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(This article was first published on <strong><a href="https://www.r-exercises.com/2018/06/21/non-linear-model-in-r-exercise/"> R-exercises</a></strong>, and kindly contributed to <a rel="nofollow" href="https://www.r-bloggers.com/">R-bloggers)</a> </div>
<p>A mechanistic model for the relationship between x and y sometimes needs parameter estimation. When model linearisation does not work,we need to use non-linear modelling.<br>
There are three main differences between non-linear and linear modelling in R:<br>
1. specify the exact nature of the equation<br>
2. replace the <code>lm()</code> with <code>nls()</code> which means nonlinear least squares<br>
3. sometimes we also need to specify the model parameters a,b, and c.</p>
<p>In this exercise, we will use the same dataset as the previous exercise in polynomial regression <a rel="nofollow" href="https://www.r-exercises.com/2018/06/07/polynomial-model-in-r-study-case-exercises/" target="_blank">here</a>. Download the data-set <a rel="nofollow" href="https://www.dropbox.com/s/9ixbug5agzmv4ek/mussel.csv?dl=0" target="_blank">here</a>.<br>
A quick overview of the dataset.<br>
Response variable = number of invertebrates (INDIV)<br>
Explanatory variable = the area of each clump (AREA)<br>
Additional possible response variables = Species richness of invertebrates (SPECIES)<br>
Answers to these exercises are available <a rel="nofollow" href="https://www.r-bloggers.com/www.r-exercises.com/2018/06/21/nonliner-model-in-r-solutions/" target="_blank">here</a>. If you obtained a different (correct) answer than those listed on the solutions page, please feel free to post your answer as a comment on that page.</p>
<p><strong>Exercise 1</strong><br>
Load dataset. Specify the model, try to use power function with <code>nls()</code> and a=0.1 and b=1 as initial parameter number</p>
<p><strong>Exercise 2</strong><br>
A quick check by creating plot residual versus fitted model since normal plot will not work</p>
<p><strong>Exercise 3</strong><br>
Try to build self start function of the powered model</p>
<p><strong>Exercise 4</strong><br>
Generate the asymptotic model </p>
<p><strong>Exercise 5</strong><br>
Compared the asymptotic model to the powered one using AIC. What can we infer?</p>
<p><strong>Exercise 6</strong><br>
Plot the model in one graph</p>
<p><strong>Exercise 7</strong><br>
Predict across the data and plot all three lines</p>
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