plot nonlinear regression conf intervals in R - r

Please help.
I have managed to fit a fairly decent nonlinear regression curve to my data using:
model2 <- nls(urine~a*(1-exp(-c*water)), data = eagle, start = list(a=550, c=0.00385))
and then I generate my plot using:
av <- seq(0,1200, 0.5)
bv <- predict (model2, data=eagle, list(water=av))
plot (urine~water, data = eagle)
lines (av,bv)
I want to draw on some dotted lines for upper and lower 95% confidence intervals. I have managed to write code for my linear regression analyses but I am struggling with the current nonlinear regression. The following code:
a <- predict (model2, newdata=data.frame(water=av), interval="confidence")
for linear regressions this gives me a dataframe with three columns for fit, lwr and upr. With my nonlinear regression it just gives me a list of numbers which I cant do anything with. Any suggestions? Is there a simple way to get upper and confidence lines for a nonlinear regression?


se.fit isnt operating apparently. Found lots of forums discussing the difficulties of fitting confidence intervals to non linear regressions in R. After a whole day of searching and banging my head against the internet I finally found a very helpful formula. Im not 100% sure how it works but it works so here it is for anyone else who needs to do this...
http://www.r-bloggers.com/predictnls-part-1-monte-carlo-simulation-confidence-intervals-for-nls-models/
Once you have produced your table of statistics for your predicted values based on a sequence of x values, you can access the lwr and upr CI value data in columns 6 and 7 of the output and plot that way.

Related

How to convert the y-axis of a plot from log(y) to y

I'm an R newbie. I want to estimate a regression of log(CONSUMPTION) on INCOME and then make a plot of CONSUMPTION and INCOME.
I can run the following regression and plot the results.
results <- lm(I(log(CONSUMPTION)) ~ INCOME, data=dataset)
effect_plot(results, pred=INCOME)
If I do this, I get log(CONSUMPTION) on the vertical axis rather than CONSUMPTION.
How can I get a plot with CONSUMPTION on the vertical axis?
Another way to ask the question is how do I convert the y-axis of a plot from log(y) to y? While my question is for the function effect_plot(), I would be happy with any plot function.
Thanks for any help you can give me.

Thank you for the responses. I was able to figure out a workaround using Poisson regression:
results1 <- glm(CONSUMPTION ~ INCOME+WEALTH, family=poisson, data=Consumption )
effect_plot(results1,pred=INCOME,data=Consumption)
This allows me to identify the effect of one variable (INCOME) even when the regression has more than one explanatory variable (INCOME+WEALTH), and plots the estimated effect with CONSUMPTION on the vertical axis rather than ln(CONSUMPTION), with INCOME on the horizontal axis.
The associated estimates are virtually identical to what I would get from the log-linear regression:
results2 <- lm(I(log(CONSUMPTION)) ~ INCOME+WEALTH, data=Consumption )
I appreciate you for taking the time to help me with my problem.

Backtransform LMM output in R

When performing linear mixed models, I have had to square-root(log) transform the data to achieve a normal distribution. Having performed the LMMs, I now want to plot the results onto a graph, but on the original scale i.e. not square-root(log) transformed.
Apparently I can use my raw (untransformed data) on a graph, and to create the predicted regression line I can use the coefficients from my LMM output to get backtransformed predicted y-values for each of my x values. This is where I'm stuck - I have no idea how to do this. Can anyone help?

{Methcomp} – Deming / orthogonal regression – goodness of fit + confidence intervals

A question following this post. I have the following data:
x1, disease symptom
y1, another disease symptom
I fitted the x1/y1 data with a Deming regression with vr (or sdr) option set to 1. In other words, the regression is a Total Least Squares regression, i.e. orthogonal regression. See previous post for the graph.
x1=c(24.0,23.9,23.6,21.6,21.0,20.8,22.4,22.6,
21.6,21.2,19.0,19.4,21.1,21.5,21.5,20.1,20.1,
20.1,17.2,18.6,21.5,18.2,23.2,20.4,19.2,22.4,
18.8,17.9,19.1,17.9,19.6,18.1,17.6,17.4,17.5,
17.5,25.2,24.4,25.6,24.3,24.6,24.3,29.4,29.4,
29.1,28.5,27.2,27.9,31.5,31.5,31.5,27.8,31.2,
27.4,28.8,27.9,27.6,26.9,28.0,28.0,33.0,32.0,
34.2,34.0,32.6,30.8)
y1=c(100.0,95.5,93.5,100.0,98.5,99.5,34.8,
45.8,47.5,17.4,42.6,63.0,6.9,12.1,30.5,
10.5,14.3,41.1, 2.2,20.0,9.8,3.5,0.5,3.5,5.7,
3.1,19.2,6.4, 1.2, 4.5, 5.7, 3.1,19.2, 6.4,
1.2,4.5,81.5,70.5,91.5,75.0,59.5,73.3,66.5,
47.0,60.5,47.5,33.0,62.5,87.0,86.0,77.0,
86.0,83.0,78.5,83.0,83.5,73.0,69.5,82.5,78.5,
84.0,93.5,83.5,96.5,96.0,97.5)
x11()
plot(x1,y1,xlim=c(0,35),ylim=c(0,100))
library(MethComp)
dem_reg <- Deming(x1, y1)
abline(dem_reg[1:2], col = "green")
I would like to know how much x1 helps to predict y1:
normally, I’d go for a R-squared, but it does not seem to be relevant; although another mathematician told me he thinks a R-squared may be appropriate. And this page suggests to calculate a Pearson product-moment correlation coefficient, which is R I believe?
partially related, there is possibly a tolerance interval. I could calculated it with R ({tolerance} package or code shown in the post), but it is not exactly what I am searching for.
Does someone know how to calculate a goodness of fit for Deming regression, using R? I looked at MetchComp pdf but could not find it (perhaps missed it though).
EDIT: following Gaurav's answers about confidence interval: R code
Firstly: confidence intervals for parameters
library(mcr)
MCR_reg=mcreg(x1,y1,method.reg="Deming",error.ratio=1,method.ci="analytical")
getCoefficients(MCR_reg)
Secondly: confidence intervals for predicted values
# plot of data
x11()
plot(x1,y1,xlim=c(0,35),ylim=c(0,100))
# Deming regression using functions from {mcr}
library(mcr) MCR_reg=mcreg(x1,y1,method.reg="Deming",error.ratio=1,method.ci="analytical")
MCR_intercept=getCoefficients(MCR_reg)[1,1]
MCR_slope=getCoefficients(MCR_reg)[2,1]
# CI for predicted values
x_to_predict=seq(0,35)
predicted_values=MCResultAnalytical.calcResponse(MCR_reg,x_to_predict,alpha=0.05)
CI_low=predicted_values[,4]
CI_up=predicted_values[,5]
# plot regression line and CI for predicted values
abline(MCR_intercept,MCR_slope, col="red")
lines(x_to_predict,CI_low,col="royalblue",lty="dashed")
lines(x_to_predict,CI_up,col="royalblue",lty="dashed")
# comments
text(7.5,60, "Deming regression", col="red")
text(7.5,40, "Confidence Interval for", col="royalblue")
text(7.5,35, "Predicted values - 95%", col="royalblue")
EDIT 2
Topic moved to Cross Validated:
https://stats.stackexchange.com/questions/167907/deming-orthogonal-regression-measuring-goodness-of-fit

There are many proposed methods to calculate goodness of fit and tolerance intervals for Deming Regression but none of them widely accepted. The conventional methods we use for OLS regression may not make sense. This is an area of active research. I don't think there many R-packages which will help you compute that since not many mathematicians agree on any particular method. Most methods for calculating intervals are based on Resampling techniques.
However you can check out the 'mcr' package for intervals...
https://cran.r-project.org/web/packages/mcr/

Confidence intervals for predicted probabilities from predict.lrm

I am trying to determine confidence intervals for predicted probabilities from a binomial logistic regression in R. The model is estimated using lrm (from the package rms) to allow for clustering standard errors on survey respondents (each respondent appears up to 3 times in the data):
library(rms)
model1<-lrm(outcome~var1+var2+var3,data=mydata,x=T,y=T,se.fit=T)
model.rob<-robcov(model1,cluster=respondent.id)
I am able to estimate a predicted probability for the outcome using predict.lrm:
predicted.prob<-predict(model.rob,newdata=data.frame(var1=1,var2=.33,var3=.5),
type="fitted")
What I want to determine is a 95% confidence interval for this predicted probability. I have tried specifying se.fit=T, but this not permissible in predict.lrm when type=fitted.
I have spent the last few hours scouring the Internet for how to do this with lrm to no avail (obviously). Can anyone point me toward a method for determining this confidence interval? Alternatively, if it is impossible or difficult with lrm models, is there another way to estimate a logit with clustered standard errors for which confidence intervals would be more easily obtainable?

The help file for predict.lrm has a clear example. Here is a slight modification of it:
L <- predict(fit, newdata=data.frame(...), se.fit=TRUE)
plogis(with(L, linear.predictors + 1.96*cbind(- se.fit, se.fit)))
For some problems you may want to use the gendata or Predict functions, e.g.
L <- predict(fit, gendata(fit, var1=1), se.fit=TRUE) # leave other vars at median/mode
Predict(fit, var1=1:2, var2=3) # leave other vars at median/mode; gives CLs

How do I plot predictions from new data fit with gee, lme, glmer, and gamm4 in R?

I have fit my discrete count data using a variety of functions for comparison. I fit a GEE model using geepack, a linear mixed effect model on the log(count) using lme (nlme), a GLMM using glmer (lme4), and a GAMM using gamm4 (gamm4) in R.
I am interested in comparing these models and would like to plot the expected (predicted) values for a new set of data (predictor variables). My goal is to compare the predicted effects for each model under particular conditions (x variables). Of particular interest is the comparison between marginal (GEE) and conditional estimates.
I think my main problem might be getting the new data in the correct form with the correct labels and attributes and such. I am still very much an R novice and struggle with this stuff (no course on this at my university unfortunately).
I currently have fitted models
gee1 lme1 lmer1 gamm1
and can extract their fixed effect coefficients and standard errors without a problem. I also don't have a problem converting them from the log scale or estimating confidence intervals accounting for the random effects.
I also have my new dataframe newdat which has 365 observations of 23 variables (average environmental data for each day of the year).
I am stuck on how to predict new count estimates from this. I played around with the model.matrix function but couldn't get it to work. For example, I tried:
mm = model.matrix(terms(glmm1), newdat) # Error in model.frame.default(object,
# data, xlev = xlev) : object is not a matrix
newdat$pcount = mm %*% fixef(glmm1)
Any suggestions or good references would be greatly appreciated. Can anyone help with the error above?

Getting predictions for lme() and lmer() is documented on http://glmm.wikidot.com/faq

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