Apply. A. Michelle Lawing Ecosystem Science and Management Texas A&M University College Sta,on, TX

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1 Apply A. Michelle Lawing Ecosystem Science and Management Texas A&M University College Sta,on, TX

2 Schedule for today My presenta,on Review New stuff Mixed, Fixed, and Random Models presenta,on Mixed, Fixed, and Random Models demonstra,on BREAK Mixed, Fixed, and Random Models tutorial

3 Homework - Programming Create a func,on that plots a random walk by using rnorm. The func,on should read in the ini,al trait value and the number of,me steps.

4 Review: Model Selec,on Use a CRITERION for evalua,ng and comparing models Use a STRATEGY for searching all the possibili,es or a subset of reasonable possibili,es

5 Review: Model Selec,on We learned about several criteria for model selec,on R2 AIC BIC Mallow s Cp Stepwise Procedures Cross Valida,on Strategy to construct models

6 Review: Bootstrap What do you do if the assump,ons of the method to evaluate data are violated? Ogen we use computer intensive approaches (the power of the computer is used to create a sampling distribu,on) Es,mate with a bootstrap Hypothesis test with a permuta,on

7 Review: Bootstrap Bootstrap is primarily used in es,ma,on Value of a parameter Probability Standard error Confidence interval

8 Permuta,on Test Generated a null distribu,on for the associa,on between two or more variables Repeated random rearrangements of one of the variables

9 Permuta,on Test Rank tests are permuta,on tests e.g., Mann- Whitney U- test Data are replaced by their ranks Ranks are permuted repeatedly to generate null distribu,on Exact probability distribu,on is known

10 Permuta,on Test Why replace data with ranks? Permute the data themselves Probability distribu,on is unknown, so we generate a large number of permuta,ons instead

11 Example of a Permuta,on Test Male sage crickets offer females their hind wings to nibble on during ma,ng. Females receive nutri,on from feeding on the wings. Johnson et al. (1999) asked Are females more likely to mate if they are hungry?

12 Sage Cricket Ma,ng

13 Example of a Permuta,on Test 24 females were divided into 2 groups 11 were starved for two days 13 were fed Frequency Starved Wai,ng,me to ma,ng was recorded Data are not normally distributed Frequency Fed Hours to feeding

14 Example of a Permuta,on Test Null hypothesis is that the mean,me to ma,ng is the same for the starved and the fed groups Alterna,ve hypothesis is that the mean,me to ma,ng is NOT the same between the two groups

15 Example of a Permuta,on Test

16 Example of a Permuta,on Test

17 Example of a Permuta,on Test

18 Permuta,on Assump,ons Samples are random Assumes the distribu,on of variables is similar in every popula,on Robust to departure from equal- shape assump,on when sample size is large These tests have lower power than parametric tests with sample size is small. Power is similar at large sample sizes.

19 Why you should only use permuta,ons as a last resort Only provide p- value Provides no es,mate of a useful parameter

20 Review: Mul,variate Ordina,on Exploratory data analysis Orders objects so that similar ones are near to each other and dissimilar ones are far away There are many ordina,on techniques

21 Review: Mul,variate Ordina,on Ordina,on math goes both ways Eigenvectors describe how to transform data from original coordinates to PCs and back again Singular vectors are the same for CA.

22 Review: Mul,variate Ordina,on Mul,ply PC scores by eigenvector matrix and add back X and Y mean to get the original X and Y scores

23 apply

24 apply Q: How can I use a loop to [ insert task here ]? A: Don t. Use one of the apply func@ons. So, what is apply and how does it work?

25 Geqng Help?apply Apply Func,ons Over Array Margins?by Apply a Func,on to a Data Frame Split by Factors?eapply?lapply?mapply?rapply?tapply Apply a Func,on Over Values in an Environment Apply a Func,on over a List or Vector Apply a Func,on to Mul,ple List or Vector Arguments Recursively Apply a Func,on to a List Apply a Func,on Over a Ragged Array

apply Descrip@on: Returns a vector or array or list of values obtained by applying a func@on to margins of an array or matrix.

26 apply Returns a vector or array or list of values obtained by applying a func@on to margins of an array or matrix. We know about vectors/arrays and func,ons, but what are these margins? Simple: either the rows (1), the columns (2) or both (1:2). By both, we mean apply the func,on to each individual value. An example:

by Descrip@on: Func@on by is an object- oriented wrapper for tapply applied to data frames. The by func,on is a lisle more complex.

27 by by is an object- oriented wrapper for tapply applied to data frames. The by func,on is a lisle more complex. The documenta,on tells you that a data frame is split by row into data frames subsesed by the values of one or more factors, and func,on FUN is applied to each subset in turn. So, we use this one where factors are involved. To illustrate, we use iris :

eapply Descrip@on: eapply applies FUN to the named values from an environment and returns the results as a list. This one is a lisle trickier, since you need to know something about environments in R.

28 eapply eapply applies FUN to the named values from an environment and returns the results as a list. This one is a lisle trickier, since you need to know something about environments in R. An environment, as the name suggests, is a self- contained object with its own variables and func,ons. To con,nue using our very simple example: I don t ogen create my own environments, but they re commonly used by R packages such as so it s good to know how to handle them.

lapply Descrip@on: lapply returns a list of the same length as X, each element of which is the result of applying FUN to the corresponding element of X.

29 lapply lapply returns a list of the same length as X, each element of which is the result of applying FUN to the corresponding element of X. That s a nice, clear descrip,on which makes lapply one of the easier apply func,ons to understand. A simple example: The lapply documenta,on tells us to consult further documenta,on for sapply, vapply and replicate. Let s do that.

sapply Descrip@on: sapply is a user- friendly version of lapply by default returning a vector or matrix if appropriate.

30 sapply sapply is a user- friendly version of lapply by default returning a vector or matrix if appropriate. That simply means that if lapply would have returned a list with elements $a and $b, sapply will return either a vector, with elements [[ a ]] and [[ b ]], or a matrix with column names a and b. Returning to our previous simple example:

vapply Descrip@on: vapply is similar to sapply, but has a pre- specified type of return value, so it can be safer (and some@mes faster) to use.

31 vapply vapply is similar to sapply, but has a pre- specified type of return value, so it can be safer (and some@mes faster) to use. A third argument is supplied to vapply, which you can think of as a kind of template for the output. The documenta,on uses the fivenum func,on as an example, so let s go with that: So, vapply returned a matrix, where the column names correspond to the original list elements and the row names to the output template. Nice!

32 replicate replicate is a wrapper for the common use of sapply for repeated evalua@on of an expression (which will usually involve random number genera@on). The replicate func,on is very useful. Give it two mandatory arguments: the number of replica,ons and the func,on to replicate; a third op,onal argument, simplify = T, tries to simplify the result to a vector or matrix. An example let s simulate 10 normal distribu,ons, each with 10 observa,ons: > replicate(10, rnorm(10))

mapply Descrip@on: mapply is a mul@variate version of sapply. mapply applies FUN to the first elements of each ( ) argument, the second elements, the third elements, and so on.

33 mapply mapply is a mul@variate version of sapply. mapply applies FUN to the first elements of each ( ) argument, the second elements, the third elements, and so on. The mapply documenta,on is full of quite complex examples, but here s a simple, silly one: Here, we sum l1$a[1] + l1$b[1] + l2$c[1] + l2$d[1] ( ) to get 64, the first element of the returned list. All the way through to l1$a[10] + l1$b[10] + l2$c[10] + l2$d[10] ( ) = 100, the last element.

tapply Descrip@on: Apply a func@on to each cell of a ragged array, that is to each (non- empty) group of values given by a unique combina@on of the levels of certain factors. That sounds complicated.

34 tapply Apply a func@on to each cell of a ragged array, that is to each (non- empty) group of values given by a unique combina@on of the levels of certain factors. That sounds complicated. It becomes clearer when the required arguments are described. Usage is tapply(x, INDEX, FUN = NULL,, simplify = TRUE), where X is an atomic object, typically a vector and INDEX is a list of factors, each of same length as X.

35 Summary of apply Things to consider What class is my input data? vector, matrix, data frame On which subsets of that data do I want the func,on to act? rows, columns, all values What class will the func,on return? How is the original data structure transformed? It s the usual input- process- output story: what do I have, what do I want and what lies in between?

Sta$s$cs & Experimental Design with R. Barbara Kitchenham Keele University

Sta$s$cs & Experimental Design with R Barbara Kitchenham Keele University 1 Comparing two or more groups Part 5 2 Aim To cover standard approaches for independent and dependent groups For two groups Student