For a logistic regression, I want to test the assumption of a lineair relation between the independent variables and the log-odds of Y.
I have read about using the Box-Tidwell test for this. Applying the test keeps resulting in errors, so I'm hoping to get some assistence on the code.
My dataset consists of about 80 variables. My dependent variabele is a dichotomous variable. My independent variables consist of continuous variables, as well as factors.
The first question I have is which Y to use in the box-tidwell.
I specified Y by running glm (family=binomial) on all the predictors and taking the log-odds:
odds = ...$fitted.values / (1-...$fitted.values)
log_odds <- log(odds)
This means that the Y I use for the box-tidwell is based on the model without the x ln(x) interactions. I'm wondering if this is the right way.
I cannot think of another way to specify the model in the Box_Tidwell.
Should I perhaps define the glm in the Box_Tidwell test, and if yes, how should I do this (i.e. which code should I use)?
The second question I have concerns the specification of X1 en X2.
I specified x1 in the BT by adding a fraction (0.01) to all continuous predictors (since BT cannot handle zeroes) and therefore first selecting all continuous predictors.
Since I read that X1 and X2 should be matrixes I did the following:
DF_numeric <- Filter(is.numeric, DF)
x <- DF_numeric + 0.01
x_matrix <- as.matrix (x)
As I understand X2 should contain variables in the model that are not candidates for transformation, so:
x2 <- Filter(is.factor, DF)
x2_matrix <- as.matrix (x2)
I get the following error, when running my BT:
BT <- boxTidwell(Y=log_odds, x1=x_matrix, x2=x2_matrix)
Error in `[[<-.data.frame`(`*tmp*`, i, value = c(250L, 250L, 194L, 250L, :
replacement has 480090 rows, data has 6155
The 480090 rows are the 6155 participants times the number of variables, but I don't know which mistake I make.
I tried different possibilities. Since the log_odds I use for the Y are not in the same dataframe as X1 en X2 I tried binding (with cbind) x1, x2 and log_odds. This however does not change the error.
Should I use different formats for Y, X or X2?
I hope I have given enough information and hope you can help me!
(I first asked this question in Cross Validated, but since it was off-topic there, I hope this is the correct place).
Thanks in advance!
Simone
Related
The toy model below stands in for one with a bunch more variables, transforms, lags, etc. Assume I got that stuff right.
My data is ordered in time, but is now formatted as an R time series, because I need to exclude certain periods, etc. I'd rather not make it a time series for this reason, because I think it would be easy to muck up, but if I need to, or it greatly simplifies the estimating process, I'd like to just use an integer sequence, such as index. below, to represent time if that is allowed.
My problem is a simple one (I hope). I would like to use the first part of my data to estimate the coefficients of the model. Then I want to use those estimates, and not estimates from a sliding window, to do one-ahead forecasts for each of the remaining values of that data. The idea is that the formula is applied with a sliding window even though it is not estimated with one. Obviously I could retype the model with coefficients included and then get what I want in multiple ways, with base R sapply, with tidyverse dplyr::mutate or purrr::map_dbl, etc. But I am morally certain there is some standard way of pulling the formula out of the lm object and then wielding it as one desires, that I just haven't been able to find. Example:
set.seed(1)
x1 <- 1:20
y1 <- 2 + x1 + lag(x1) + rnorm(20)
index. <- x1
data. <- tibble(index., x1, y1)
mod_eq <- y1 ~ x1 + lag(x1)
lm_obj <- lm(mod_eq, data.[1:15,])
and I want something along the lines of:
my_forecast_values <- apply_eq_to_data(eq = get_estimated_equation(lm_obj), my_data = data.[16:20])
and the lag shouldn't give me an error.
Also, this is not part of my question per se, but I could use a pointer to a nice tutorial on using R formulas and the standard estimation output objects produced by lm, glm, nls and the like. Not the statistics, just the programming.
The common way to use the coefficients is by calling the predict(), coefficients(), or summary() function on the model object for what it is worth. You might try the ?predict.lm() documentation for details on formula.
A simple example:
data.$lagx <- dplyr::lag(data.$x1, 1) #create lag variable
lm_obj1 <- lm(data=data.[2:15,], y1 ~ x1 + lagx) #create model object
data.$pred1 <- predict(lm_obj1, newdata=data.[16,20]) #predict new data; needs to have same column headings
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 have about 90 variables stored in data[2-90]. I suspect about 4 of them will have a parabola-like correlation with data[1]. I want to identify which ones have the correlation. Is there an easy and quick way to do this?
I have tried building a model like this (which I could do in a loop for each variable i = 2:90):
y <- data$AvgRating
x <- data$Hamming.distance
x2 <- x^2
quadratic.model = lm(y ~ x + x2)
And then look at the R^2/coefficient to get an idea of the correlation. Is there a better way of doing this?
Maybe R could build a regression model with the 90 variables and chose the ones which are significant itself? Would that be in any way possible? I can do this in JMP for linear regression, but I'm not sure I could do non-linear regression with R for all the variables at ones. Therefore I was manually trying to see if I could see which ones are correlated in advance. It would be helpful if there was a function to use for that.
You can use nlcor package in R. This package finds the nonlinear correlation between two data vectors.
There are different approaches to estimate a nonlinear correlation, such as infotheo. However, nonlinear correlations between two variables can take any shape.
nlcor is robust to most nonlinear shapes. It works pretty well in different scenarios.
At a high level, nlcor works by adaptively segmenting the data into linearly correlated segments. The segment correlations are aggregated to yield the nonlinear correlation. The output is a number between 0 to 1. With close to 1 meaning high correlation. Unlike a pearson correlation, negative values are not returned because it has no meaning in nonlinear relationships.
More details about this package here
To install nlcor, follow these steps:
install.packages("devtools")
library(devtools)
install_github("ProcessMiner/nlcor")
library(nlcor)
After you install it,
# Implementation
x <- seq(0,3*pi,length.out=100)
y <- sin(x)
plot(x,y,type="l")
# linear correlation is small
cor(x,y)
# [1] 6.488616e-17
# nonlinear correlation is more representative
nlcor(x,y, plt = T)
# $cor.estimate
# [1] 0.9774
# $adjusted.p.value
# [1] 1.586302e-09
# $cor.plot
As shown in the example the linear correlation was close to zero although there was a clear relationship between the variables that nlcor could detect.
Note: The order of x and y inside the nlcor is important. nlcor(x,y) is different from nlcor(y,x). The x and y here represent 'independent' and 'dependent' variables, respectively.
Fitting a generalized additive model, will help you identify curvature in the
relationships between the explanatory variables. Read the example on page 22 here.
Another option would be to compute mutual information score between each pair of variables. For example, using the mutinformation function from the infotheo package, you could do:
set.seed(1)
library(infotheo)
# corrleated vars (x & y correlated, z noise)
x <- seq(-10,10, by=0.5)
y <- x^2
z <- rnorm(length(x))
# list of vectors
raw_dat <- list(x, y, z)
# convert to a dataframe and discretize for mutual information
dat <- matrix(unlist(raw_dat), ncol=length(raw_dat))
dat <- discretize(dat)
mutinformation(dat)
Result:
| | V1| V2| V3|
|:--|---------:|---------:|---------:|
|V1 | 1.0980124| 0.4809822| 0.0553146|
|V2 | 0.4809822| 1.0943907| 0.0413265|
|V3 | 0.0553146| 0.0413265| 1.0980124|
By default, mutinformation() computes the discrete empirical mutual information score between two or more variables. The discretize() function is necessary if you are working with continuous data transform the data to discrete values.
This might be helpful at least as a first stab for looking for nonlinear relationships between variables, such as that described above.
I've run an anova using the following code:
aov2 <- aov(amt.eaten ~ salt + Error(bird / salt),data)
If I use view(aov2) I can see the residuals within the structure of aov2, but I would like to extract them in a way that doesn't involve cutting and pasting. Can someone help me out with the syntax?
Various versions of residuals(aov2) I have been using only produce NULL
I just learn that you can use proj:
x1 <- gl(8, 4)
block <- gl(2, 16)
y <- as.numeric(x1) + rnorm(length(x1))
d <- data.frame(block, x1, y)
m <- aov(y ~ x1 + Error(block), d)
m.pr <- proj(m)
m.pr[['Within']][,'Residuals']
The reason that you cannot extract residuals from this model is that you have specified a random effect due to the bird salt ratio (???). Here, each unique combination of bird and salt are treated like a random cluster having a unique intercept value but common additive effect associated with a unit difference in salt and the amount eaten.
I can't conceive of why we would want to specify this value as a random effect in this model. But in order to sensibly analyze residuals, you may want to calculate fitted differences in each stratum according to the fitted model and optimal intercept. I think this is tedious work and not very informative, however.