New Methods in Ecology

Complex statistical tests, and why we should be cautious!

Complex tests

• Logistic Regression

• Principal Components Analysis

• Cluster AnalysisMultivariate

• Multivariate tests mean you have a single explanatory variable, but multiple response variables.

Logistic Regression

Logistic Regression Insects were exposed to a pesticide to

determine the effectiveness of the treatment. The response is dead individuals from a sample

Dose Dead Batch1 2 1003 10 9010 49 9830 96 100100 98 100

Linear regression on the proportions killed vs dose

dose

At dose 0, Proportion killed is less than 0 (negative deaths?) and greater than dose 4, get > 100% mortality!

P(kill) = ax + b

Need to ensure the model is bounded by 0 and 1, build a new equation

No longer have impossible predictions, and the model fits better

dose

P(ki

ll)

€

P(Kill) = 1- P(survived)

P(survived) =e(ax+b )

1+ e(ax+b )

dose

P(ki

ll)Can now look at what proportion would be killed

at a particular dosage

€

P(Kill) = 1- P(survived)

P(survived) =e(ax+b )

1+ e(ax+b )

Logistic regression issues…• Implementing and coding the model can be difficult• Can be tough to work through the equation• Is it easier to design around the issue?

Dose Dead Batch1 2 1003 10 10010 49 10030 96 100100 98 100

• Use the same number in each batch, use “number dead” as the response variable?

€

#Killed = ax +b€

P(survived) =e(ax+b )

1+ e(ax+b )

Multivariate Statistics

• Single explanatory variable, multiple response variables

• Multivariate tests can be useful and insightful• Can be deeply confusing• Very often misused• Difficult to explain the results• Used to mask bad designs, confuse/impress

stupid people.

Parrots in Bonaire

www.parrotwatch.org

Sam Williams

Sam collected a load of data on different aspects of the birds’ biology

Parrots in Bonaire

• What to do with all this?• 1 descriptive variable (nest)• Multiple response variables• Principal component analysis…

Principal Component Analysis• Obtains values for as many principle

components as there are response variables• Each PC accounts for some more of the total

variation• Each nest has a PC value for each PC• Each response variable has a rotation value for

each PC• What do these PC values and rotation values

relate to?• God knows

Principal Component Output

Principle Component

Scree plot, first few Principal components account for much of the variation

Principal Component Output

Biplot of the first 2 principle components

Can be used to look for correlations

Some significance tests (redundancy analysis)

Lots of noise!

Other use of PCA• each nest/individual/replicate has a value of

each Principal component

• Can use these values as a response variable, and subject to other tests

• Called “Dimensionality Reduction”

Salmon Genomics and Survival

• Gene expression data for ~16000 genes, from ~300 fish.

• Each fish is a replicate, each gene is a response variable

• 16000 genes is lot of data, and a lot of variation.

• Do a PCA on the genes, use the PC values as a response variable

• Reduces the dimension of the data, rather than 16000 response variables, now have 1 (PC1, or PC2)

• Can then use this in other tests.

Salmon Genomics and Survival

Salmon Genomics and Survival

Principle component

• Related value of PC1 to survival of the fish, showed a correlation for one stock

days

Prop

ortio

n su

rviv

ing Scotch Chilko Adams

Salmon Genomics and Survival

• Condensed the gene expression data into something useable

• Method insanely complex and computer intensive• Still don’t really know what PC1 is!

Cluster Analysis

• Like PCA, a multivariate method• Unlike PCA, looks for patterns within the data• Produces a hierarchical cluster• Groups similar individuals together• Unsupervised• Have to then decide where groups lie• Try and relate the grouping to something else?

Cluster Analysis

Multivariate Summary• Multivariate statistics are useful for data

mining• Often used when data collection was done

improperly/you’ve been given data sets• Can indicate how to proceed• Can be very messy• Totally opposite to the a priori “carry out an

experiment to test a hypothesis” idea.

• Can be very useful and insightful if used properly

• More complex doesn’t necessarily mean better

• Can be difficult to interpret• Remember the golden rule – know how to

analyse the type of data you will collect, before you collect it!

Complex stats Summary