# Re: [R] Basic vector operations was: Function to approximatecomplex integral

From: Christos Hatzis <christos_at_silicoinsights.com>
Date: Thu 20 Apr 2006 - 05:45:30 EST

You get the same result with

sum(outer(a,b))

-Christos

-----Original Message-----
From: r-help-bounces@stat.math.ethz.ch
[mailto:r-help-bounces@stat.math.ethz.ch] On Behalf Of jim holtman Sent: Wednesday, April 19, 2006 3:32 PM
To: Doran, Harold
Cc: r-help@stat.math.ethz.ch
Subject: Re: [R] Basic vector operations was: Function to approximatecomplex integral

You can always write your own function that will take the values, multiply and then sum them:

> a <- c(2,3)
> b <- c(4,5,6)
> total <- 0
> for (i in a) total <- sum(total, i * b) total
 75
>

On 4/19/06, Doran, Harold <HDoran@air.org> wrote:
>
> Dear List
>
> I apologize for the multiple postings. After being in the weeds on this
> problem for a while I think my original post may have been a little
> cryptic. I think I can be clearer. Essentially, I need the following
>
> a <- c(2,3)
> b <- c(4,5,6)
>
> (2*4) + (2*5) + (2*6) + (3*4) + (3*5) +(3*6)
>
> But I do not know of a built in function that would do this. Any
> suggestions?
>
> -----Original Message-----
> From: r-help-bounces@stat.math.ethz.ch
> [mailto:r-help-bounces@stat.math.ethz.ch] On Behalf Of Doran, Harold
> Sent: Wednesday, April 19, 2006 11:51 AM
> To: r-help@stat.math.ethz.ch
> Subject: [R] Function to approximate complex integral
>
>
>
> I am writing a small function to approximate an integral that cannot be
> evaluated in closed form. I am partially successful at this point and am
> experiencing one small, albeit important problem. Here is part of my
> function below.

>
> This is a psychometric problem for dichotomously scored test items where
> x is a vector of 1s or 0s denoting whether the respondent answered the
> item correctly (1) or otherwise (0), b is a vector of item difficulties,
> and theta is an ability estimate for the individual.
>
> rasch <- function(b,theta){
> 1 / ( 1 + exp(b - theta))
> }
>
> The function rasch gives the probability of a correct response to item i
> conditional on theta, the individuals ability estimate
>
> myfun <- function(x, b, theta){
> sum(rasch(b, theta)^x * ( 1 - rasch(b,theta) )^(1-x) * dnorm(theta))
> }
>
> This is the likelihood function assuming the data are Bernoulli
> distributed multiplied by a population distribution.
>
> Now, when x,b, and theta are of equal length the function works fine as
> below x <- c(1,1,0)
> b <- c(-2,-1,0)
> t <- c(-2,-1.5,-1)
> > myfun(x,b,t)
>  0.2527884
>
> However, I want theta to be a vector of discrete values that will be
> larger than both x and b, something like
>
> t <- seq(-5, 0, by = .01)
>
> However, this gives me the error
> > myfun(x,b,t)
>
> Warning messages:
> 1: longer object length
> is not a multiple of shorter object length in: b - theta
>
> So, for the problem above, I want item 1 to be evaluated at theta 1
> through theta q and then item 2 is evaluated at theta 1 and through
> theta q and so forth for each item.
>
> Can anyone recommend a way for me to modify my function above to
> accomplish this?
>

> Harold
>
>
> [[alternative HTML version deleted]]
>
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>

```--
Jim Holtman
Cincinnati, OH
+1 513 646 9390 (Cell)
+1 513 247 0281 (Home)

What the problem you are trying to solve?

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