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# Performing a relative rate test

Section author: Gavin Huttley

From cogent import all the components we need

    >>> from cogent import LoadSeqs, LoadTree
    >>> from cogent.evolve.models import HKY85
    >>> from cogent.maths import stats

Get your alignment and tree.

    >>> aln = LoadSeqs(filename = "data/long_testseqs.fasta")
    >>> t = LoadTree(filename = "data/test.tree")

Create a HKY85 model.

    >>> sm = HKY85()

Make the controller object and limit the display precision (to decrease the chance that small differences in estimates cause tests of the documentation to fail).

    >>> lf = sm.makeLikelihoodFunction(t, digits=2, space=3)

Set the local clock for humans & Howler Monkey. This method is just a special interface to the more general `setParamRules` method.

    >>> lf.setLocalClock("Human", "HowlerMon")

Get the likelihood function object this object performs the actual likelihood calculation.

    >>> lf.setAlignment(aln)

Optimise the function capturing the return optimised lnL, and parameter value vector.

    >>> lf.optimise()

View the resulting maximum-likelihood parameter values.

    >>> lf.setName("clock")
    >>> print lf
    clock
    =====
    kappa
    -----
     4.10
    -----
    ===========================
         edge   parent   length
    ---------------------------
        Human   edge.0     0.04
    HowlerMon   edge.0     0.04
       edge.0   edge.1     0.04
        Mouse   edge.1     0.28
       edge.1     root     0.02
    NineBande     root     0.09
     DogFaced     root     0.11
    ---------------------------
    ==============
    motif   mprobs
    --------------
        T     0.23
        C     0.19
        A     0.37
        G     0.21
    --------------

We extract the log-likelihood and number of free parameters for later use.

    >>> null_lnL = lf.getLogLikelihood()
    >>> null_nfp = lf.getNumFreeParams()

Clear the local clock constraint, freeing up the branch lengths.

    >>> lf.setParamRule('length', is_independent=True)

Run the optimiser capturing the return optimised lnL, and parameter value vector.

    >>> lf.optimise()

View the resulting maximum-likelihood parameter values.

    >>> lf.setName("non clock")
    >>> print lf
    non clock
    =====
    kappa
    -----
     4.10
    -----
    ===========================
         edge   parent   length
    ---------------------------
        Human   edge.0     0.03
    HowlerMon   edge.0     0.04
       edge.0   edge.1     0.04
        Mouse   edge.1     0.28
       edge.1     root     0.02
    NineBande     root     0.09
     DogFaced     root     0.11
    ---------------------------
    ==============
    motif   mprobs
    --------------
        T     0.23
        C     0.19
        A     0.37
        G     0.21
    --------------

These two lnL’s are now used to calculate the likelihood ratio statistic it’s degrees-of-freedom and the probability of observing the LR.

    >>> LR = 2 * (lf.getLogLikelihood() - null_lnL)
    >>> df = lf.getNumFreeParams() - null_nfp
    >>> P = stats.chisqprob(LR, df)

Print this and look up a $\chi^2$ with number of edges - 1 degrees of freedom.

    >>> print "Likelihood ratio statistic = ", LR
    Likelihood ratio statistic =  2.7...
    >>> print "degrees-of-freedom = ", df
    degrees-of-freedom =  1
    >>> print "probability = ", P
    probability =  0.09...