R help - May 2007 - Generating Data using Formulas

Hello, 
 
My name is Christian Falde.  I am new to R. 
 
My problem is this.  I am attempting to learn R on my own. In so doing I am
using some problems from Davidson and MacKinnon  Econometric Theory and Methods
to do so.  This is because I can already do the some of the problems in SAS so I
am attempting to rework them using R. Seemed logical to me, now I am stuck and
its really bugging me.
 
 
The problem is this 
 
Generate a data set sample size of 25  with the formula  y=1+.8*y(t-1)+ u. 
Where y is the dependent, y(t-1) is the dependent variable lagged one peroid,
and u is the classical error term.  Assume y0=0 and the u is NID(0,1). Use this
sample to compute the OLS estimates B1 (1) and B2(.8).  Repeat at least 100
times and find the average of the B's.  Use these average to estimate the
bias of the ols estimators.
 
To start I did the following non lagged program.  
 
final<-function(i,j){x<-function(i) {10*i}
y<-function(i,j) {1+.8*10*i+100*rnorm(j)}
datathreeone<- data.frame(replicate(100,coef(lm(y(i,j)~x(i)))))
rowMeans(datathreeone)}
final(1:25,25)
final(1:50,50)
final(1:100,100)
final(1:200,200)
final(1:10000,10000)
 
 
Now the "only" thing I need to to is change ".8*10*i"  which
is exogenous to ".8* y(t-1) ".
 
There are two reasons why I did it this way. I needed the rnorm(i) to generate a
new set of u's each replication, and I wanted to be able to use the function
as i did to make the results more concise.
 
For the lag in SAS we used an if then else logic relating to the number of
observation.  This in R would have to be linked to the invisable row number.  I
think I need an index variable for the row.  Perhaps, sorry thinking while
typing.
 
Another reason why I am stuck, the lag function was seemingly straight forward.
 
lag (x, k=1)
 
yet x  has to be a matrix  so when I tried to do it like above with y as a
function R complained.
 
I have been working on this for a couple of days now so everything is begining
to not make sense.  It just seems to me to get the matrix to work out I would
need to have two matrices.
 
dependent        and           explanatory
y1                 =     sum (  1 +.8*0 + 100*rnorm(i))
y2                 =     sum ( 1 +.8* (dependent row 1) + 100*rnorm(i))
etc  
 
I just am not sure how to do that. 
 
Please help and thank you for your time, 
 
christian falde            
 
 
 
 
 
 
 
 
 
 
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Christian,

The formula language is not suited to such recursive useage 
AFAICS.

You can _vectorize_ your code like this:

cmat <- outer( 1:25, 1:25, function(y,x) ifelse( x>y, 0, 0.8^(y-x) ) )
res <- replicate(1000,{
 	y <- 1 + cmat %*% rnorm(25)
 	coef(lm(y[-1]~y[-25]))
 			})
rowMeans(res) # mean of 1000 replicates

HTH,

Chuck

On Tue, 29 May 2007, Chrisitan Falde wrote:
> Hello,
>
> My name is Christian Falde.  I am new to R.
>
> My problem is this.  I am attempting to learn R on my own. In so doing I 
> am using some problems from Davidson and MacKinnon Econometric Theory 
> and Methods to do so.  This is because I can already do the some of the 
> problems in SAS so I am attempting to rework them using R. Seemed 
> logical to me, now I am stuck and its really bugging me.
>
>
> The problem is this
>
> Generate a data set sample size of 25 with the formula y=1+.8*y(t-1)+ u. 
> Where y is the dependent, y(t-1) is the dependent variable lagged one 
> peroid, and u is the classical error term.  Assume y0=0 and the u is 
> NID(0,1). Use this sample to compute the OLS estimates B1 (1) and 
> B2(.8).  Repeat at least 100 times and find the average of the B's. 
> Use these average to estimate the bias of the ols estimators.
>
> To start I did the following non lagged program.
>
> final<-function(i,j){x<-function(i) {10*i}
> y<-function(i,j) {1+.8*10*i+100*rnorm(j)}
> datathreeone<- data.frame(replicate(100,coef(lm(y(i,j)~x(i)))))
> rowMeans(datathreeone)}
> final(1:25,25)
> final(1:50,50)
> final(1:100,100)
> final(1:200,200)
> final(1:10000,10000)
>
>
> Now the "only" thing I need to to is change ".8*10*i" 
which is
> exogenous to ".8* y(t-1) ".
>
> There are two reasons why I did it this way. I needed the rnorm(i) to 
> generate a new set of u's each replication, and I wanted to be able to 
> use the function as i did to make the results more concise.
>
> For the lag in SAS we used an if then else logic relating to the number 
> of observation.  This in R would have to be linked to the invisable row 
> number.  I think I need an index variable for the row.  Perhaps, sorry 
> thinking while typing.
>
> Another reason why I am stuck, the lag function was seemingly straight
forward.
>
> lag (x, k=1)
>
> yet x has to be a matrix so when I tried to do it like above with y as a 
> function R complained.
>
> I have been working on this for a couple of days now so everything is 
> begining to not make sense.  It just seems to me to get the matrix to 
> work out I would need to have two matrices.
>
> dependent        and           explanatory
> y1                 =     sum (  1 +.8*0 + 100*rnorm(i))
> y2                 =     sum ( 1 +.8* (dependent row 1) + 100*rnorm(i))
> etc
>
> I just am not sure how to do that.
>
> Please help and thank you for your time,
>
> christian falde
>
[snip]

Charles C. Berry                        (858) 534-2098
                                          Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu	         UC San Diego
http://biostat.ucsd.edu/~cberry/         La Jolla, San Diego 92093-0901