09.03.2021

# Nlme function r example

By Gronris

You can report issue about the content on this page here Want to share your content on R-bloggers? Fitting mixed models has become very common in biology and recent developments involve the manipulation of the variance-covariance matrix for random effects and residuals. I have been struggling with this issue very often in the last years and I thought it might be useful to publish a few examples in this blog, to save collegues from a few headaches.

The first example in this series relates to a randomised complete block design with three replicates, comparing winter wheat genotypes. The experiment was repeated in seven years in the same location.

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Please, note that this dataset shows the data for eight genotypes, but the model that we want to fit requires that the number of environments is higher than the number of genotypes. Therefore, we have to make a subset, at the beginning, removing a couple of genotypes. This model is often used in stability analyses for multi-environment experiments and I will closely follow the coding proposed in Piepho :. Such an assumption may be questioned, but we will not do it now, for the sake of simplicity.

Furthermore, it is reasonable that, if an environment is good for one genotype, it may also be good for other genotypes, so that yields in each environment are correlated, although the correlations can be different for each couple of genotypes. Piepho has shown how the above model can be coded by using SAS and I translated his code into R. This model is rather complex and may take long to converge.

Indeed, agronomists and plant breeders often adopt a two-steps fitting procedure: in the first step, the means across blocks are calculated for all genotypes in all environments. In the second step, these means are used to fit an environmental variance model. Furthermore, we need to be able to assume similar variances within all experiments. I would also like to give an example of this two-step analysis method.

See the code below. As the design is perfectly balanced, the diagonal elements of the above matrix correspond to the variances of genotypes across environments:. Strictly speaking, those variances are not the environmental variances, as they also contain the within-experiment and within block random variability, which needs to be separately estimated during the first step. To leave a comment for the author, please follow the link and comment on their blog: R on The broken bridge between biologists and statisticians.

Want to share your content on R-bloggers? The environmental variance model Fitting mixed models has become very common in biology and recent developments involve the manipulation of the variance-covariance matrix for random effects and residuals. Thanks for reading! Linear mixed-effects models using R: a step-by-step approach. Springer, Berlin. Muhammad Yaseen, Kent M. Eskridge and Ghulam Murtaza R package version 0.

Agronomy Journal 91, — Pinheiro, J. Springer-Verlag Inc. Never miss an update! Subscribe to R-bloggers to receive e-mails with the latest R posts. You will not see this message again.You can report issue about the content on this page here Want to share your content on R-bloggers? In this post, I am not going to talk about real complex models. However, I am going to talk about models that are often overlooked by agronomists and biologists, while they may be necessary in several circumstances, especially with field experiments.

The point is that field experiments are very often laid down in blocks, using split-plot designs, strip-plot designs or other types of designs with grouping factors blocks, main-plots, sub-plots. Indeed, observations in the same group are correlated, as they are more alike than observations in different groups. What happens if we neglect the grouping factors? We break the independence assumption and our inferences are invalid Onofri et al.

To my experience, field scientists are totally aware of this issue when they deal with ANOVA-type models e. We might be tempted to neglect the block effect and run a linear regression analysis of yield against density. This is clearly wrong I am violating the independence assumption and inefficient, as any block-to-block variability goes into the residual error term, which is, therefore, inflated. Some of my collegues would take the means for densities and use those to fit a linear regression model two-steps analysis.

By doing so, block-to-block variability is cancelled out and the analysis becomes more efficient. However, such a solution is not general, as it is not feasible, e.

With the appropriate approach, sound analyses can also be made in two-steps Damesa et al. From my point of view, it is reasonable to search for more general solutions to deal with one-step analyses.

Based on our experience with traditional ANOVA models, we might think of taking the block effect as fixed and fit it as and additive term. See the code below.

With regression, this solution is not convincing. Indeed, the above model assumes that the blocks produce an effect only on the intercept of the regression line, while the slope is unaffected. Is this a reasonable assumption? I vote no.

The p-level confirms that the block had a significant effect both on the intercept and on the slope. To describe such an effect we need 20 parameters in the model, which is not very parsimonious.

And above all: which regression line do we use for predictions? Taking the block effect as fixed is clearly sub-optimal with regression models. The question is: can we fit a simpler and clearer model? The answer is: yes.Join Stack Overflow to learn, share knowledge, and build your career. Connect and share knowledge within a single location that is structured and easy to search. The gls function is used to fit the extended linear model, using either maximum likelihood, or restricted maximum likelihood.

It can be veiwed as an lme function without the argument random. For further details, it would be instructive to compare the lme analysis of the orthodont dataset starting on p of the same book with the gls analysis starting on p To begin, compare. Notice that the estimates of the fixed effects are the same to 6 decimal placesbut the standard errors are different, as is the correlation matrix. In principle the only difference is that gls can't fit models with random effects, whereas lme can.

R Coding for Econometrics, Part 5: The lm() function: Extracting and Presenting Regression Results

Asked 11 years, 6 months ago. Active 9 years, 2 months ago. Viewed 17k times. In the nlme package there are two functions for fitting linear models lme and gls.

What are the differences between them in terms of the types of models that can be fit, and the fitting process? What is the design rational for having two functions to fit linear mixed models where most other systems e. Update: Added bounty. Interested to know differences in the fitting process, and the rational. Improve this question. Ian Fellows. Ian Fellows Ian Fellows Add a comment. Active Oldest Votes. To begin, compare orth.Non linear mixed effects NLME modeling is a standard method for pharmacometric analyses.

In mixed effects modeling, fixed effects include the average parameters of the population and covariates, whereas the random effects account for residual random variability between individuals. Inter-individual variability is quantified and its dependence on covariates is assessed. Often, users are faced with the decision which platform to use or are missing the training to make optimal use of both platforms.

In the following, a novel approach to NLME modeling is explained, which concentrates on making modeling more user-friendly and accessible by shifting the focus from the software to modeling. It is still in its infancy but developing quickly. And it is open source! The generation and execution of longitudinal NLME models is split into two main steps. Such a project can then be executed and further analyzed see the Chapter about Model Evalution. The data needs to be in IQRnlmeData format. The minimally required columns for this format are:. This is a ODE based format, described earlier in this book. This speeds up the execution of an NLME model tremendously. In IQR Tools a structural model is always defined in terms of its differential equations.

IQR Tools by default uses the MU referencing see for example here for the implementation of parameter transformations and covariates. A drawback of MU referencing is that covariates implemented in this way need to be time independent. Even if they are coded in the dataset in a time dependent manner, only the first value will be considered by SAEM and thus in reality it will be turned into a time invariant covariate.

In order to implement time varying covariates, IQR Tools uses something called regression parameters. Each regression parameter is simply a column in the dataset with a name. This name can appear in a structural model as a parameter and will receive the values from the column in the dataset. No interpolation is done over time. Carry forward of the last value is used. For NONMEM users the difference to the typical implementation of time varying covariates might not be obvious - as all seems to be as always.

Things to remember : When implementing time varying covariates in NLME models with IQR Tools, the respective columns need to be defined as regression parameters we will see this in examples below. This is also possible in the case of time invariant covariates and complex covariate models that cannot be implemented using MU referencing.

This first example is important as many concepts will be introduced. Following examples will then only focus on the things that can be done differently and not repeat the basics. An example dataset is provided in the material, based on the ubiquitous Theophylline dataset.You can report issue about the content on this page here Want to share your content on R-bloggers?

It is widely known that the yield of a genotype in different environments depends on environmental covariates, such as the amount of rainfall in some critical periods of time.

Apart from rain, also temperature, wind, solar radiation, air humidity and soil characteristics may concur to characterise a certain environment as good or bad and, ultimately, to determine yield potential. A graphical example may be useful; in the figure below we have two genotypes tested in 10 environments. Now, the problem is: how do we determine such value from a multi-environment genotype experiment?

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New Delhi, India. First of all, we need to define an environmental index, which can describe the yield potential in each of the seven environments. This step is ok with balanced data and it is clear that a high environmental index identifies the favorable environments, while a low negative environmental index identifies unfavorable environments. Now, it is possible to regress the yield data for each genotype against the environmental indices, according to the following joint regression model:. As we have seen in the figure above, the average yield of a genotype in each environment cannot be exactly described by the regression against the environmental indices in other words: the observed means do not lie along the regression line.

We also change the fixed block effect into a random effect and remove the intercept, to more strictly adhere to the parameterisation of Equation 1. You can use the code in the box below as a guidance to fit a Finlay-Wilkinson model. In the previous analyses we used the plot data to fit a joint regression model. In order to reduce the computational burden, it may be useful to split the analyses in two-steps:.

The results of the two approaches are not necessarily the same, as some information in the first step is lost in the second. Indeed, for a balanced experiment, it is:. Subsequently, the environmental means are calculated and centered, by subtracting the overall mean.

Now, we fit Equation 2 to the means. In the code below we assume homoscedasticity and, thus, we are fitting the Finlay-Wilkinson model. In the box below, we allow for different variances for each genotype and, therefore, we fit the Eberarth-Russel model. I would like to conclude by saying that a joint regression model, the way I have fitted it here, is simple and intuitively appealing, although it has been criticized for a number of reasons.

On the contrary, linear regression makes the assumption that the levels of explanatory variables are precisely known and not sampled. Alternative methods of fitting joint regression models have been proposed see Piepho,but they are slightly more complex and I will deal with them in a future post.

To leave a comment for the author, please follow the link and comment on their blog: R on The broken bridge between biologists and statisticians. Want to share your content on R-bloggers? NOTE -- Important change from versions. What is an environmental index? Fitting a joint regression model in two-steps Equation 2 In the previous analyses we used the plot data to fit a joint regression model. Finlay-Wilkinson model modFinlay t VarA Happy coding!

References Eberhart, S. Stability parameters for comparing verieties.This generic function fits a linear mixed-effects model in the formulation described in Laird and Ware but allowing for nested random effects. The methods lme. Changes to the fixed-effects formula -- see update. By default the variables are taken from the environment from which lme is called. In this case, the grouping structure formula will be derived from the data used to fit the linear mixed-effects model, which should inherit from class " groupedData " ; iv a named list of formulas or pdMat objects as in iiiwith the grouping factors as names.

The order of nesting will be assumed the same as the order of the order of the elements in the list; v an reStruct object. See the documentation on pdClasses for a description of the available pdMat classes. Defaults to a formula consisting of the right hand side of fixed. See the documentation of corClasses for a description of the available corStruct classes.

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Defaults to NULLcorresponding to no within-group correlations. If given as a formula, it is used as the argument to varFixedcorresponding to fixed variance weights. See the documentation on varClasses for a description of the available varFunc classes. Defaults to NULLcorresponding to homoscedastic within-group errors. This can be a logical vector, or a numeric vector indicating which observation numbers are to be included, or a character vector of the row names to be included.

All observations are included by default. If "REML" the model is fit by maximizing the restricted log-likelihood. If "ML" the log-likelihood is maximized. Defaults to "REML". The default action na. Defaults to an empty list. See the contrasts. An object of class "lme" representing the linear mixed-effects model fit.

Generic functions such as printplot and summary have methods to show the results of the fit. See lmeObject for the components of the fit. The functions residcoeffittedfixed. The function does not do any scaling internally: the optimization will work best when the response is scaled so its variance is of the order of one.

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The computational methods follow the general framework of Lindstrom and Bates The model formulation is described in Laird and Ware The variance-covariance parametrizations are described in Pinheiro and Bates The different correlation structures available for the correlation argument are described in Box, Jenkins and ReinselLittell et aland Venables and Ripley The use of variance functions for linear and nonlinear mixed effects models is presented in detail in Davidian and Giltinan Box, G.

Davidian, M. Laird, N. Lindstrom, M. Littell, R. Pinheiro, J. Venables, W.This generic function fits a nonlinear mixed-effects model in the formulation described in Lindstrom and Bates but allowing for nested random effects. If data is given, all names used in the formula should be defined as parameters or variables in the data frame. The method function nlme.

By default the variables are taken from the environment from which nlme is called. The f1, A 1 on the right hand side of the formula s indicates a single fixed effects for the corresponding parameter s.

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In this case, the grouping structure formula will be given in groupsor derived from the data used to fit the nonlinear mixed-effects model, which should inherit from class groupedData ,; iii a named list of formulas, lists of formulas, or pdMat objects as in iiwith the grouping factors as names.

The order of nesting will be assumed the same as the order of the order of the elements in the list; iv an reStruct object. See the documentation on pdClasses for a description of the available pdMat classes. Defaults to fixedresulting in all fixed effects having also random effects. The order of nesting, when multiple levels are present, is taken from left to right i. If declared as a numeric vector, it is converted internally to a list with a single component fixedgiven by the vector.

The fixed component is required, unless the model function inherits from class selfStartin which case initial values will be derived from a call to nlsList. An optional random component is used to specify initial values for the random effects and should consist of a matrix, or a list of matrices with length equal to the number of grouping levels. Each matrix should have as many rows as the number of groups at the corresponding level and as many columns as the number of random effects in that level.

See the documentation of corClasses for a description of the available corStruct classes. Defaults to NULLcorresponding to no within-group correlations. If given as a formula, it is used as the argument to varFixedcorresponding to fixed variance weights. See the documentation on varClasses for a description of the available varFunc classes.

Defaults to NULLcorresponding to homoscedastic within-group errors.

Customary weight conversions

This can be a logical vector, or a numeric vector indicating which observation numbers are to be included, or a character vector of the row names to be included. All observations are included by default. If "REML" the model is fit by maximizing the restricted log-likelihood. If "ML" the log-likelihood is maximized. Defaults to "ML". The default action na. Defaults to an empty list. If TRUE information on the evolution of the iterative algorithm is printed. Generic functions such as printplot and summary have methods to show the results of the fit.

See nlmeObject for the components of the fit.