I have a response variable (A) which I transformed (logA) and predictor (B) from data (X) which are both continuous. How do I check the linearity between the two variables using Generalized Additive Model (GAM) in R. I use the following code
model <- gamlss(logA ~ pb(B) , data = X, trace = F)
but I am not sure about it, can I add "family=Poisson" in the code when logA is continuous in GLM? Any thoughts on this?
Thanks in advance
If your dependent variable is a count variable, you can use family=PO() without log transformation. With family=PO() a log link is already applied to transform the variable. See help page for gamlss family and also vignette on count regression section 2.1.
So it will go like:
library(gamlss)
fit = gamlss(gear ~ pb(mpg),data=mtcars,family=PO())
You can see that the predictions are log transformed and you need to take the exponential:
with(mtcars,plot(mpg,gear))
points(mtcars$mpg,exp(predict(fit,what="mu")),col="blue",pch=20)
Related
I am following a course on R. At the moment, we are working with logistic regression. The basic form we are taught is this one:
model <- glm(
formula = y ~ x1 + x2,
data = df,
family = quasibinomial(link = "logit"),
weights = weight
)
This makes perfectly sense to me. However, then we are being recommended to use the following to get coefficients and heteroscedasticity-robust inference:
model_rob <- lmtest::coeftest(model, sandwich::vcovHC(model))
This confuses me bit. Reading about vcovHC is states that it creates a "heteroskedasticity-consistent estimation". Why would you do this when doing logistic regression? I taught it did not assume homoscedasticity? Also, I am not sure what the coeftest does?
Thank you!
You're right - homoscedasticity (residuals at each level of the predictor have the same variance), is not an assumption in logistic regression. However, the binary response in logistic regression is heteroscedastic (0 or 1) which is why a corresponding estimator should be consistent with it. I guess that is what is meant with "heteroscedasticity-consistent". As #MrFlick already pointed out, if you would like more information on that topic, Cross Validated is likely to be the place to be. The coeftest produces the Wald test statistic of the estimated coefficients. These tests give you some information on whether a predictor (independent variable) seems to be associated to the dependent variable according to your data.
I have two variables, x and y, each of which has an error in x and y associated with each point. I'm trying to fit a linear regression model in R which takes account of the error in both variables. I see that you can use weights in lm() to weight the regression based on errors but as far as I can see this can only incorporate errors on one variable. Is there any way to fit a linear model which takes into account errors on both of the variables?
Thanks to #Stéphane Laurent for the answer.
The package "deming" contains a function to do exactly this.
I want to fit the following data to a Weibull distribution multiplied by a.
datos: enter link description here
y=b1*(1-exp(-(x/b2)^b3)
However, I could not find a solution using the nls function in R.
Could someone guide me down the path to follow in order to find a solution?
The code used is the following:
ajuste_cg<-nls(y~b1*(-exp(-((x/b2)^b3))),data=d,start=list(b1=1000,b2=140,b3=20), trace=T,control = list(maxiter=10000000))
Thanks!
I suggest you to use the package survival. It is made for implementing parametric survival regressions (Weibull models included, of course). Here's the code:
library(survival)
weibull_model = survreg(Surv(time, event) ~ expalatory_variables, dist="weibull")
The Surv() object that you see instead of a y is an R "survival object", and works like your dependent variable in a survival regression. The time and event variables must represent duration and event occurrence (0 or 1), respectively.
Please replace explanatory_variables with your appropriate set of variables.
I have a data set with both continuous and categorical variables. In the end I want to build a logistic regression model to calculate the probability of a response dichotomous variable.
Is it acceptable, or even a good idea, to apply a log linear model to the categorical variables in the model to test their interactions, and then use the indicated interactions as predictors in the logistic model?
Example in R:
Columns in df: CategoricalA, CategoricalB, CategoricalC, CategoricalD, CategoricalE, ContinuousA, ContinuousB, ResponseA
library(MASS)
#Isolate categorical variables in new data frame
catdf <- df[,c("CategoricalA","CategoricalB","CategoricalC", "CategoricalD", "CategoricalE")]
#Create cross table
crosstable <- table(catdf)
#build log-lin model
model <- loglm(formula = ~ CategoricalA * CategoricalB * CategoricalC * CategoricalD * CategoricalE, data = crosstable)
#Use step() to build better model
automodel <- step(object = model, direction = "backward")
Then build a logistic regresion using the output of automodeland the values of ContinuousA and ContinuousB in order to predict ResponseA (which is binary).
My hunch is that this is not ok, but I cant find the answer definitively one way or the other.
Short answer: Yes. You can use any information in the model that will be available in out-of-time or 'production' run of the model. Whether this information is good, powerful, significant, etc. is a different question.
The logic is that a model can have any type of RHS variable, be it categorical, continuous, logical, etc. Furthermore, you can combine RHS variables to create one RHS variable and also apply transformations. The log linear model of categorical is nothing by a transformed linear combination of raw variables (that happen to be categorical). This method would not be violating any particular modeling framework.
I have a stationary time series to which I want to fit a linear model with an autoregressive term to correct for serial correlation, i.e. using the formula At = c1*Bt + c2*Ct + ut, where ut = r*ut-1 + et
(ut is an AR(1) term to correct for serial correlation in the error terms)
Does anyone know what to use in R to model this?
Thanks
Karl
The GLMMarp package will fit these models. If you just want a linear model with Gaussian errors, you can do it with the arima() function where the covariates are specified via the xreg argument.
There are several ways to do this in R. Here are two examples using the "Seatbelts" time series dataset in the datasets package that comes with R.
The arima() function comes in package:stats that is included with R. The function takes an argument of the form order=c(p, d, q) where you you can specify the order of the auto-regressive, integrated, and the moving average component. In your question, you suggest that you want to create a AR(1) model to correct for first-order autocorrelation in the errors and that's it. We can do that with the following command:
arima(Seatbelts[,"drivers"], order=c(1,0,0),
xreg=Seatbelts[,c("kms", "PetrolPrice", "law")])
The value for order specifies that we want an AR(1) model. The xreg compontent should be a series of other Xs we want to add as part of a regression. The output looks a little bit like the output of summary.lm() turned on its side.
Another alternative process might be more familiar to the way you've fit regression models is to use gls() in the nlme package. The following code turns the Seatbelt time series object into a dataframe and then extracts and adds a new column (t) that is just a counter in the sorted time series object:
Seatbelts.df <- data.frame(Seatbelts)
Seatbelts.df$t <- 1:(dim(Seatbelts.df)[1])
The two lines above are only getting the data in shape. Since the arima() function is designed for time series, it can read time series objects more easily. To fit the model with nlme you would then run:
library(nlme)
m <- gls(drivers ~ kms + PetrolPrice + law,
data=Seatbelts.df,
correlation=corARMA(p=1, q=0, form=~t))
summary(m)
The line that begins with "correlation" is the way you pass in the ARMA correlation structure to GLS. The results won't be exactly the same because arima() uses maximum likelihood to estimate models and gls() uses restricted maximum likelihood by default. If you add method="ML" to the call to gls() you will get identical estimates you got with the ARIMA function above.
What is your link function?
The way you describe it sounds like a basic linear regression with autocorrelated errors. In that case, one option is to use lm to get a consistent estimate of your coefficients and use Newey-West HAC standard errors.
I'm not sure the best answer for GLM more generally.