Suggest me best statistical test

Question

I have data of frequency of 10 males( birds) voice across age. And I want to study how peak frequency ( one of the acoustic parameter in bird's call) of males call changes as they age. Call data taken from particular age is dependent from its previous. My dependent variable is peak frequently of call at that particular age and independent variable is Age. In 2weeks I have taken 6 readings each day...so I am considering it age 1...then next 2 weeks I did same, that I called age 2...this goes on...I did same for all 10 birds till they died I want to look at peak frequency ( one of the acoustic parameter in bird's call) and see how it changes with age. Please suggest me suitable statistical method. Till now, I have done Wilcoxin matched pairs test to see inter week Significant differences. Is it right to do?

Answer 1

What is not clear from your question is if your objective is:

1. Show peak frequency is dependent on age
2. Show how peak frequency changes with age

One way to achieve both is using a regression model: $ f_{peak} = w_1. age + w_2 .bird + \epsilon$,

where:

• bird is a categorical predictor that takes values $\{bird_1, bird_2,\ldots, bird_{10}\}$.
• $f_{peak}$ is the peak acoustic frequency for a bird
• $w_1, w_2$ are model parameters that you estimate using least squares.
• $\epsilon$ is the model error

You may need to transform $f_{peak}$ (see box-cox transforms) to get linearity.

HTH.

Edit: If a linear model is not a good fit, you can explore spline regression with GAMs so $f_peak = \beta_a s(age) + \beta_b s(bird) + \epsilon$ where $s(.)$ is a smoothing spline.

Answer 2

I want to look at peak frequency (one of the acoustic parameter in bird's call) and see how it changes with age.

First, look at the data. Plot peak frequency against age for each of the birds. That's the best way to see the relationship between peak frequency and age.

Please suggest me suitable statistical method.

Some type of regression of peak frequency against age would seem to be best, as suggested in another answer, but it will probably not be a simple model in which peak frequency is linearly associated with age. When you don't have a particular functional form for such a relationship based on your knowledge of the subject matter, you can let the data tell you the form by using a flexible method like regression splines. Section 2.4 of Frank Harrell's course notes or book outlines these methods, with an emphasis on restricted cubic ("natural") splines. Restricted cubic splines are implemented in R by the ns() function and the rcs() function in Harrell's rms package. For example, with rms you could specify rcs(age) as the predictor instead of just age.

I have data of frequency of 10 males( birds) voice across age... Call data taken from particular age is dependent from its previous.

Although you could use individual birds as predictors in your regression, that's probably not the most efficient way to use your data. You can account for the intra-individual correlations in the data in several ways. The Harrell references discuss longitudinal data in Chapter 7. As you seem to have different numbers of observations among the birds, generalized least squares or mixed models (with birds as random effects) would seem to be the best choices.