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Behavioral Economic (be) Easy (ez) Demand

Behavioral economic demand is gaining in popularity. The motivation behind beezdemand was to create an alternative tool to conduct these analyses. This package is not necessarily meant to be a replacement for other softwares; rather, it is meant to serve as an additional tool in the behavioral economist’s toolbox. It is meant for researchers to conduct behavioral economic (be) demand the easy (ez) way.

Note About Use

Currently, this version (0.1.0) is the first minor release and is stable. I encourage you to use it but be aware that, as with any software release, there might be (unknown) bugs present. I’ve tried hard to make this version usable while including the core functionality (described more below). However, if you find issues or would like to contribute, please open an issue on my GitHub page or email me.

Installing beezdemand

The latest stable version of beezdemand (currently v.0.1.0) can be found on CRAN and installed using the following command. The first time you install the package, you may be asked to select a CRAN mirror. Simply select the mirror geographically closest to you.

install.packages("beezdemand")

library(beezdemand)

GitHub Release

To install a stable release directly from GitHub, first install and load the devtools package. Then, use install_github to install the package and associated vignette. You don’t need to download anything directly from GitHub, as you should use the following instructions:

install.packages("devtools")

devtools::install_github("brentkaplan/beezdemand", build_vignettes = TRUE)

library(beezdemand)

GitHub Development Version

To install the development version of the package, specify the development branch in install_github:

devtools::install_github("brentkaplan/beezdemand@develop")

Using the Package

Example Dataset

An example dataset of responses on an Alcohol Purchase Task is provided. This object is called apt and is located within the beezdemand package. These data are a subset of from the paper by Kaplan & Reed (2018). Participants (id) reported the number of alcoholic drinks (y) they would be willing to purchase and consume at various prices (x; USD). Note the format of the data, which is called “long format”. Long format data are data structured such that repeated observations are stacked in multiple rows, rather than across columns. First, take a look at an extract of the dataset apt, where I’ve subsetted rows 1 through 10 and 17 through 26:

id x y
1 19 0.0 10
2 19 0.5 10
3 19 1.0 10
4 19 1.5 8
5 19 2.0 8
6 19 2.5 8
7 19 3.0 7
8 19 4.0 7
9 19 5.0 7
10 19 6.0 6
17 30 0.0 3
18 30 0.5 3
19 30 1.0 3
20 30 1.5 3
21 30 2.0 2
22 30 2.5 2
23 30 3.0 2
24 30 4.0 2
25 30 5.0 2
26 30 6.0 2

The first column contains the row number. The second column contains the id number of the series within the dataset. The third column contains the x values (in this specific dataset, price per drink) and the fourth column contains the associated responses (number of alcoholic drinks purchased at each respective price). There are replicates of id because for each series (or participant), several x values were presented.

Converting from Wide to Long and Vice Versa

Take for example the format of most datasets that would be exported from a data collection software such as Qualtrics or SurveyMonkey or Google Forms:

## the following code takes the apt data, which are in long format, and converts
## to a wide format that might be seen from data collection software
wide <- spread(apt, x, y)
colnames(wide) <- c("id", paste0("price_", seq(1, 16, by = 1)))
knitr::kable(wide[1:5, 1:10])
id price_1 price_2 price_3 price_4 price_5 price_6 price_7 price_8 price_9
19 10 10 10 8 8 8 7 7 7
30 3 3 3 3 2 2 2 2 2
38 4 4 4 4 4 4 4 3 3
60 10 10 8 8 6 6 5 5 4
68 10 10 9 9 8 8 7 6 5

A dataset such as this is referred to as “wide format” because each participant series contains a single row and multiple measurements within the participant are indicated by the columns. This data format is fine for some purposes; however, for beezdemand, data are required to be in “long format” (in the same format as the example data described earlier). In order to convert to the long format, some steps will be required.

First, it is helpful to rename the columns to what the prices actually were. For example, for the purposes of our example dataset, price_1 was $0.00 (free), price_2 was $0.50, price_3 was $1.00, and so on.

## make an object to hold what will be the new column names
newcolnames <- c("id", "0", "0.5", "1", "1.50", "2", "2.50", "3", 
                 "4", "5", "6", "7", "8", "9", "10", "15", "20")
## current column names
colnames(wide)
 [1] "id"       "price_1"  "price_2"  "price_3"  "price_4"  "price_5" 
 [7] "price_6"  "price_7"  "price_8"  "price_9"  "price_10" "price_11"
[13] "price_12" "price_13" "price_14" "price_15" "price_16"
## replace current column names with new column names
colnames(wide) <- newcolnames

## how new data look (first 5 rows only)
knitr::kable(wide[1:5, ])
id 0 0.5 1 1.50 2 2.50 3 4 5 6 7 8 9 10 15 20
19 10 10 10 8 8 8 7 7 7 6 6 5 5 4 3 2
30 3 3 3 3 2 2 2 2 2 2 2 2 1 1 1 1
38 4 4 4 4 4 4 4 3 3 3 3 2 2 2 0 0
60 10 10 8 8 6 6 5 5 4 4 3 3 2 2 0 0
68 10 10 9 9 8 8 7 6 5 5 5 4 4 3 0 0

Now we can convert into a long format using some of the helpful functions in the tidyverse package (make sure the package is loaded before trying the commands below).

## using the dataframe 'wide', we specify the key will be 'price', the values 
## will be 'consumption', and we will select all columns besides the first ('id')
long <- tidyr::gather(wide, price, consumption, -id)

## we'll sort the rows by id
long <- arrange(long, id)

## view the first 20 rows
knitr::kable(long[1:20, ])
id price consumption
19 0 10
19 0.5 10
19 1 10
19 1.50 8
19 2 8
19 2.50 8
19 3 7
19 4 7
19 5 7
19 6 6
19 7 6
19 8 5
19 9 5
19 10 4
19 15 3
19 20 2
30 0 3
30 0.5 3
30 1 3
30 1.50 3

Two final modifications we will make will be to (1) rename our columns to what the functions in beezdemand will expect to see: id, x, and y, and (2) ensure both x and y are in numeric format.

colnames(long) <- c("id", "x", "y")

long$x <- as.numeric(long$x)
long$y <- as.numeric(long$y)
knitr::kable(head(long))
id x y
19 0.0 10
19 0.5 10
19 1.0 10
19 1.5 8
19 2.0 8
19 2.5 8

The dataset is now “tidy” because: (1) each variable forms a column, (2) each observation forms a row, and (3) each type of observational unit forms a table (in this case, our observational unit is the Alcohol Purchase Task data). To learn more about the benefits of tidy data, readers are encouraged to consult Hadley Wikham’s essay on Tidy Data.

Obtain Descriptive Data

Descriptive values of responses at each price can be obtained easily. The resulting table includes mean, standard deviation, proportion of zeros, number of NAs, and minimum and maximum values. If bwplot = TRUE, a box-and-whisker plot is also created and saved. By default, this location is a folder named “plots” one level up from the current working directory. The user may additionally specify the directory that the plot should save into, the type of file (either "png" or "pdf"), and the filename. Notice the red crosses indicate the mean. Defaults are shown here:

GetDescriptives(dat = apt, bwplot = FALSE, outdir = "../plots/", device = "png", 
                filename = "bwplot")

To actually run the code and generate the file, we will turn bwplot = TRUE. The function will create a folder one level higher than the current folder (i.e., the ../ portion) and save the file, “bwplot.png” in the folder.

GetDescriptives(dat = apt, bwplot = TRUE, outdir = plotdir, device = "png", 
                filename = "bwplot")

And here is the table that is returned from the function:

Price Mean Median SD PropZeros NAs Min Max
0 6.8 6.5 2.62 0.0 0 3 10
0.5 6.8 6.5 2.62 0.0 0 3 10
1 6.5 6.5 2.27 0.0 0 3 10
1.5 6.1 6.0 1.91 0.0 0 3 9
2 5.3 5.5 1.89 0.0 0 2 8
2.5 5.2 5.0 1.87 0.0 0 2 8
3 4.8 5.0 1.48 0.0 0 2 7
4 4.3 4.5 1.57 0.0 0 2 7
5 3.9 3.5 1.45 0.0 0 2 7
6 3.5 3.0 1.43 0.0 0 2 6
7 3.3 3.0 1.34 0.0 0 2 6
8 2.6 2.5 1.51 0.1 0 0 5
9 2.4 2.0 1.58 0.1 0 0 5
10 2.2 2.0 1.32 0.1 0 0 4
15 1.1 0.5 1.37 0.5 0 0 3
20 0.8 0.0 1.14 0.6 0 0 3

Change Data

There are certain instances in which data are to be modified before fitting, for example when using an equation that logarithmically transforms y values. The following function can help with modifying data:

ChangeData(dat = apt, nrepl = 1, replnum = 0.01, rem0 = FALSE, remq0e = FALSE, 
           replfree = NULL)

Identify Unsystematic Responses

Using the following function, we can examine the consistency of demand data using Stein et al.’s (2015) alogrithm for identifying unsystematic responses. Default values shown, but they can be customized.

CheckUnsystematic(dat = apt, deltaq = 0.025, bounce = 0.1, reversals = 0, ncons0 = 2)
id TotalPass DeltaQ DeltaQPass Bounce BouncePass Reversals ReversalsPass NumPosValues
19 3 0.2112 Pass 0 Pass 0 Pass 16
30 3 0.1437 Pass 0 Pass 0 Pass 16
38 3 0.7885 Pass 0 Pass 0 Pass 14
60 3 0.9089 Pass 0 Pass 0 Pass 14
68 3 0.9089 Pass 0 Pass 0 Pass 14

Analyze Demand Data

Results of the analysis return both empirical and derived measures for use in additional analyses and model specification. Equations include the linear model, exponential model, and exponentiated model. Soon, I will be including the nonlinear mixed effects model, mixed effects versions of the exponential and exponentiated model, and others. However, currently these models are not yet supported.

Obtaining Empirical Measures

Empirical measures can be obtained separately on their own:

GetEmpirical(dat = apt)
id Intensity BP0 BP1 Omaxe Pmaxe
19 10 NA 20 45 15
30 3 NA 20 20 20
38 4 15 10 21 7
60 10 15 10 24 8
68 10 15 10 36 9

Obtaining Derived Measures

FitCurves() has several important arguments that can be passed. For the purposes of this document, focus will be on the two contemporary demand equations.

Note: Fitting with an equation (e.g., "linear", "hs") that doesn’t work happily with zero consumption values results in the following. One, a message will appear saying that zeros are incompatible with the equation. Two, because zeros are removed prior to finding empirical (i.e., observed) measures, resulting BP0 values will be all NAs (reflective of the data transformations). The warning message will look as follows:

Warning message:
Zeros found in data not compatible with equation! Dropping zeros!

The simplest use of FitCurves() is shown here, only needing to specify dat and equation. All other arguments shown are set to their default values.

FitCurves(dat = apt, equation = "hs", agg = NULL, detailed = FALSE, 
          xcol = "x", ycol = "y", idcol = "id", groupcol = NULL)

Which is equivalent to:

FitCurves(dat = apt, equation = "hs")

Note that this ouput returns a message (No k value specified. Defaulting to empirical mean range +.5) and the aforementioned warning (Warning message: Zeros found in data not compatible with equation! Dropping zeros!). With detailed = FALSE, the only output is the dataframe of results (broken up to show the different types of results). This example fits the exponential equation proposed by Hursh & Silberberg (2008):

id Intensity BP0 BP1 Omaxe Pmaxe
19 10 NA 20 45 15
30 3 NA 20 20 20
38 4 NA 10 21 7
60 10 NA 10 24 8
68 10 NA 10 36 9

Empirical Measures

Equation Q0d K Alpha R2
hs 10.475734 1.031479 0.0046571 0.9660008
hs 2.932406 1.031479 0.0134557 0.7922379
hs 4.523155 1.031479 0.0087935 0.8662632
hs 10.492133 1.031479 0.0102231 0.9664814
hs 10.651760 1.031479 0.0061262 0.9699408

Fitted Measures

Q0se Alphase N AbsSS SdRes Q0Low Q0High AlphaLow AlphaHigh
0.4159581 0.0002358 16 0.0193354 0.0371632 9.583593 11.367876 0.0041515 0.0051628
0.2506946 0.0017321 16 0.0978350 0.0835955 2.394720 3.470093 0.0097408 0.0171706
0.2357693 0.0008878 14 0.0259083 0.0464653 4.009458 5.036853 0.0068592 0.0107277
0.6219724 0.0005118 14 0.0236652 0.0444083 9.136972 11.847295 0.0091080 0.0113382
0.3841063 0.0002713 14 0.0109439 0.0301992 9.814865 11.488656 0.0055350 0.0067173

Uncertainty and Model Information

EV Omaxd Pmaxd Omaxa
2.0496977 45.49394 14.393108 47.84770
0.7094191 15.74587 17.796228 16.56052
1.0855465 24.09418 17.654531 25.34076
0.9337419 20.72481 6.546547 21.79707
1.5581899 34.58471 10.760891 36.37405

Derived Measures

Here, the simplest form is shown specifying another equation, "koff". This fits the modified exponential equation proposed by Koffarnus et al. (2015):

FitCurves(dat = apt, equation = "koff")
id Intensity BP0 BP1 Omaxe Pmaxe
19 10 NA 20 45 15
30 3 NA 20 20 20
38 4 15 10 21 7
60 10 15 10 24 8
68 10 15 10 36 9

Empirical Measures

Equation Q0d K Alpha R2
koff 10.131767 1.429419 0.0029319 0.9668576
koff 2.989613 1.429419 0.0093716 0.8136932
koff 4.607551 1.429419 0.0070562 0.8403625
koff 10.371088 1.429419 0.0068127 0.9659117
koff 10.703627 1.429419 0.0044361 0.9444897

Fitted Measures

Q0se Alphase N AbsSS SdRes Q0Low Q0High AlphaLow AlphaHigh
0.2438729 0.0001663 16 2.908243 0.4557758 9.608712 10.654822 0.0025752 0.0032886
0.1721284 0.0013100 16 1.490454 0.3262837 2.620434 3.358792 0.0065620 0.0121812
0.3078231 0.0010631 16 4.429941 0.5625161 3.947336 5.267766 0.0047761 0.0093362
0.4069382 0.0004577 16 5.010982 0.5982703 9.498292 11.243884 0.0058310 0.0077945
0.4677467 0.0003736 16 8.350830 0.7723263 9.700410 11.706844 0.0036349 0.0052373

Uncertainty and Model Information

EV Omaxd Pmaxd Omaxa
1.9957818 46.56622 15.140905 46.70800
0.6243741 14.56810 16.052915 14.61245
0.8292621 19.34861 13.833934 19.40752
0.8588915 20.03993 6.365580 20.10095
1.3190323 30.77608 9.472147 30.86979

Derived Measures

By specifying agg = "Mean", y values at each x value are aggregated and a single curve is fit to the data (disregarding error around each averaged point):

FitCurves(dat = apt, equation = "hs", agg = "Mean")
id Intensity BP0 BP1 Omaxe Pmaxe
mean 6.8 NA 20 23.1 7

Empirical Measures

Equation Q0d K Alpha R2
hs 7.637436 1.429419 0.0066817 0.9807508

Fitted Measures

Q0se Alphase N AbsSS SdRes Q0Low Q0High AlphaLow AlphaHigh
0.3258955 0.0002218 16 0.02187 0.039524 6.93846 8.336413 0.0062059 0.0071574

Uncertainty and Model Information

EV Omaxd Pmaxd Omaxa
0.875742 20.43309 8.813584 20.49531

Derived Measures

By specifying agg = "Pooled", y values at each x value are aggregated and a single curve is fit to the data and error around each averaged point (but disregarding within-subject clustering):

FitCurves(dat = apt, equation = "hs", agg = "Pooled")
id Intensity BP0 BP1 Omaxe Pmaxe
pooled 6.8 NA 20 23.1 7

Empirical Measures

Equation Q0d K Alpha R2
hs 6.592488 1.031479 0.0085032 0.460412

Fitted Measures

Q0se Alphase N AbsSS SdRes Q0Low Q0High AlphaLow AlphaHigh
0.4260507 0.0007125 146 4.677846 0.1802361 5.750367 7.434609 0.0070949 0.0099115

Uncertainty and Model Information

EV Omaxd Pmaxd Omaxa
1.122607 24.91675 12.52644 26.20589

Derived Measures

Share k Globally; Fit Other Parameters Locally

As mentioned earlier, in the function FitCurves, when k = "share" this parameter will be a shared parameter across all datasets (globally) while estimating \(Q_0\) and \(\alpha\) locally. While this works, it may take some time with larger sample sizes.

FitCurves(dat = apt, equation = "hs", k = "share")
id Intensity BP0 BP1 Omaxe Pmaxe
19 10 NA 20 45 15
30 3 NA 20 20 20
38 4 NA 10 21 7
60 10 NA 10 24 8
68 10 NA 10 36 9

Empirical Measures

Equation Q0d K Alpha R2
hs 10.014576 3.31833 0.0011616 0.9820968
hs 2.766313 3.31833 0.0033331 0.7641766
hs 4.485810 3.31833 0.0024580 0.8803145
hs 9.721379 3.31833 0.0024219 0.9705985
hs 10.293139 3.31833 0.0015879 0.9722310

Fitted Measures

Q0se Alphase N AbsSS SdRes Q0Low Q0High AlphaLow AlphaHigh
0.2429150 0.0000308 16 0.0101816 0.0269677 9.493575 10.535577 0.0010955 0.0012277
0.2192797 0.0003739 16 0.1110490 0.0890622 2.296005 3.236621 0.0025312 0.0041350
0.2074990 0.0001963 14 0.0231862 0.0439566 4.033709 4.937912 0.0020302 0.0028858
0.4371060 0.0000778 14 0.0207584 0.0415916 8.769006 10.673751 0.0022523 0.0025914
0.3179671 0.0000523 14 0.0101100 0.0290259 9.600348 10.985930 0.0014740 0.0017018

Uncertainty and Model Information

EV Omaxd Pmaxd Omaxa
1.4241862 44.55169 13.160540 44.55206
0.4963281 15.52624 16.603785 15.52637
0.6730395 21.05416 13.884786 21.05433
0.6830746 21.36808 6.502492 21.36826
1.0418474 32.59129 9.366898 32.59155

Derived Measures

Compare Values of \(\alpha\) and \(Q_0\) via Extra Sum-of-Squares F-Test

When one has multiple groups, it may be beneficial to compare whether separate curves are preferred over a single curve. This is accomplished by the Extra Sum-of-Squares F-test. This function (using the argument compare) will determine whether a single \(\alpha\) or a single \(Q_0\) is better than multiple \(\alpha\)s or \(Q_0\)s. A single curve will be fit, the residual deviations calculated and those residuals are compared to residuals obtained from multiple curves. A resulting F statistic will be reporting along with a p value.

## setting the seed initializes the random number generator so results will be 
## reproducible
set.seed(1234)

## manufacture random grouping
apt$group <- NA
apt[apt$id %in% sample(unique(apt$id), length(unique(apt$id))/2), "group"] <- "a"
apt$group[is.na(apt$group)] <- "b"

## take a look at what the new groupings look like in long form
knitr::kable(apt[1:20, ])
id x y group
19 0.0 10 a
19 0.5 10 a
19 1.0 10 a
19 1.5 8 a
19 2.0 8 a
19 2.5 8 a
19 3.0 7 a
19 4.0 7 a
19 5.0 7 a
19 6.0 6 a
19 7.0 6 a
19 8.0 5 a
19 9.0 5 a
19 10.0 4 a
19 15.0 3 a
19 20.0 2 a
30 0.0 3 b
30 0.5 3 b
30 1.0 3 b
30 1.5 3 b
## in order for this to run, you will have had to run the code immediately
## preceeding (i.e., the code to generate the groups)
ef <- ExtraF(dat = apt, equation = "koff", k = 2, groupcol = "group", verbose = TRUE)
[1] "Null hypothesis: alpha same for all data sets"
[1] "Alternative hypothesis: alpha different for each data set"
[1] "Conclusion: fail to reject the null hypothesis"
[1] "F(1,156) = 0.0298, p = 0.8631"

A summary table (broken up here for ease of display) will be created when the option verbose = TRUE. This table can be accessed as the dfres object resulting from ExtraF. In the example above, we can access this summary table using ef$dfres:

Group Q0d K R2 Alpha
Shared NA NA NA NA
a 8.489634 2 0.6206444 0.0040198
b 5.848119 2 0.6206444 0.0040198
Not Shared NA NA NA NA
a 8.503442 2 0.6448801 0.0040518
b 5.822075 2 0.5242825 0.0039376

Fitted Measures

Group N AbsSS SdRes
Shared NA NA NA
a 160 387.0945 1.570213
b 160 387.0945 1.570213
Not Shared NA NA NA
a 80 249.2764 1.787695
b 80 137.7440 1.328890

Uncertainty and Model Information

Group EV Omaxd Pmaxd
Shared NA NA NA
a 0.8795301 22.63159 8.453799
b 0.8795301 22.63159 12.272265
Not Shared NA NA NA
a 0.8725741 22.45260 8.373320
b 0.8978945 23.10414 12.584550

Derived Measures

Group Omaxa Notes
Shared NA NA
a 22.63190 converged
b 22.63190 converged
Not Shared NA NA
a 22.45291 converged
b 23.10445 converged

Convergence and Summary Information

When verbose = TRUE, objects from the result can be used in subsequent graphing. The following code generates a plot of our two groups. We can use the predicted values already generated from the ExtraF function by accessing the newdat object. In the example above, we can access these predicted values using ef$newdat. Note that we keep the linear scaling of y given we used Koffarnus et al. (2015)’s equation fitted to the data.

## be sure that you've loaded the tidyverse package (e.g., library(tidyverse))
ggplot(apt, aes(x = x, y = y, group = group)) +
  ## the predicted lines from the sum of squares f-test can be used in subsequent
  ## plots by calling data = ef$newdat
  geom_line(aes(x = x, y = y, group = group, color = group), 
            data = ef$newdat[ef$newdat$x >= .1, ]) +
  stat_summary(fun.data = mean_se, aes(width = .05, color = group), 
               geom = "errorbar") +
  stat_summary(fun.y = mean, aes(fill = group), geom = "point", shape = 21, 
               color = "black", stroke = .75, size = 4) +
  scale_x_log10(limits = c(.4, 50), breaks = c(.1, 1, 10, 100)) +
  scale_color_discrete(name = "Group") +
  scale_fill_discrete(name = "Group") +
  labs(x = "Price per Drink", y = "Drinks Purchased") +
  theme(legend.position = c(.85, .75)) +
  ## theme_apa is a beezdemand function used to change the theme in accordance
  ## with American Psychological Association style
  theme_apa()

Plots

Plots can be created using the PlotCurves function. This function takes the output from FitCurves when the argument from FitCurves, detailed = TRUE. The default will be to save figures into a plots folder created one directory above the current working directory. Figures can be saved as either PNG or PDF. If the argument ask = TRUE, then plots will be shown interactively and not saved (ask = FALSE is the default). Graphs can automatically be created at both an aggregate and individual level.

As a demonstration, let’s first use FitCurves on the apt dataset, specifying k = "share" and detailed = T. This will return a list of objects to use in PlotCurves. In PlotCurves, we will feed in our new object, out, and tell the function to save the plots in the directory "../plots/" and ask = FALSE because we don’t want R to interactively show us each plot. Because we have 10 datasets in our apt example, 10 plots will be created and saved in the "../plots/" directory.

out <- FitCurves(dat = apt, equation = "hs", k = "share", detailed = T)
Warning: Zeros found in data not compatible with equation! Dropping zeros!

Beginning search for best-starting k

Best k fround at 0.93813356574003 = err: 0.744881846162718

Searching for shared K, this can take a while...
PlotCurves(dat = out, outdir = plotdir, device = "png", ask = F)
10 plots saved in man/figures/

We can also make a plot of the mean data. Here, we again use FitCurves, this time calculating a k from the observed range of the data (thus not specifying any k) and specifying agg = "Mean".

mn <- FitCurves(dat = apt, equation = "hs", agg = "Mean", detailed = T)
No k value specified. Defaulting to empirical mean range +.5
PlotCurves(dat = mn, outdir = plotdir, device = "png", ask = F)
1 plots saved in man/figures/
list.files("../plots/")
 [1] "Participant-106.png"  "Participant-113.png"  "Participant-142.png" 
 [4] "Participant-156.png"  "Participant-188.png"  "Participant-19.png"  
 [7] "Participant-30.png"   "Participant-38.png"   "Participant-60.png"  
[10] "Participant-68.png"   "Participant-mean.png"

Learn More About Functions

To learn more about a function and what arguments it takes, type “?” in front of the function name.

?CheckUnsystematic
CheckUnsystematic          package:beezdemand          R Documentation

Systematic Purchase Task Data Checker

Description:

     Applies Stein, Koffarnus, Snider, Quisenberry, & Bickels (2015)
     criteria for identification of nonsystematic purchase task data.

Usage:

     CheckUnsystematic(dat, deltaq = 0.025, bounce = 0.1, reversals = 0,
       ncons0 = 2)

Arguments:

     dat: Dataframe in long form. Colums are id, x, y.

  deltaq: Numeric vector of length equal to one. The criterion by which
          the relative change in quantity purchased will be compared.
          Relative changes in quantity purchased below this criterion
          will be flagged. Default value is 0.025.

  bounce: Numeric vector of length equal to one. The criterion by which
          the number of price-to-price increases in consumption that
          exceed 25% of initial consumption at the lowest price,
          expressed relative to the total number of price increments,
          will be compared. The relative number of price-to-price
          increases above this criterion will be flagged. Default value
          is 0.10.

reversals:Numeric vector of length equal to one. The criterion by
          which the number of reversals from number of consecutive (see
          ncons0) 0s will be compared. Number of reversals above this
          criterion will be flagged. Default value is 0.

  ncons0: Number of consecutive 0s prior to a positive value is used to
          flag for a reversal. Value can be either 1 (relatively more
          conservative) or 2 (default; as recommended by Stein et al.,
          (2015).

Details:

     This function applies the 3 criteria proposed by Stein et al.,
     (2015) for identification of nonsystematic purchase task data. The
     three criteria include trend (deltaq), bounce, and reversals from
     0. Also reports number of positive consumption values.

Value:

     Dataframe

Author(s):

     Brent Kaplan <bkaplan.ku@gmail.com>

Examples:

     ## Using all default values
     CheckUnsystematic(apt, deltaq = 0.025, bounce = 0.10, reversals = 0, ncons0 = 2)
     ## Specifying just 1 zero to flag as reversal
     CheckUnsystematic(apt, deltaq = 0.025, bounce = 0.10, reversals = 0, ncons0 = 1)

Acknowledgments

Special thanks to the following people who helped provide feedback on this document:

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