统计代写|R语言代写R language代考|NTRES6100

统计代写|R语言代写R language代考|Fitting linear models

In $\mathrm{R}$, the models to be fitted are described by “model formulas” such as $\mathrm{y} \sim \mathrm{x}$ which we read as $y$ is explained by $x$. Model formulas are used in different contexts: fitting of models, plotting, and tests like $t$-test. The syntax of model formulas is consistent throughout base $\mathrm{R}$ and numerous independently developed packages. However, their use is not universal, and several packages extend the basic syntax to allow the description of specific types of models.

As most things in R, model formulas can be stored in variables. In addition, contrary to the usual behavior of other statistical software, the result of a model fit is returned as an object, containing the different components of the fit. Once the model has been fitted, different methods allow us to extract parts and/or further manipulate the results obtained by fitting a model. Most of these methods have implementations for model fit objects for different types of statistical models. Consequently, what is described in this chapter using linear models as examples, also applies in many respects to the fit of models not described here.

The $\mathrm{R}$ function $7 \mathrm{~m}$ () is used to fit linear models. If the explanatory variable is continuous, the fit is a regression. If the explanatory variable is a factor, the fit is an analysis of variance (ANOVA) in broad terms. However, there is another meaning of ANOVA, referring only to the tests of significance rather to an approach to model fitting. Consequently, rather confusingly, results for tests of significance for fitted parameter estimates can both in the case of regression and ANOVA, be presented in an ANOVA table. In this second, stricter meaning, ANOVA means a test of significance based on the ratios between pairs of variances.

统计代写|R语言代写R language代考|Non-linear regression

Function n7s() is R’s workhorse for fitting non-linear models. By non-linear it is meant non-linear in the parameters whose values are being estimated through fitting the model to data. This is different from the shape of the function when plotted-i.e., polynomials of any degree are linear models. In contrast, the Michaelis-Menten equation used in chemistry and the Gompertz equation used to describe growth are non-linear models in their parameters.

While analytical algorithms exist for finding estimates for the parameters of linear models, in the case of non-linear models, the estimates are obtained by approximation. For analytical solutions, estimates can always be obtained, except in infrequent pathological cases where reliance on floating point numbers with limited resolution introduces rounding errors that “break” mathematical algorithms that are valid for real numbers. For approximations obtained through iteration, cases when the algorithm fails to converge onto an answer are relatively common. Iterative algorithms attempt to improve an initial guess for the values of the parameters to be estimated, a guess frequently supplied by the user. In each iteration the estimate obtained in the previous iteration is used as the starting value, and this process is repeated one time after another. The expectation is that after a finite number of iterations the algorithm will converge into a solution that “cannot” be improved further. In real life we stop iteration when the improvement in the fit is smaller than a certain threshold, or when no convergence has been achieved after a certain maximum number of iterations. In the first case, we usually obtain good estimates; in the second case, we do not obtain usable estimates and need to to do is to try different starting values and if this also fails, switch to a different computational algorithm. These steps usually help, but not always. Good starting values are in many cases crucial and in some cases “guesses” can be obtained using either graphical or analytical approximations.

For functions for which computational algorithms exist for “guessing” suitable starting values, R provides a mechanism for packaging the function to be fitted together with the function generating the starting values. These functions go by the name of self-starting functions and relieve the user from the burden of guessing and supplying suitable starting values. The self-starting functions available in R are ssasymp(), ssasympoff(), ssasymporig(), ssbiexp(), ssfot (), ssfp10), ssgompertz (), sslogis(), sSmicmen(), and ssweibu110. Function se1fstart() can be used to define new ones. All these functions can be used when fitting models with n1s or n1me. Please, check the respective help pages for details.

R语言代考

统计代写|R语言代写R language代考|Non-linear regression

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