Tag Archives: statistics

My First R Package (Part 3)

After refactoring my programming so that it was only about 10 lines of code, using 12 functions I wrote an loaded in via the source command, I went through all the steps in Part 1 of this blog post and Part 2 of this blog post to set up the R package infrastructure using testthis in RStudio. Then things started humming along with the rest of the setup:

> use_mit_license("Nicole Radziwill")
✔ Setting active project to 'D:/R/easyMTS'
✔ Setting License field in DESCRIPTION to 'MIT + file LICENSE'
✔ Writing 'LICENSE.md'
✔ Adding '^LICENSE\\.md$' to '.Rbuildignore'
✔ Writing 'LICENSE'

> use_testthat()
✔ Adding 'testthat' to Suggests field in DESCRIPTION
✔ Creating 'tests/testthat/'
✔ Writing 'tests/testthat.R'
● Call `use_test()` to initialize a basic test file and open it for editing.

> use_vignette("easyMTS")
✔ Adding 'knitr' to Suggests field in DESCRIPTION
✔ Setting VignetteBuilder field in DESCRIPTION to 'knitr'
✔ Adding 'inst/doc' to '.gitignore'
✔ Creating 'vignettes/'
✔ Adding '*.html', '*.R' to 'vignettes/.gitignore'
✔ Adding 'rmarkdown' to Suggests field in DESCRIPTION
✔ Writing 'vignettes/easyMTS.Rmd'
● Modify 'vignettes/easyMTS.Rmd'

> use_citation()
✔ Creating 'inst/'
✔ Writing 'inst/CITATION'
● Modify 'inst/CITATION'

Add Your Dependencies

> use_package("ggplot2")
✔ Adding 'ggplot2' to Imports field in DESCRIPTION
● Refer to functions with `ggplot2::fun()`
> use_package("dplyr")
✔ Adding 'dplyr' to Imports field in DESCRIPTION
● Refer to functions with `dplyr::fun()`

> use_package("magrittr")
✔ Adding 'magrittr' to Imports field in DESCRIPTION
● Refer to functions with `magrittr::fun()`
> use_package("tidyr")
✔ Adding 'tidyr' to Imports field in DESCRIPTION
● Refer to functions with `tidyr::fun()`

> use_package("MASS")
✔ Adding 'MASS' to Imports field in DESCRIPTION
● Refer to functions with `MASS::fun()`

> use_package("qualityTools")
✔ Adding 'qualityTools' to Imports field in DESCRIPTION
● Refer to functions with `qualityTools::fun()`

> use_package("highcharter")
Registered S3 method overwritten by 'xts':
  method     from
  as.zoo.xts zoo 
Registered S3 method overwritten by 'quantmod':
  method            from
  as.zoo.data.frame zoo 
✔ Adding 'highcharter' to Imports field in DESCRIPTION
● Refer to functions with `highcharter::fun()`

> use_package("cowplot")
✔ Adding 'cowplot' to Imports field in DESCRIPTION
● Refer to functions with `cowplot::fun()`

Adding Data to the Package

I want to include two files, one data frame containing 50 observations of a healthy group with 5 predictors each, and another data frame containing 15 observations from an abnormal or unhealthy group (also with 5 predictors). I made sure the two CSV files I wanted to add to the package were in my working directory first by using dir().

> use_data_raw()
✔ Creating 'data-raw/'
✔ Adding '^data-raw$' to '.Rbuildignore'
✔ Writing 'data-raw/DATASET.R'
● Modify 'data-raw/DATASET.R'
● Finish the data preparation script in 'data-raw/DATASET.R'
● Use `usethis::use_data()` to add prepared data to package

> mtsdata1 <- read.csv("MTS-Abnormal.csv") %>% mutate(abnormal=1)
> usethis::use_data(mtsdata1)
✔ Creating 'data/'
✔ Saving 'mtsdata1' to 'data/mtsdata1.rda'

> mtsdata2 <- read.csv("MTS-Normal.csv") %>% mutate(normal=1)
> usethis::use_data(mtsdata2)
✔ Saving 'mtsdata2' to 'data/mtsdata2.rda'

Magically, this added my two files (in .rds format) into my /data directory. (Now, though, I don’t know why the /data-raw directory is there… maybe we’ll figure that out later.) I decided it was time to commit these to my repository again:

Following the instruction above, I re-knit the README.Rmd and then it was possible to commit everything to Github again. At which point I ended up in a fistfight with git, again saved only by my software engineer partner who uses Github all the time:

I think it should be working. The next test will be if anyone can install this from github using devtools. Let me know if it works for you… it works for me locally, but you know how that goes. The next post will show you how to use it 🙂

install.packages("devtools")
install_github("NicoleRadziwill/easyMTS")

SEE WHAT WILL BECOME THE easyMTS VIGNETTE –>

A Decade of PhD: What I’ve Learned from Academia and Industry

Today is Cinco de Mayo! It’s also the 10th Anniversary of my PhD defense…. something I carefully timed for late afternoon on this day in 2009. (I wanted to make sure I could celebrate the joyful occasion — or drown my sorrows — with 2-for-1 margaritas. Fortunately, the situation was liquid joy; unfortunately, I still got a hangover.)

I’m writing this post to share what I’ve learned about the value of getting a PhD (is there value?) and the applicability of PhD-level work to industry. If you’re considering more education, maybe this will help you decide whether it’s the right choice. If you’re in industry and trying to figure out whether to hire PhDs, some of what I write here might help. But first, some background!

I never even thought I’d get a PhD — it certainly didn’t happen out of intent or design. My family was poor and I studied ridiculously hard so I could “escape it.” I didn’t think I was smart enough for a PhD, even though I started college at 16 taking half undergrad classes and half grad classes in meteorology. I aced my grad classes and very maturely ignored my required classes, so I got kicked out. (At the same time, I wasn’t really fitting in with people… my roommate called me “Nerdcole”.) When I was let back in the department head wouldn’t let me take any grad classes so I got bored and burned out… not surprising since I was supporting myself, and working three jobs to make that happen. I quit school to work at an e-commerce startup when I was 18. A few months later, thanks to (good) peer pressure, I took 3 credit by exams to see if it would get me over the finish line, and thanks to some side skills I had picked up in vector calculus and statistics, it worked and I got the BS. But I was still left with a pretty bad GPA, and even worse self esteem, and I was convinced no one would ever let me into grad school.

I figured I’d focus on industry and help companies grow. There was no other choice.

The Back Story

After spending a couple years building web sites and storefronts (a huge feat in 1995 and 1996!) I took a job at a national lab as a systems analyst, supporting older scientists and engineers and helping them get work done. The main lesson I learned during this time was: Alignment between strategy and objectives doesn’t come for free (teams of people have to spend dedicated time on it), and most people are really disorganized. There had to be a better way to get work done.

A few years later, I was a traveling Solutions Architect, parachuted once or twice a month into CRM software implementation fiascos around the globe. My job was to figure out what to do to turn these jobs around — was it a people problem? An architecture problem? A training problem? A systems thinking problem? A little of everything? I had a couple weeks to make a recommendation, and then I was on to the next project (results were usually pretty good). But since this required evaluating technology decisions in the context of business and financial constraints, my boss suggested that I use the tuition benefits offered by my job to get an MBA. I had taken 9 credits of science and industrial engineering classes since I’d graduated, so I contacted two of the local MBA schools to see if they’d accept me and my credits. Sure enough, one of them did! I took evening classes for a year and a half, and eventually ended up with an MBA. But I never thought I could (or would) go farther — I’m not that smart, I’d tell myself. Also, it’s expensive. Also, a PhD would probably make me less marketable. (All lies, spoken by a lack of confidence.)

Shortly thereafter, the travel started to get to me (I was flying at least three days a week), so I looked for an opportunity to grow and cultivate a software development organization. (That’s how I ended up in Data Management at NRAO.) A little management led to a lot of management. A few years later one of the organization’s leaders said it was “too bad I didn’t have a PhD” — because in a highly scientific and technical organization, it would give me more credibility and make me a better leader.

“Will you pay for it?” I asked. “Sure,” they said. I just had to find a suitable program that wouldn’t require me to go full time. I’ve always loved learning, and I couldn’t resist the temptation of free education — even if it meant I’d have to balance the demands of a challenging full-time job and a first-time baby at the same time. That’s how much I love learning, just for learning’s sake! I still didn’t think a PhD had that much value, unless you were studying to be a lab scientist or you were dead set on becoming a historian and teaching for the rest of your life. None of these personas was me, but the free education thing sold me, and I didn’t really think about how relevant this step was to my career direction until much later.

Fortunately, I found the perfect program for me — a hybrid academic/practitioner PhD that would help me develop the research and analytical skills to solve practical problems in business and industrial technology.

The next few years were pretty rough, and by the time I got my PhD, I was in my 14th year of post-college professional employment. First lesson learned: it’s probably not the best move to start PhD coursework when you have a three-month old. I have no idea how I made it through.

Shortly after graduating, the impacts of the financial crisis hit our federally funded organization and I was able to segue into a second career as a college professor, teaching data science and manufacturing/EHSQ classes. For the past year, I’ve been back in industry (maybe permanently; we’ll see) and have a better sense of the value of PhDs in industry.

Value of Getting a PhD

There are lots of reasons I’m happy with the time I spent getting a PhD, other than the fact that it helped me get an entirely new job when the economy was down:

  • First and foremost, I’m a better critical thinker. It’s now my nature to look at all parts of a problem, examine the interactions between them, and make sure I have all the required background information needed to start working on a problem.
  • I’m a better writer too. I look at reports and presentations I wrote years ago, and can see all the holes and places where I made assumptions that weren’t valid.
  • I developed a new appreciation for clarity. Researchers want to make sure their messages, methodologies, and models are clear and unambiguous… through the contrast, I was able to recognize that in industry, there’s often pressure to skip due diligence and move fast to perform. This pressure leads to ambiguity, which tends towards what I call “intellectual waste” – people assuming that they see a problem or a project in the same way because they haven’t taken the time to guarantee clarity.
  • It’s easier for me to quickly determine whether information might be true or false, or whether there are gaps that need to be closed before moving forward. (It’s possible that this skill is more from grading and evaluating student work… something that’s orders of magnitude harder than it seems.)
  • I realized that words matter. Really thinking about how one person will respond to a word or phrase, and whether it conveys the meaning that you intend, is a craft — that’s enhanced by working with collaborators.
  • And although I knew this one prior to the PhD, I found that data matters. Where did your data come from? Can you access the original? What kind of people (or instruments) gathered it? Can you trust them? The quality of your data — and the suitability of the methods you choose — will impact the quality and integrity of the conclusions you generate from it. Awareness of these factors is essential.

Value of Caution

One of the biggest lessons was the most surprising. Early on in the PhD program I was told that my opinion didn’t count — regardless of how many years of experience I had. Every statement I made had to be backed up and cited, preferably using material that had been peer-reviewed by other qualified people. At first I was kind of offended by this… didn’t these academics have any sense of the value of actual real-world employment? Apparently not.

But something funny happened as I developed the habit of looking for solid references, distilling their messages, and citing them accurately: I became more careful. And in the evolution of my caution and attention to detail, the quality of my work — ANY work — improved tremendously. I was able to learn from what other people had discovered, and anticipate (and resolve) problems in advance. I learned that “standing on the shoulders of giants” actually means figuring out when solved problems already exist so you don’t waste time reinventing wheels.

Something else funny happened as soon as I graduated: all of a sudden, people were asking me for my opinion. But the habit of due diligence was so ingrained that I couldn’t express my opinion… I was compelled to back it up with facts!

(I think this was the point all along. Go figure.)

The beauty of going through the entire messy process of PhD coursework and comps and research and defense and editing — the entire end-to-end process, not cutting out in the middle anywhere — it gave me the discipline and process to root out accurate and complete answers to problems. Or at the very least, to be able to call out the gaps to get there.

There’s a lot of pressure in industry to move fast, but due diligence is still critical for accurate self-assessment and effective cross-functional communication. Slowing down and figuring out how you know what you know — and making sure everyone is literally on the same page — can help your organization achieve its goals more quickly.

Value of PhDs to Industry

So employers (especially in tech) — should you hire PhDs? Yes. Here’s why:

  • PhDs are trained to find gaps in knowledge and understanding. Is your strategic plan grounded in reality, or is it just wishful thinking? Are your Project Charters well scoped, budgeted, and planned out? Is your workforce prepared to carry out your strategic initiatives?
  • Many PhDs with experience teaching undergrads are great at making complex topics accessible to other audiences. This is fantastic for training, cross-training, and marketing.
  • PhDs love research and writing, and can help you with gathering and interpreting data and content marketing.
  • PhDs love learning. Want to be on the cutting edge? They’re great in R&D… they can help you distill new insights from research papers and interpret and apply them accurately.
  • If you want to do AI or machine learning, or anything that uses Big Data, make sure you have at least one PhD statistician with practical analytical experience. They can prevent you from spending millions on dead ends and help you apply Occam’s Razor to avoid unnecessary complexity (the kind that can lead to technical debt later).

Will there be drawbacks? Sure. The habit of caution may need to be tempered somewhat — you don’t have to probe to the bottom of an issue to generate useful information that a business can use to make progress.

Bottom line… don’t be afraid of PhDs! We are mere mortals who just happen to have spent several years trying to figure out how to get to the core — the fundamental truth — of a complex problem. As a result we know how to approach problems like this — problems that many businesses have lots of. (We are not overqualified at all… we just have an extra skill set in something you desperately need, but may not realize you need it.)

Getting a PhD was challenging, frustrating, and maddening at times (especially the final part of getting your camera-ready text ready for ProQuest). I never planned to do it, but I’d totally do it again. I think my only regret is that I got a PhD in a hybrid business/industrial engineering discipline… it allowed me the freedom to pursue my interests, but if I was at the same crossroads now, I’d get a PhD in statistics to complement my MBA. Overall, this is a pretty tiny regret.

Object of Type Closure is Not Subsettable

I started using R in 2004. I started using R religiously on the day of the annular solar eclipse in Madrid (October 3, 2005) after being inspired by David Hunter’s talk at ADASS.

It took me exactly 4,889 days to figure out what this vexing error means, even though trial and error helped me move through it most every time it happened! I’m so moved by what I learned (and embarrassed that it took so long to make sense), that I have to share it with you.

This error happens when you’re trying to treat a function like a list, vector, or data frame. To fix it, start treating the function like a function.

Let’s take something that’s very obviously a function. I picked the sampling distribution simulator from a 2015 blog post I wrote. Cut and paste it into your R console:

sdm.sim <- function(n,src.dist=NULL,param1=NULL,param2=NULL) {
   r <- 10000  # Number of replications/samples - DO NOT ADJUST
   # This produces a matrix of observations with  
   # n columns and r rows. Each row is one sample:
   my.samples <- switch(src.dist,
	"E" = matrix(rexp(n*r,param1),r),
	"N" = matrix(rnorm(n*r,param1,param2),r),
	"U" = matrix(runif(n*r,param1,param2),r),
	"P" = matrix(rpois(n*r,param1),r),
        "B" = matrix(rbinom(n*r,param1,param2),r),
	"G" = matrix(rgamma(n*r,param1,param2),r),
	"X" = matrix(rchisq(n*r,param1),r),
	"T" = matrix(rt(n*r,param1),r))
   all.sample.sums <- apply(my.samples,1,sum)
   all.sample.means <- apply(my.samples,1,mean)   
   all.sample.vars <- apply(my.samples,1,var) 
   par(mfrow=c(2,2))
   hist(my.samples[1,],col="gray",main="Distribution of One Sample")
   hist(all.sample.sums,col="gray",main="Sampling Distribution\nof
	the Sum")
   hist(all.sample.means,col="gray",main="Sampling Distribution\nof the Mean")
   hist(all.sample.vars,col="gray",main="Sampling Distribution\nof
	the Variance")
}

The right thing to do with this function is use it to simulate a bunch of distributions and plot them using base R. You write the function name, followed by parenthesis, followed by each of the four arguments the function needs to work. This will generate a normal distribution with mean of 20 and standard deviation of 3, along with three sampling distributions, using a sample size of 100 and 10000 replications:

sdm.sim(100, src.dist="N", param1=20, param2=3)

(You should get four plots, arranged in a 2×2 grid.)

But what if we tried to treat sdm.sim like a list, and call the 3rd element of it? Or what if we tried to treat it like a data frame, and we wanted to call one of the variables in the column of the data frame?

> sdm.sim[3]
Error in sdm.sim[3] : object of type 'closure' is not subsettable

> sdm.sim$values
Error in sdm.sim$values : object of type 'closure' is not subsettable

SURPRISE! Object of type closure is not subsettable. This happens because sdm.sim is a function, and its data type is (shockingly) something called “closure”:

> class(sdm.sim)
[1] "function"

> typeof(sdm.sim)
[1] "closure"

I had read this before on Stack Overflow a whole bunch of times, but it never really clicked until I saw it like this! And now that I had a sense for why the error was occurring, turns out it’s super easy to reproduce with functions in base R or functions in anyfamiliar packages you use:

> ggplot$a
Error in ggplot$a : object of type 'closure' is not subsettable

> table$a
Error in table$a : object of type 'closure' is not subsettable

> ggplot[1]
Error in ggplot[1] : object of type 'closure' is not subsettable

> table[1]
Error in table[1] : object of type 'closure' is not subsettable

As a result, if you’re pulling your hair out over this problem, check and see where in your rogue line of code you’re treating something like a non-function. Or maybe you picked a variable name that competes with a function name. Or maybe you got your operations out of order. In any case, change your notation so that your function is doing function things, and your code should start working.

But as Luke Smith pointed out, this is not true for functional sequences (which you can also write as functions). Functional sequences are those chains of commands you write when you’re in tidyverse mode, all strung together with %>% pipes:

Luke’s code that you can cut and paste (and try), with the top line that got cut off by Twitter, is:

fun1 <- . %>% 
    group_by(col1) %>% 
    mutate(n=n+h) %>% 
    filter(n==max(n)) %>% 
    ungroup() %>% 
    summarize(new_col=mean(n))

fun2 <- fun1[-c(2,5)] 

Even though Luke’s fun1 and fun2 are of type closure, they are subsettable because they contain a sequence of functions:

> typeof(fun1)
[1] "closure"

> typeof(fun2)
[1] "closure"

> fun1[1]
Functional sequence with the following components:

 1. group_by(., col1)

Use 'functions' to extract the individual functions. 

> fun1[[1]]
function (.) 
group_by(., col1)

Don’t feel bad! This problem has plagued all of us for many, many hours (me: years), and yet it still happens to us more often than we would like to admit. Awareness of this issue will not prevent you from attempting things that give you this error in the future. It’s such a popular error that there have been memes about it and sad valentines written about it:

SCROLL DOWN PAST STEPH’S TWEET TO SEE THE JOKE!!

(Also, if you’ve made it this far, FOLLOW THESE GOOD PEOPLE ON TWITTER: @stephdesilva @djnavarro @lksmth – They all share great information on data science in general, and R in particular. Many thanks too to all the #rstats crowd who shared in my glee last night and didn’t make me feel like an idiot for not figuring this out for ALMOST 14 YEARS. It seems so simple now.

Steph is also a Microsoft whiz who you should definitely hire if you need anything R+ Microsoft. Thanks to all of you!)

Analytic Hierarchy Process (AHP) using preferenceFunction in ahp

Yesterday, I wrote about how to use gluc‘s new ahp package on a simple Tom-Dick-Harry one level decision making problem using Analytic Hierarchy Process (AHP). One of the cool things about that package is that in addition to specifying the pairwise comparisons directly using Saaty’s scale (below, from https://kristalaace2014.wordpress.com/2014/05/14/w12_al_vendor-evaluation/)…

saaty-scale

…you can also describe each of the Alternatives in terms of descriptive variables which you can use inside a function to make the pairwise comparisons automatically. This is VERY helpful if you have lots of criteria, subcriteria, or alternatives to evaluate!! For example, I used preferenceFunction to compare 55 alternatives using 6 criteria and 4 subcriteria, and was very easily able to create functions to represent my judgments. This was much easier than manually entering all the comparisons.

This post shows HOW I replaced some of my manual comparisons with automated comparisons using preferenceFunction. (The full YAML file is included at the bottom of this post for you to use if you want to run this example yourself.) First, recall that the YAML file starts with specifying the alternatives that you are trying to choose from (at the bottom level of the decision hierarchy) and some variables that characterize those alternatives. I used the descriptions in the problem statement to come up with some assessments between 1=not great and 10=great:

[code language=”bash” gutter=”false”]
#########################
# Alternatives Section
# THIS IS FOR The Tom, Dick, & Harry problem at
# https://en.wikipedia.org/wiki/Analytic_hierarchy_process_%E2%80%93_leader_example
#
Alternatives: &alternatives
# 1= not well; 10 = best possible
# Your assessment based on the paragraph descriptions may be different.
Tom:
age: 50
experience: 7
education: 4
leadership: 10
Dick:
age: 60
experience: 10
education: 6
leadership: 6
Harry:
age: 30
experience: 5
education: 8
leadership: 6
#
# End of Alternatives Section
#####################################
[/code]

Here is a snippet from my original YAML file specifying my AHP problem manually ():

[code language=”bash” gutter=”false”]
children:
Experience:
preferences:
– [Tom, Dick, 1/4]
– [Tom, Harry, 4]
– [Dick, Harry, 9]
children: *alternatives
Education:
preferences:
– [Tom, Dick, 3]
– [Tom, Harry, 1/5]
– [Dick, Harry, 1/7]
children: *alternatives
[/code]

And here is what I changed that snippet to, so that it would do my pairwise comparisons automatically. The functions are written in standard R (fortunately), and each function has access to a1 and a2 (the two alternatives). Recursion is supported which makes this capability particularly useful. I tried to write a function using two of the characteristics in the decision (a1$age and a1$experience) but this didn’t seen to work. I’m not sure whether the package supports it or not. Here are my comparisons rewritten as functions:

[code language=”bash” gutter=”false”]
children:
Experience:
preferenceFunction: >
ExperiencePreference <- function(a1, a2) {
if (a1$experience < a2$experience) return (1/ExperiencePreference(a2, a1))
ratio <- a1$experience / a2$experience
if (ratio < 1.05) return (1)
if (ratio < 1.2) return (2)
if (ratio < 1.5) return (3)
if (ratio < 1.8) return (4)
if (ratio < 2.1) return (5) return (6) } children: *alternatives Education: preferenceFunction: >
EducPreference <- function(a1, a2) {
if (a1$education < a2$education) return (1/EducPreference(a2, a1))
ratio <- a1$education / a2$education
if (ratio < 1.05) return (1)
if (ratio < 1.15) return (2)
if (ratio < 1.25) return (3)
if (ratio < 1.35) return (4)
if (ratio < 1.55) return (5)
return (5)
}
children: *alternatives
[/code]

To run the AHP with functions in R, I used this code (I am including the part that gets the ahp package, in case you have not done that yet). BE CAREFUL and make sure, like in FORTRAN, that you line things up so that the words START in the appropriate columns. For example, the “p” in preferenceFunction MUST be immediately below the 7th character of your criterion’s variable name.

[code language=”bash” gutter=”false”]
devtools::install_github("gluc/ahp", build_vignettes = TRUE)
install.packages("data.tree")

library(ahp)
library(data.tree)

setwd("C:/AHP/artifacts")
nofxnAhp <- LoadFile("tomdickharry.txt")
Calculate(nofxnAhp)
fxnAhp <- LoadFile("tomdickharry-fxns.txt")
Calculate(fxnAhp)

print(nofxnAhp, "weight")
print(fxnAhp, "weight")
[/code]

You can see that the weights are approximately the same, indicating that I did a good job at developing functions that represent the reality of how I used the variables attached to the Alternatives to make my pairwise comparisons. The results show that Dick is now the best choice, although there is some inconsistency in our judgments for Experience that we should examine further. (I have not examined this case to see whether rank reversal could be happening).

[code language=”bash” gutter=”false”]
> print(nofxnAhp, "weight")
levelName weight
1 Choose the Most Suitable Leader 1.00000000
2 ¦–Experience 0.54756924
3 ¦ ¦–Tom 0.21716561
4 ¦ ¦–Dick 0.71706504
5 ¦ °–Harry 0.06576935
6 ¦–Education 0.12655528
7 ¦ ¦–Tom 0.18839410
8 ¦ ¦–Dick 0.08096123
9 ¦ °–Harry 0.73064467
10 ¦–Charisma 0.26994992
11 ¦ ¦–Tom 0.74286662
12 ¦ ¦–Dick 0.19388163
13 ¦ °–Harry 0.06325174
14 °–Age 0.05592555
15 ¦–Tom 0.26543334
16 ¦–Dick 0.67162545
17 °–Harry 0.06294121

> print(fxnAhp, "weight")
levelName weight
1 Choose the Most Suitable Leader 1.00000000
2 ¦–Experience 0.54756924
3 ¦ ¦–Tom 0.25828499
4 ¦ ¦–Dick 0.63698557
5 ¦ °–Harry 0.10472943
6 ¦–Education 0.12655528
7 ¦ ¦–Tom 0.08273483
8 ¦ ¦–Dick 0.26059839
9 ¦ °–Harry 0.65666678
10 ¦–Charisma 0.26994992
11 ¦ ¦–Tom 0.74286662
12 ¦ ¦–Dick 0.19388163
13 ¦ °–Harry 0.06325174
14 °–Age 0.05592555
15 ¦–Tom 0.26543334
16 ¦–Dick 0.67162545
17 °–Harry 0.06294121

> ShowTable(fxnAhp)
[/code]

tomdick-ahp-fxns

Here is the full YAML file for the “with preferenceFunction” case.

[code language=”bash” gutter=”false”]
#########################
# Alternatives Section
# THIS IS FOR The Tom, Dick, & Harry problem at
# https://en.wikipedia.org/wiki/Analytic_hierarchy_process_%E2%80%93_leader_example
#
Alternatives: &alternatives
# 1= not well; 10 = best possible
# Your assessment based on the paragraph descriptions may be different.
Tom:
age: 50
experience: 7
education: 4
leadership: 10
Dick:
age: 60
experience: 10
education: 6
leadership: 6
Harry:
age: 30
experience: 5
education: 8
leadership: 6
#
# End of Alternatives Section
#####################################
# Goal Section
#
Goal:
# A Goal HAS preferences (within-level comparison) and HAS Children (items in level)
name: Choose the Most Suitable Leader
preferences:
# preferences are defined pairwise
# 1 means: A is equal to B
# 9 means: A is highly preferrable to B
# 1/9 means: B is highly preferrable to A
– [Experience, Education, 4]
– [Experience, Charisma, 3]
– [Experience, Age, 7]
– [Education, Charisma, 1/3]
– [Education, Age, 3]
– [Age, Charisma, 1/5]
children:
Experience:
preferenceFunction: >
ExperiencePreference <- function(a1, a2) {
if (a1$experience < a2$experience) return (1/ExperiencePreference(a2, a1))
ratio <- a1$experience / a2$experience
if (ratio < 1.05) return (1)
if (ratio < 1.2) return (2)
if (ratio < 1.5) return (3)
if (ratio < 1.8) return (4)
if (ratio < 2.1) return (5) return (6) } children: *alternatives Education: preferenceFunction: >
EducPreference <- function(a1, a2) {
if (a1$education < a2$education) return (1/EducPreference(a2, a1))
ratio <- a1$education / a2$education
if (ratio < 1.05) return (1)
if (ratio < 1.15) return (2)
if (ratio < 1.25) return (3)
if (ratio < 1.35) return (4)
if (ratio < 1.55) return (5)
return (5)
}
children: *alternatives
Charisma:
preferences:
– [Tom, Dick, 5]
– [Tom, Harry, 9]
– [Dick, Harry, 4]
children: *alternatives
Age:
preferences:
– [Tom, Dick, 1/3]
– [Tom, Harry, 5]
– [Dick, Harry, 9]
children: *alternatives
#
# End of Goal Section
#####################################
[/code]

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