R help - Apr 2006 - Basic vector operations was: Function to approximate complex integral

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 at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Doran, Harold
Sent: Wednesday, April 19, 2006 11:51 AM
To: r-help at 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)
[1] 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]]

______________________________________________
R-help at stat.math.ethz.ch mailing list
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PLEASE do read the posting guide!
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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
[1] 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)
> [1] 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]]
>
> ______________________________________________
> R-help@stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide!
> http://www.R-project.org/posting-guide.html
>
> ______________________________________________
> R-help@stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide!
> http://www.R-project.org/posting-guide.html
>


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

What the problem you are trying to solve?

	[[alternative HTML version deleted]]

"Doran, Harold" <HDoran at air.org> wrote:

[...]
> 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?
How about:

sum(a %o% b)

?%o%

Cheers,

-- 
Seb

You get the same result with

sum(outer(a,b))

-Christos 

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of jim holtman
Sent: Wednesday, April 19, 2006 3:32 PM
To: Doran, Harold
Cc: r-help at 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
[1] 75
>

On 4/19/06, Doran, Harold <HDoran at 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 at stat.math.ethz.ch
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Doran, Harold
> Sent: Wednesday, April 19, 2006 11:51 AM
> To: r-help at 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)
> [1] 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]]
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide!
> http://www.R-project.org/posting-guide.html
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide!
> http://www.R-project.org/posting-guide.html
>


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

What the problem you are trying to solve?

	[[alternative HTML version deleted]]

______________________________________________
R-help at stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html

On Wed, 2006-04-19 at 15:25 -0400, Doran, Harold 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?
<SNIP>

Unless I am missing something, how about:
> sum(a %x% b)
[1] 75

See ?"%x%"

You could also use outer():
> sum(outer(a, b, "*"))
[1] 75

See ?outer

HTH,

Marc Schwartz