# Chapter 4: Distance-based linear models (DISTLM) and distance-based redundancy analysis (dbRDA)

Key references

Method: Legendre & Anderson (1999), McArdle & Anderson (2001)

Permutation methods: Freedman & Lane (1983), Anderson & Legendre (1999), Anderson & Robinson (2001), Anderson (2001b)

#### 4.1 General description

Key references Method:, Permutation methods: , , , DISTLM is a routine for analysing and ...

#### 4.2 Rationale

Just as PERMANOVA does a partitioning of variation in a data cloud described by a resemblance mat...

#### 4.3 Partitioning

Consider an (N × p) matrix of response variables Y, where N = the number of samples and p = the n...

#### 4.4 Simple linear regression (Clyde macrofauna)

In our first example of DISTLM, we will examine the relationship between the Shannon diversity (H...

#### 4.5 Conditional tests

More generally, when X contains more than one variable, we may also be interested in conditional ...

#### 4.6 (Holdfast invertebrates)

To demonstrate conditional tests in DISTLM, we will consider the number of species inhabiting hol...

#### 4.7 Assumptions & diagnostics

Thus far, we have only done examples for a univariate response variable in Euclidean space, using...

#### 4.8 Building models

In many situations, a scientist may have measured a large number of predictor variables that coul...

#### 4.9 Cautionary notes

Before proceeding, a few cautionary notes are appropriate with respect to building models. First,...

#### 4.10 (Ekofisk macrofauna)

We shall now use the DISTLM tool to identify potential parsimonious models for benthic macrofauna...

#### 4.11 Visualising models: dbRDA

We may wish to visualise a given model in the multivariate space of our chosen resemblance matrix...

#### 4.12 Vector overlays in dbRDA

Something which certainly should come as no surprise is to see the X variables playing an importa...

#### 4.13 dbRDA plot for Ekofisk

Let us examine the constrained dbRDA ordination for the parsimonious model obtained earlier using...

#### 4.14 Analysing variables in sets (Thau lagoon bacteria)

In some situations, it is useful to be able to partition variability in the data cloud according ...

#### 4.15 Categorical predictor variables (Oribatid mites)

Sometimes the predictor variables of interest are not quantitative, continuous variables, but rat...

#### 4.16 DISTLM versus BEST/ BIOENV

On the face of it, the DISTLM routine might be thought of as playing a similar role to PRIMER’s B...