:
coef(model)[2] <- 60
This code doesn't work of course, but you should get the idea. Note: it is obviously possible to just double values in memory column in data frame, but I'm looking for more elegant solution, affecting model, not data.
The following code is a bit complicated because lm() minimizes residual sum of squares and with a fixed, non optimal coefficient it is no longed minimal, so that would be against what lm() is trying to do and the only way is to fix all the rest coefficients too.
To do that, we have to know coefficients of the unrestricted model first. All the adjustments have to be done by changing formula of your model, e.g. we have
price ~ memory + screen_size, and of course there is a hidden intercept. Now neither changing the data directly nor using I(c*memory) is good idea. I(c*memory) is like temporary change of data too, but to change only one coefficient by transforming the variables would be much more difficult.
So first we change price ~ memory + screen_size to price ~ offset(c1*memory) + offset(c2*screen_size). But we haven't modified the intercept, which now would try to minimize residual sum of squares and possibly become different than in original model. The final step is to remove the intercept and to add a new, fake variable, i.e. which has the same number of observations as other variables:
price ~ offset(c1*memory) + offset(c2*screen_size) + rep(c0, length(memory)) - 1
# Function to fix coefficients
setCoeffs <- function(frml, weights, len){
el <- paste0("offset(", weights[-1], "*",
unlist(strsplit(as.character(frml)[-(1:2)], " +\\+ +")), ")")
el <- c(paste0("offset(rep(", weights[1], ",", len, "))"), el)
as.formula(paste(as.character(frml)[2], "~",
paste(el, collapse = " + "), " + -1"))
}
# Example data
df <- data.frame(x1 = rnorm(10), x2 = rnorm(10, sd = 5),
y = rnorm(10, mean = 3, sd = 10))
# Writing formula explicitly
frml <- y ~ x1 + x2
# Basic model
mod <- lm(frml, data = df)
# Prime coefficients and any modifications. Note that "weights" contains
# intercept value too
weights <- mod$coef
# Setting coefficient of x1. All the rest remain the same
weights[2] <- 3
# Final model
mod2 <- update(mod, setCoeffs(frml, weights, nrow(df)))
# It is fine that mod2 returns "No coefficients"
Also, probably you are going to use mod2 only for forecasting (actually I don't know where else it could be used now) so that could be made in a simpler way, without setCoeffs:
# Data for forecasting with e.g. price unknown
df2 <- data.frame(x1 = rpois(10, 10), x2 = rpois(5, 5), y = NA)
mat <- model.matrix(frml, model.frame(frml, df2, na.action = NULL))
# Forecasts
rowSums(t(t(mat) * weights))
It looks like you are doing optimization, not model fitting (though there can be optimization within model fitting). You probably want something like the optim function or look into linear or quadratic programming (linprog and quadprog packages).
If you insist on using modeling tools like lm then use the offset argument in the formula to specify your own multiplyer rather than computing one.
I am very new to R (mostly program in SQL) but was faced with a problem that SQL couldn't help me with. I'll try to simplify the problem below.
Assume I have a set of data with 100 rows where each row has a different weight associated with it. Out of those 100 rows of data, 5 have an X value that is top-coded at 1000. Also assume that X can be represented by the linear equation X ~ Y + Z + U + 0 (want a positive value so I don't want a Y-intercept).
Now, without taking the weights of each row of data into consideration, the formula I used in R was:
fit = censReg(X ~ Y + Z + U + 0, left = -Inf, right = 1000, data = dataset)
If I computed summary(fit) I would get 0 left-censored values, 95 uncensored values, and 5 right censored values which is exactly what I want, minus the fact that the weights haven't been sufficiently added into the mix. I checked the reference manual on the censReg function and it doesn't seem like it accepts a weight argument.
Is there something I'm missing about the censReg function or is there another function that would be of better use to me? My end goal is to estimate X in the cases where it is censored (i.e. the 5 cases where it is 1000).
You should use Tobit regression for this situation, it is designed specifically to linearly model latent variables such as the one you describe.
The regression accounts for your weights and the censored observations, which can be seen in the derivation of the log-likelihood function for the Type I Tobit (upper and lower bounded).
Tobit regression can be found in the VGAM package using the vglm function with a tobit control parameter. An excellent example can be found here:
http://www.ats.ucla.edu/stat/r/dae/tobit.htm