My response variable is Yijk corresponding to the recovery time of
patient i (i=1,...,I)
with treatment j (j=1,...,J)
and measured at time k (k=1,...,K)
I would like to fit the following model:Model equation, where:
μ is a global fixed intercept
αj is a fixed effect for the treatment
bik is a random effect with the following covariance structure. Denote bi the K-dimensional vector of effect for the patient i, then its variance-covariance matrix would have the following AR(1) structure.
Variance covariance matrix
uijk is the usual error term with variance σ²
Consider the following line of command:
lme(recovery ~ treatment, method="REML", random=~1|patient, correlation=corAR1,form=~time|patient,data=data)
Several questions:
What does this correlation argument correspond to? The structure of covariance of what? Is that the var-cov matrix which I defined as R?
Does the line actually do what I would like to?
If not, what does it do?
If not, is there a way to do what I would like to?
Thank you in advance!
First, you have a command lme, I will assume that is meant to be nlme because a) lme isn't an R command in any package that I know of or that R could find and b) correlation isn't an option in lme4
Second, in the documentation for nlme they have this:
an optional corStruct object describing the within-group correlation
structure. See the documentation of corClasses for a description of
the available corStruct classes. Defaults to NULL, corresponding to no
within-group correlations.
and in corClasses it says
corAR1 autoregressive process of order 1.
So, the answers to your first two questions appears to be "Yes".
Related
I read the glmmTMB package vignettes (https://cran.r-project.org/web/packages/glmmTMB/vignettes/covstruct.html) and have the following questions:
In the vignetts, they fit the model using
glmmTMB(y~ar1(times+0|group),data=dat0)
and mentioned that the time+0 correspondes to a design matrix Z linking observation vector y (rows) with a random effects vector u(columns)"
What's the meaning of +0? Is there any difference with (times|group), (times+1|group) and (1|group)?
Are there any comprehensive summary about the syntax of the covariance structure?
If I want to fit a Negtive binomial model when outcome y_{ij} is generated from R function: rnbinom(mu=x_{ij}beta+b_i+e_{ij},size=1), where i is the group index and j is the individual index, and b_i～N(0,1), e_{ij}~N(0,1). Would the following code correctly specify to model?
dat <- data.frame(y,x,group)
glmmTMB(y~x+(1|group),data=dat,family=nbinom2)
Any suggestion and help is appreciated. Thanks in advance for your help!
I am currently trying to fit a linear model to count data, where the errors are following a poisson distribution. Namely I would like to minimize the following
where I have i samples. β is a vector with m coefficients and x is consisting of m independent (explanatory) variables. β should sum up to 1 and each coefficient should be larger than 0.
I am using R and I tried the package glmc without much success. The only example in the documentation is only confusing me, as I don't get how the constraint matrix Amat is enforcing a constraint on the coefficients. Is there any other example I could have a look at or another package?
I also tried solving this analytically with medium success.
Any help is appreciated!
kind regards, Lena
I’m working with the software R and XLStat. I’ve conducted an one-way ANOVA (my categorical variable is 3 modal (1,2,3) and my response variable is quantitative on scale 1-10).
I’ve conducted this ANOVA on R and XLStat and the outputs for the F fisher, p-value, coefficient estimations, t-values, std error … are exactly the same.
However, XLstat offers an extra output : the standardized coefficients (called too beta coefficients). Firstly, I was surprised, because I didn’t think we could calculate beta coefficient for a categorical variable and according to the bibliography I read, it doesn’t have any sense.
Anyway, I tried to find these coefficients with R, thanks to the unique formula I found : beta = estimate * sd(x)/sd(y). sd(x) being the standard deviation of the categorical variable (which is automatically transformed as numeric variable with R, in order to calculate sd(x), seems logical ) and sd(y) being the standard deviation of my response variable.
The first beta I obtained with R is the same than in XLstat , but not the second and the third. Given that the first one is the same with R and XLStat, I suppose that Xlstat convert too the categorical variable in numeric variable (which is senseless but this is not the question).
Moreover, I conducted the anova on Statistica in order to see if XLStat did any mistake but its outputs for the beta coefficients are the same than in Xlstat …
So, my question is this one : what is the formula to obtain the beta coefficient in a one way Anova ?
Then, I would like to ask you about the relevance of these beta coefficients for a categorical variable. According to my thoughts and publications I read, it doesn't have any sense …
ps contrasts in R and Xlstat are sum(ai)=0. For beta coefficients, XLStat remove the intercept. I guess this fact could be important but I don't know somehow
The formula for obtaining beta coefficients from metric coefficients for an ANOVA is the same as for a linear regression. The coefficients have no sensible interpretation (for categorical variables), but standardized coefficients are useful in comparing the relative effects of IVs with different metrics.
In R, either use scale() to transform the data to z-scores before fitting the model, or use lm.beta() instead of lm().
It is not clear why you would obtain different beta coefficients with XLStat, but it could have something to do with degrees of freedom if it's not an error. This example compares the lm.beta() function in R with SAS and obtains the same coefficients.
I'm new to R and statistical modelling, and am looking to use the lmmlasso library in r to fit a mixed effects model, selecting only the best fixed effects out of ~300 possible variables.
For this model I'd like to include both a fixed intercept, a random effect, and a random intercept. Looking at the manual on CRAN, I've come across the following:
x: matrix of dimension ntot x p including the fixed-effects
covariables. An intercept has to be included in the first column as
(1,...,1).
z: random effects matrix of dimension ntot x q. It has to be a matrix,
even if q=1.
While it's obvious what I need to do for the fixed intercept I'm not quite sure how to include both a random intercept and effect. Is it exactly the same as the fixed matrix, where I include (1...1) in my first column?
In addition to this, I'm looking to validate the resulting model I get with another dataset. For lmmlasso is there a function similar to predict in lme4 that can be used to compute new predictions based on the output I get? Alternatively, is it viable/correct to construct a new model using lmer using the variables with non-zero coefficients returned by lmmlasso, and then use predict on the new model?
Thanks in advance.
I would really appreciate any help with specifying probability weights in R without using the Lumley survey package. I am conducting mediation analysis in R using the Imai et al mediation package, which does not currently support svyglm.
The code I am currently running is:
olsmediator_basic<-lm(poledu ~ gateway_strict_alt + gender_n + spline1 + spline2 + spline3,
data = unifiedanalysis, weights = designweight).
However, I'm unsure if this is weighting the data correctly. The reason is that this code yields standard errors that differ from those I am getting in Stata. The Stata code I am running is:
reg poledu gateway_strict_alt gender_n spline1 spline2 spline3 [pweight=designweight]).
I was wondering if the weights option in R may not be for inverse probability weights, but I was unable to determine this from the documentation, this forum or elsewhere. If I am missing something, I really apologize - I am new to R as well as to this forum.
Thank you in advance for your help.
The R documentation specifies that the weights parameter of the lm function is inversely proportional to the variance of the observations. This is the definition of analytic weights, or aweights in Stata.
Have a look at the ipw package for inverse probability weighting.
To correct a previous answer - I looked up the manual on weights and found the following description for weights in lm
Non-NULL weights can be used to indicate that different observations have different variances (with the values in weights being inversely proportional to the variances); or equivalently, when the elements of weights are positive integers w_i, that each response y_i is the mean of w_i unit-weight observations (including the case that there are w_i observations equal to y_i and the data have been summarized).
These are actually frequency weights (fweights in stata). They multiply out the observation n number of times as defined by the weight vector. Probability weights, on the other hand, refer to the probability that observations group is included in the population. Doing so adjusts the impact of the observation on the coefficients, but not on the standard errors, as they don't change the number of observations represented in the sample.