Hello,

I have been using a single categorical variable to fit evolutionary rate versus various parameters.

I was wondering if there is a way to use, say, two categorical variables each with the same number of categories and link them to get a joint probability using some kind of bivariate distribution?

I'm essentially fitting a line and I would like to have something like three different lines with unique slopes and intercepts, rather than having three intercepts all with the same slope.

Also, is this scalable to multivariate distributions?

Thanks,

Austin

Hi Austin,

You can define up to 32 categorical variables for a likelihood function. In your example it sounds like the variables are independent, so you can define them along the lines of the example in Multimedia File Viewing and Clickable Links are available for Registered Members only!!  You need to Login for the section "Site-to-site rate heterogeneity" (especially see the twocat example starting on page 53).

Sergei

What if the variables are dependent on each other?

Thanks,
Austin

Hi Austin,

You can do this as well, basically by defining the joint distribution P(X,Y) as P(X|Y) * P(Y) (or P(Y|X) * P(X)), i.e. one variable is explicitly defined using a set of conditional distributions. Something like this should work (for discrete valued distributions):

[code]
category c = (2, {{0.7,0.3}}, MEAN,  , {{1,2}}, 1,2);
category d = (2, {{0.5,0.5}{0.2,0.8}}, MEAN, c , {{3,4}}, 3,4);
[/code]

The joint probability of P(c,d) is

P(1,3) = 0.7*0.5 = 0.35;
P(1,4) = 0.7*0.5 = 0.35;
P(2,3) = 0.3*0.2 = 0.06;
P(2,4) = 0.3*0.8 = 0.24;

When you define d in the example above, the 2nd argument defines the matrix of conditional probabilities (1st row for the 1st value of c, 2nd row for the 2nd value of c ...) and using 'c' in place of the standard density argument tells HyPhy that d depends on c.

Sergei

HTH,
Sergei

It seems HYPHY will not allow a categorical variable to depend on another categorical variable?

Am I doing something wrong?

Here's the output:

[code]global wa_p1 = 1/2;
wa_p1:<1;


global wa_1 = 1;
global wa_2 = 1;

categFreqMatrix={{1,1}};
categRateMatrix={{wa_1,wa_2}};

category wa  = (2, categFreqMatrix , MEAN, ,categRateMatrix, 0, 1e25);


global wb_p1 = 1/2;
wb_p1:<1;


global wb_1 = 1;
global wb_2 = 1;

categFreqMatrix={{wb_p1,(1-wb_p1)}};
categRateMatrix={{wb_1,wb_2}};

category wb  = (2, categFreqMatrix , MEAN, wa,categRateMatrix, 0, 1e25);


Error:
1e-25*(_x_-0)Can't have a category variable depend on a category variable.

Function call stack
1 : Category variable: {wb,2,categFreqMatrix,MEAN,wa,categRateMatrix,0,1e25}
-------
2 : ExecuteCommands in string gdDefString using basepath /home/agm854/RSA_Stuffs/Using_Smaller_Set/nonzero_k_2cats_dep/catmat_pro_2/.
-------
3 : BuildCategory(Cat_Num,Cat_Name_2,Cat_Name_1)[/code]

Hi Austin,

For "wb", HyPhy expects you to supply a 2x2 matrix for the frequencies, i.e. two conditional distributions (one for wa = wa_1 and another for wa = wa_2).

Sergei

[code]
global wa_p1 = 1/2;
wa_p1:<1;


global wa_1 = 1;
global wa_2 = 1;

categFreqMatrix={{0.5,0,5}};
categRateMatrix={{wa_1,wa_2}};

category wa  = (2, categFreqMatrix , MEAN, ,categRateMatrix, 0, 1e25);


global wb_p1 = 1/2;
wb_p1:<1;
global wb_p2 = 1/2;
wb_p2:<1;


global wb_1 = 1;
global wb_2 = 1;

categFreqMatrix={{wb_p1,(1-wb_p1)},
                      {wb_p2,(1-wb_p2)}};
                     
categRateMatrix={{wb_1,wb_2}};

category wb  = (2, categFreqMatrix , MEAN, wa,categRateMatrix, 0, 1e25);

[/code]