Regression¶

EcoPy provides a wrapper for scipy.optimize.leastsq. This wrapper allows users to specify a non-linear function and receive parameter estimates, statistics, log-likelihoods, and AIC.

nls

class nls(func, p0, xdata, ydata)¶

nls takes a function (func), initial parameter estimates (p0), predictor variables (xdata), and a response (ydata) and passes these to scipy.optimize.leastsq. It returns an object of class nls.

Parameters

func: function: A function that returns the quantity to be minimized. See documentation for scipy.optimize.leastsq.
p0: dictionary: A dictionary of initial parameter estimates for every parameter to be estimated in the function.
xdata: numpy.ndarray: A numpy.ndarray of predictor variables. See example below for how to include multiple predictors.
ydata: numpy.ndarray: A numpy.ndarray of the response variable.

Attributes

cov¶: Variance-covariance matrix of parameters

inits¶: Initial parameter estimates

logLik¶: Log-likelihood of the function

nparm¶: Number of parameters estimated

parmEsts¶: Parameter estimates

parmSE¶: Standard error of each parameter

RMSE¶: Root mean square error

pvals¶: p-values of each parameter

tvals¶: t-values of each parameter

Methods

classmethod AIC(k=2)¶: Returns AIC for the given model. Argument k determines the correction applied to the number of parameters

classmethod summary()¶: Returns a regression summary table

Examples

First, load the urchin data:

import ecopy as ep
import numpy as np

urchins = ep.load_data('urchins')

Next, make the X and Y matrices:

Y = np.array(urchins['Respiration])*24
X = np.array(urchins[['UrchinMass', 'Temp']])

Define the least-squares function to be optimized:

def tempMod(params, X, Y):
        a = params[0]
        b = params[1]
        c = params[2]
        mass = X[:,0]
        temp = X[:,1]
        yHat = a*mass**b*temp**c
        err = Y - yHat
        return(err)

Create a dictionary of initial estimates for each parameter:

p0 = {'a':1, 'b':1, 'c': 1}

Run the model and check the summary tables:

tMod = ep.nls(tempMod, p0, X, Y)
tMod.summary()

Non-linear least squares
Model: tempMod
Parameters:
        Estimate        Std. Error      t-value                 P(>|t|)
a        0.0002  0.0002  0.8037  0.4302
c        0.3346  0.1485  2.2533  0.0345
b        1.5209  0.3448  4.4112  0.0002

Residual Standard Error:  0.0371
Df: 22

tMod.AIC()

AIC:  -88.9664797962