Re: [R] Heuristic optimisation?

2008-10-15 Thread paulandpen
Ajay,

Bayesm deals with this very issue in choice modelling (a form of econometric 
modelling as outlined in the article).  I think those guys (the developers of 
Bayesm) and the apprach they recommend for navigating the likelihood function 
through a bayesian approachs makes a lot of sense to me, in fact I think they 
are really onto something amazing here.

I am still trying to get the execution side of things from this package 
adequately sorted for my own purposes.   

Paul


 Ajay Shah [EMAIL PROTECTED] wrote:
 
 I wondered was people on this list felt about this article:
   http://www.voxeu.org/index.php?q=node/2363
 which talks about the problems of obtaining sound answers in numerical
 optimisation in settings such as MLE or NLS.
 
 -- 
 Ajay Shah  
 http://www.mayin.org/ajayshah  
 [EMAIL PROTECTED] 
 http://ajayshahblog.blogspot.com
 *(:-? - wizard who doesn't know the answer.
 
 __
 R-help@r-project.org mailing list
 https://stat.ethz.ch/mailman/listinfo/r-help
 PLEASE do read the posting guide 
 http://www.R-project.org/posting-guide.html
 and provide commented, minimal, self-contained, reproducible code.

__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


Re: [R] Regression with nominal data

2008-09-07 Thread paulandpen
Soren,

It sounds like you are new to R so I will refer you to some packages that I 
think some people would find more user friendly as beginners.  

Zelig is excellent.  You could run a series of logistic regressions coding your 
dependent variables as follows (a versus b, a versus c, b versus c)  

See the website below

http://gking.harvard.edu/zelig/docs/index.html

Alternatively you could try Rattle

See the website below

http://rattle.togaware.com/rattle-features.html

Or you could try Rcmder

HTH Paul


 [EMAIL PROTECTED] wrote:
 
 Hi,
 
 y is nominal (3 categories), x1 to 3 is scale. What I want is a  
 regression, showing the probability to fall in one of the three  
 categories of y according to the x. How can I perform such a  
 regression in R?
 
 Thanks for your help
 
 Sören
 
 __
 R-help@r-project.org mailing list
 https://stat.ethz.ch/mailman/listinfo/r-help
 PLEASE do read the posting guide 
 http://www.R-project.org/posting-guide.html
 and provide commented, minimal, self-contained, reproducible code.

__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


Re: [R] New to R. Question about very large files

2008-08-14 Thread paulandpen

Hi Richard,

It is if you use Rattle.  Rattle allows you to do that for quite a few types 
of models and has a really nice GUI interface.  It has been developed for 
the purposes of datamining, and given your use of the term score in your 
post, I assume in part that this is what you are looking for.  You can 
import a random sample of cases (a training percentage from the total 
dataset) and the package will use the remainder of your sample for testing 
and scoring.  Rattle is very sophisticated in terms of the algorithms it 
offers, and once you get going in R, SAS will become obselete (just 
kidding).


Sorry if I am wrong here about what you need.

Welcome . Paul

- Original Message - 
From: Richard Palmer [EMAIL PROTECTED]

To: r-help@r-project.org
Sent: Thursday, August 14, 2008 10:40 PM
Subject: [R] New to R. Question about very large files



.. I am new to R but experienced in SAS.  SAS has the capability to let me
develop a model from a sample and use the results to score the records of
another file which won't fit in memory.  Is this straightforward in R or
does it require coding to do the scoring in segments?  Can someone point 
me

to sample code that I can copy or modify to do this quickly?

--
Richard Palmer

Home 508 877-3862
Cell 508 982-7266

[[alternative HTML version deleted]]

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

and provide commented, minimal, self-contained, reproducible code.



__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


[R] error with .dll file and RGtk2

2008-07-24 Thread paulandpen

Hi all,

I am getting the following error message.

Does somebody know what needs to happen here?

I have tried re-installing the RGtk2 package and also downloading a .dll 
file and installing it in the RGtk2 file folder


Error in dyn.load(x, as.logical(local), as.logical(now)) :
   unable to load shared library 
'C:/PROGRA~1/R/R-25~1.1/library/RGtk2/libs/RGtk2.dll':

 LoadLibrary failure:  The specified module could not be found.

Thanks in advance

Paul

__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


Re: [R] Excel Trend Function

2008-07-13 Thread paulandpen

Hi Felipe,

Daniel mentions imputation is a disputed practice.  There are 
recommendations and rules of thumb for its use.  I am not sure that 
imputation is disputed.  I would be interested to see some links to articles 
recommending against its use.


Paul


- Original Message - 
From: Felipe Carrillo [EMAIL PROTECTED]

To: [EMAIL PROTECTED]
Sent: Sunday, July 13, 2008 5:46 AM
Subject: [R] Excel Trend Function



Hi:
I have a dataset and need to interpolate for missing days. In Excel I 
either average from sampled days from above and below the missing days or 
use the TREND function to make up for the missing values. I have been 
reading about na.approx, is this function similar to the TREND function? 
Which is the best recommendable way to make up for missing data?

Here's my dataset: weeks 17,18,26 and 46 have 0 daysSamp.

Year Week daysSamp Lower TotalPD Upper varTotalPD
2006 47 6 126988 188259 249530 1045878675
2006 48 7 189155 253350 317545 1148102355
2006 49 7 103300 132741 162182 241480186
2006 50 6 11801 252576 493352 16151006813
2006 51 7 2348 3671 4994 487926
2006 52 5 2606 29901 57196 215454181
2006 2 7 2968 4513 6058 664723
2006 3 7 1128 1889 2650 161231
2006 4 7 479 963 1447 65196
2006 5 7 2819 4413 6007 708094
2006 6 6 -1009 3128 7264 4766743
2006 7 7 -5239 10769 26777 71387835
2006 8 7 150 503 856 34685
2006 9 7 1858 2989 4120 356562
2006 10 7 193 494 795 25281
2006 11 7 125 346 567 13627
2006 12 7 432 767 1102 31189
2006 13 7 1229 1867 2505 113569
2006 14 7 813 1339 1865 77140
2006 15 4 -66 124 315 10105
2006 16 7 152 903 1654 157242
2006 17 0
2006 18 0
2006 19 5 0 0 0 0
2006 20 4 0 0 0 0
2006 21 5 0 0 0 0
2006 22 6 0 0 0 0
2006 23 7 -65 285 635 34112
2006 24 6 0 0 0 0
2006 25 7 0 0 0 0
2006 26 0
2006 27 4 228 931 1634 137726
2006 28 4 801 2231 3662 569977
2006 29 4 4544 9242 13939 6147522
2006 30 5 15798 28465 41131 44697915
2006 31 5 25398 41049 56701 68245523
2006 32 5 48197 82216 116235 322416917
2006 33 5 142980 230411 317841 2129630128
2006 34 5 227141 360468 493794 4952314336
2006 35 5 467244 756325 1045405 23281569629
2006 36 5 281049 463331 645614 9256900449
2006 37 2 227636 620330 1013023 42961663047
2006 38 3 478990 983472 1487954 70903343603
2006 39 7 539690 846522 1153354 26228718974
2006 40 7 320959 457866 594773 5221891252
2006 41 7 427561 582452 737343 6683813344
2006 42 7 271788 351103 430418 1752614293
2006 43 7 165019 208853 252687 535301133
2006 44 7 91514 117390 143266 186537178
2006 45 7 59061 79187 99313 112842787
2006 46 0

Felipe D. Carrillo
Supervisory Fishery Biologist
Department of the Interior
US Fish  Wildlife Service
 California, USA

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

and provide commented, minimal, self-contained, reproducible code.



__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


Re: [R] Cluster on both categorical and numerical data

2008-06-18 Thread paulandpen

okay,

when you cluster information, you can have two inputs

raw data information which the algorithms converts have into a matrix and 
then processes


a pre-processed matrix which you create yourself to input into a package

essentially, packages will have a default assumption about the data you are 
using or the type of matrix you are using


these matrices are often defined in simplistic terms as either a similarity 
or dissimilarity matrix


think of a correlation matrix as an example of a matrix which represents 
similarity


i think you will need to create a dissimilarity matrix (think of something 
that is like a correlation matrix which measures similarity in the 
diagonals) and it is the opposite of this (technically not correct, but you 
get the idea I hope)


i use clustan graphics for all my clustering needs and gower's coefficient 
is the input i use when i have mixed variables


if you pre-process (create a dissimilarity matrix) using Gowers algorithm, 
then specify this everything should work fine


once you get this sorted, it should be all straight-forward

PD

- Original Message - 
From: Chua Siang Li [EMAIL PROTECTED]

To: r-help@r-project.org
Sent: Wednesday, June 18, 2008 7:46 PM
Subject: [R] Cluster on both categorical and numerical data




  Hello there.  Is there any function in R that can do cluster on a set of
  data that has both categorical and numerical variables?  thanks.
  siangli
__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide 
http://www.R-project.org/posting-guide.html

and provide commented, minimal, self-contained, reproducible code.



__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


Re: [R] Fractional Factorial Design

2008-04-28 Thread paulandpen

alg-design will do the trick

regards paul


- Original Message - 
From: Caio Azevedo [EMAIL PROTECTED]

To: R - discussion list [EMAIL PROTECTED]
Sent: Monday, April 28, 2008 11:11 PM
Subject: [R] Fractional Factorial Design



Hi all,

Does anybody know if it is possible to build a fractional factorial design
in R? That is, suppose that we want do design an experiment with 3 factors
with 2, 3 and 3 levels, respectivly. However we want to consider, let's 
say,
only 6 from all possible level combinations. Does R design such 
experiment?


Thanks in advance,

Caio

[[alternative HTML version deleted]]

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

and provide commented, minimal, self-contained, reproducible code.



__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


Re: [R] Fractional Factorial Design

2008-04-28 Thread paulandpen

Caio,

using algdesign code below (this produces a full factorial 2*3*3 full 
design)



gen.factorial(c(2,3,3))


  X1 X2 X3
1  -1 -1 -1
2   1 -1 -1
3  -1  0 -1
4   1  0 -1
5  -1  1 -1
6   1  1 -1
7  -1 -1  0
8   1 -1  0
9  -1  0  0
10  1  0  0
11 -1  1  0
12  1  1  0
13 -1 -1  1
14  1 -1  1
15 -1  0  1
16  1  0  1
17 -1  1  1
18  1  1  1

using  ...

optFederov(~.,dat,6)


here is a design that is produced with six trials

  X1 X2 X3
3   1 -1 -1
4  -1  1 -1
13 -1 -1  1
15  1 -1  1
16 -1  1  1
18  1  1  1

This does the job with good efficiency.

I would be interested to know what your objection to this is S

Regards Paul


- Original Message - 
From: Caio Azevedo [EMAIL PROTECTED]

To: R - discussion list [EMAIL PROTECTED]
Sent: Monday, April 28, 2008 11:11 PM
Subject: [R] Fractional Factorial Design



Hi all,

Does anybody know if it is possible to build a fractional factorial design
in R? That is, suppose that we want do design an experiment with 3 factors
with 2, 3 and 3 levels, respectivly. However we want to consider, let's 
say,
only 6 from all possible level combinations. Does R design such 
experiment?


Thanks in advance,



[[alternative HTML version deleted]]

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

and provide commented, minimal, self-contained, reproducible code.



__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


Re: [R] Fractional Factorial Design

2008-04-28 Thread paulandpen

Excellent points Steve,

I am ever expanding my understanding in the area and power is an interesting 
one.  I do a lot of choice modelling myself, and I am confounded (grin) by 
the optimal way to develop designs with conditional levels (deliberate 
confounds) etc.


Thanks for that.

Regards P


- Original Message - 
From: S Ellison [EMAIL PROTECTED]
To: Caio Azevedo [EMAIL PROTECTED]; paulandpen 
[EMAIL PROTECTED]; R - discussion list 
[EMAIL PROTECTED]

Sent: Tuesday, April 29, 2008 1:48 AM
Subject: Re: [R] Fractional Factorial Design



Paul;

You asked

using  ...
optFederov(~.,dat,6)
... does the job with good efficiency.

I would be interested to know what your objection to this is S


I have no issue with AlgDesign in principle, but the question was
specifically about _fractional_ factorials, so I answered that.

As to which is best - well, first pick your definition of 'best'. Both
can improve drastically on full factorials. For me, he advantage of a
fractional factorial is that it retains balance and, more importantly
from a design perspective, I get to choose which effects are confounded
and can arrange matters so that some effects are guaranteed
unconfounded. The deterministic nature of the selection also makes it a
bit easier to build power considerations into the process if you're so
minded. The price of that is that the number of observations is
typically larger than the smallest algorithmic design that might do a
broadly similar job, though never as large as a full factorial.
As I see it, the main advantage of algorithmic design is that you get
to pick the size of the experiment. A second plus is that you can handle
arbitrarily constrained designs much more easily, which is a feature
I've sometimes found important. The disadvantage is that you may incur
bias in some of the effect estimates, and because the selection process
to fit an arbitrary experiment size typically involves some random
selection from a candidate list, you don't necessarily get to choose
which effects are biased. I guess you will also have a more interesting
job deciding how many observations you need for a given power, if that's
relevant.


Steve E.


***
This email and any attachments are confidential. Any u...{{dropped:8}}


__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


Re: [R] optFederov/AlgDesign - help avail?

2008-04-22 Thread paulandpen
I would suggest reading this attachment below.

http://support.sas.com/techsup/technote/ts722d.pdf

OptFedreov is the go for you, you are correct.

I don't know of anybody who has come up with design principles in choice 
modelling that apply to logit and probit models etc.

We all assume that what is good for linear models in principle,  is also 
good for choice models, even when the utilities we are estimating are 
non-linear.

I think it is important to recognise that d-efficiency is the best method of 
evaluation for choice designs and you should be aiming for an orthogonal 
array in your design as suggested in this article

if you are using traditional logit and MNL, please make sure you allow 
enough choices and enough cases to complete the choices, and also that your 
algorithms are geared towards repeated choices if you are using a stated 
preference approach where people are answering a number of choice 
alternatives

Bob Wheeler may be able to comment further, but i think you are on the right 
track

Thanks Paul

- Original Message - 
From: zubin [EMAIL PROTECTED]
To: r-help@r-project.org
Sent: Monday, April 21, 2008 9:59 PM
Subject: [R] optFederov/AlgDesign - help avail?


 Hello, we are needing to generate optimal (Fractional) designs for
 discrete choice applications, where we will be using logistic regression
 or multinomial logit as the modeling technique.

 It looks like optFederov, in the AlgDesign package may work, but not
 sure if this algorithm works when the variable of interest is binary or
 nominal?

 Anyone who are experts in this area, anyone interested in consulting
 with us in this topic (if so, email me we can arrange)?

 Or can confirm/deny optFederov can work in the discrete case?

 thx!

 __
 R-help@r-project.org mailing list
 https://stat.ethz.ch/mailman/listinfo/r-help
 PLEASE do read the posting guide 
 http://www.R-project.org/posting-guide.html
 and provide commented, minimal, self-contained, reproducible code.


__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


Re: [R] optFederov/AlgDesign - help avail?

2008-04-22 Thread paulandpen
of yeah, and your design needs to account for main effects and interactions 
if you intend to model them, so make sure to program that into algdesign as 
well


- Original Message - 
From: zubin [EMAIL PROTECTED]
To: r-help@r-project.org
Sent: Monday, April 21, 2008 9:59 PM
Subject: [R] optFederov/AlgDesign - help avail?


 Hello, we are needing to generate optimal (Fractional) designs for
 discrete choice applications, where we will be using logistic regression
 or multinomial logit as the modeling technique.

 It looks like optFederov, in the AlgDesign package may work, but not
 sure if this algorithm works when the variable of interest is binary or
 nominal?

 Anyone who are experts in this area, anyone interested in consulting
 with us in this topic (if so, email me we can arrange)?

 Or can confirm/deny optFederov can work in the discrete case?

 thx!

 __
 R-help@r-project.org mailing list
 https://stat.ethz.ch/mailman/listinfo/r-help
 PLEASE do read the posting guide 
 http://www.R-project.org/posting-guide.html
 and provide commented, minimal, self-contained, reproducible code.


__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


Re: [R] Conjoint Analysis in R??

2007-12-06 Thread paulandpen
Faisal,

can you elaborate further on your conjoint design

there is bayesm which offers a hierarchical bayes approach to analysing 
choice data

MLogit available through zelig (see below)

http://gking.harvard.edu/zelig/docs/index.html

MNP as a standalone package for the probit model

thanks Paul


- Original Message - 
From: faisal afzal siddiqui [EMAIL PROTECTED]
To: R Help [EMAIL PROTECTED]
Sent: Thursday, December 06, 2007 6:00 PM
Subject: [R] Conjoint Analysis in R??


 Pls advise how I can use R in conjoint analysis??

 regds
 Faisal Afzal Siddiqui
 Karachi, Pakistan


 
 
 Looking for last minute shopping deals?

 __
 R-help@r-project.org mailing list
 https://stat.ethz.ch/mailman/listinfo/r-help
 PLEASE do read the posting guide 
 http://www.R-project.org/posting-guide.html
 and provide commented, minimal, self-contained, reproducible code.


__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


Re: [R] cluster analysis

2007-11-02 Thread paulandpen
AMINA SHAHZADI,

The eternal question.

What I do is that I generate a range of solutions, profile them on variables 
used to cluster the data into groups and any other information I have to 
profile the cluster groups on and then present the solutions to a group of 
others to assess meaningfulness, debate on the solutions and attempt to 
reach a consensus etc

In many cases, eg, for algorithms based on k-means and hierarchical 
clustering, you are using an exploratory technique and there are no 
right/wrong answers to this

Having used cluster analysis for years some things to look at because there 
is no way to answer this statistically (unless you are using a latent class 
type model with goodness of fit measures) are the following

1.  What is the minimum size you believe to be robust for a single cluster 
(eg n=30, n=100) etc because the larger the number of clusters you generate 
relative to sample size, the smaller your clusters will be and there must be 
a cut-off point defined upon which you are not prepared to go any lower...
2. If you run the clusters through different algorithms, how comparable are 
the results (cluster stability)
2.  What differences emerge between 2, 3, 4 cluster solutions etc (as you 
utilise larger numbers of clusters, does this still produce a meaningful 
result in that the clusters are distinct and unique, or are you just cutting 
larger clusters into smaller clusters without generating unique and usable 
information...  Examine the clusters via a series of cross tabs (as you go 
from 2 to 3 to 4 cluster solutions) what happens to the members within 
clusters, are they distributed differently etc

Thanks Paul

- Original Message - 
From: amna khan [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Sent: Friday, November 02, 2007 2:19 AM
Subject: [R] cluster analysis


 Hi Sir

 How can we select the optimum number of clusters?

 Best Regards

 -- 
 AMINA SHAHZADI
 Department of Statistics
 GC University Lahore, Pakistan.

 [[alternative HTML version deleted]]

 __
 R-help@r-project.org mailing list
 https://stat.ethz.ch/mailman/listinfo/r-help
 PLEASE do read the posting guide 
 http://www.R-project.org/posting-guide.html
 and provide commented, minimal, self-contained, reproducible code.


__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.


[R] query on random.seed not found error in code

2007-09-27 Thread paulandpen
Hi,

I am trying to use AlgDesign and am partially successful

Two lines of code are taken from the help file
1. Line 1 (below) works fine
 dat-gen.factorial(levels=3,nVars=3,varNames=c(A,B,C))

2. Line 2 (below) does not work fine
 desD-optFederov(~quad(A,B,C),dat,nTrials=14,eval=TRUE)

Here is the result I get

Error in optFederov(~quad(A, B, C), dat, nTrials = 14, eval = TRUE) :
object .Random.seed not found

What do i need to do, to introduce this object into the process?

Thanks in advance

Paul



- Original Message - 
From: marcg [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Sent: Thursday, September 27, 2007 5:21 PM
Subject: [R] different colors for two wireframes in same plot


 Hello R,

 According to:

 g - expand.grid(x = 1:10, y = 5:15, gr = 1:2)
 g$z - log((g$x^g$g + g$y^2) * g$gr)
 wireframe(z ~ x * y, data = g, groups = gr,
  scales = list(arrows = FALSE),
  drape = TRUE, colorkey = TRUE,
  screen = list(z = 30, x = -60))

 i have two wireframes in one plot.

 How could i change the color of the top - one to transparent (or only the 
 grid). I want to give insight to the lower layer.

 Could one make an if-statment like (if gr==1 do drape=F or color=none) if 
 gr=2 do drape=T, colorkey=T)

 Thanks for your help

 Marc

 -- 
 Pt! Schon vom neuen GMX MultiMessenger gehört?
 Der kanns mit allen: http://www.gmx.net/de/go/multimessenger

 __
 R-help@r-project.org mailing list
 https://stat.ethz.ch/mailman/listinfo/r-help
 PLEASE do read the posting guide 
 http://www.R-project.org/posting-guide.html
 and provide commented, minimal, self-contained, reproducible code.



__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.