Judgment and Decision Making, vol. 5, no. 1, February 2010. pp. 5463
Implementation of the MultipleMeasure Maximum Likelihood strategy classification method in R: Addendum to Glöckner (2009) and practical guide for applicationMarc Jekel^{*} 
One major challenge to behavioral decision research is to identify the cognitive processes underlying judgment and decision making. Glöckner (2009) has argued that, compared to previous methods, process models can be more efficiently tested by simultaneously analyzing choices, decision times, and confidence judgments. The MultipleMeasure Maximum Likelihood (MMML) strategy classification method was developed for this purpose and implemented as a readytouse routine in STATA, a commercial package for statistical data analysis. In the present article, we describe the implementation of MMML in R, a free package for data analysis under the GNU general public license, and we provide a practical guide to application. We also provide MMML as an easytouse R function. Thus, prior knowledge of R programming is not necessary for those interested in using MMML.
Keywords: strategy classification, maximum likelihood, R.
It has been repeatedly argued that individuals make adaptive use of different decision strategies (Payne, Bettman, & Johnson, 1993; Gigerenzer & Todd, 1999) and that the application of the respective strategy might depend on different factors such as participants’ characteristics (e.g., intelligence; Bröder, 2003; Hilbig, 2008), effort accuracy tradeoffs (Payne, Bettman, & Johnson, 1988), learning experiences (Rieskamp, 2006), presentation format (Glöckner & Betsch, 2008a; Bröder & Schiffer, 2003) and situational forces (e.g., time pressure, Payne et al., 1988). Some strategies might be entirely based on deliberate computations (for an overview, see Payne et al., 1988). Others, by contrast, might partially rely on automaticintuitive processes (for an overview, see Glöckner & Witteman, 2010a). Glöckner and Betsch (2008a) showed that classic process tracing methods such as Mouselab (Payne et al., 1988) might hinder information search processes that are necessary for applying automatic processes. Furthermore, taking into account intuitiveautomatic processes, many strategies make essentially the same choice predictions (i.e., weighted compensatory information integration; e.g., Brehmer, 1994; Busemeyer & Townsend, 1993; Busemeyer & Johnson, 2004; Glöckner & Betsch, 2008b; see also Hammond, Hamm, Grassia, & Pearson, 1987; Brunswik, 1955). Glöckner (2009) showed that, considering strategies that make different choice predictions, people can be more efficiently classified by applying the MultipleMeasure Maximum Likelihood strategy classification method (MMML) as compared to relying on a choicebased strategy classification alone (Bröder & Schiffer, 2003; Bröder, 2010). Furthermore, the MMML method also allows us to differentiate between strategies that make the same choice predictions, given that decision time predictions aid discrimination.
Preparing an experiment to generate data for the application of the MMML method comprises three basic steps: (1) choose dependent measures (and specify the distributions of those measures), (2) choose a set of strategies, (3) select items that differentiate between the considered strategies and derive predictions on the dependent measures. Then the fit of the predictions of the strategies to individuals’ empirical data is calculated using MMML and the strategy most likely accounting for individuals’ behavior is identified. Glöckner (2009) provided an implementation of the MMML method in STATA – a commercial package for data analysis. To facilitate the access to the MMML method, we introduce the implementation of the MMML method in R – a noncommercial, publicly available, and open source package for data analysis.
Parameter Description Observed n_{jk} number of choices of type of tasks j congruent to strategy k x_{T}^{→} vector of participant’s decision times x_{C}^{→} vector of participant’s confidence judgments Estimated є_{k} error rate of choices for strategy k µ_{T} mean of decision times σ_{T} standard deviation of decision times R_{T} scaling parameter for decision times µ_{C} mean of confidence judgments σ_{C} standard deviation of confidence judgments R_{C} scaling parameter for confidence judgments Given t_{Ti} contrast weight for the decision time of task i t_{Ci} contrast weight for the confidence judgment of task i
In the following, we will present the key elements of the MMML method and introduce the variables used in Equation 1 (see below). For more details, see Glöckner (2009; 2010).
The default dependent measures analyzed in the MMML method are choices, decision times, and confidence judgments (Glöckner, 2009). For choices, it is assumed that participants apply strategies with an equal error rate for all types of tasks/trials (see also Bröder & Schiffer, 2003; Bröder, 2010). Hence, the number of choices congruent with strategy predictions should be binomially distributed. Let k be the index number for strategies and j the index number for task types considered. The frequencies of decisions in line with the predictions of a strategy for each task type, n_{jk} , and the total number of tasks per type, n_{j} , can then be used to estimate the error rate є_{k} which maximizes the fit between predictions and individual choices (see first part of Equation 1).
For (logtransformed) decision times (T) and confidence judgments (C), we assume that each observation x_{T} (x_{C}) from the total vector of observations x_{T}^{→} (x_{C}^{→}) stems from a normal distribution with mean µ_{Tk}=µ_{T}+t_{Ti}R_{T} (µ_{Ck}=µ_{C}+t_{Ci}R_{C}) and variance σ_{T}^{2} (σ_{C}^{2}). R_{T} (R_{C}) is a scaling parameter and t_{Ti} (t_{Ci}) is the prediction/contrast derived from strategy k (see next paragraph for details). The coefficients µ_{T}, σ_{T}, R_{T}, µ_{C}, σ_{C}, and R_{C} need to be estimated through maximum likelihood estimation. All variables are included in normal distribution functions that constitute part 2 and part 3 of Equation 1. Descriptions for all variables can be found in Table 1.
The likelihood of a data vector for each strategy and participant can therefore be calculated by (Glöckner, 2009, Equation 8, p. 191):
L_{total}=p(n_{jk}, 
 _{T}, 
 _{C}k,є_{k},µ_{T},σ_{T},R_{T},µ_{C},σ_{C},R_{C})= 

 (1−є_{k})^{njk}є_{k}^{(nj−njk)}× 

 e 
 × 

 e 
 . 
(1)
To take the number of free parameters into account in model evaluation, we compare the BIC values instead of the loglikelihoods for strategy classification. The BIC values can be calculated by (Glöckner, 2009, Equation 9, p. 191): BIC=−2ln(L_{total})+ln (N_{obs})N_{p}.
L_{total} is the likelihood of the data given the application of the respective strategy (Equation 1). N_{obs} is the number of task types times the number of dependent measures. N_{p} is the number of the parameters that need to be estimated. If the strategy makes differentiated predictions for choices, decision times, and confidence over task types, overall seven parameters are estimated (є_{k},µ_{T}, σ_{T}, R_{T}, µ_{C}, σ_{C}, and R_{C}). For strategies that predict all equal decision times or confidence judgments (e.g., an equalweightsrule in tasks in which the number of attributes per choice option is held constant), one parameter less is estimated (R_{T} or R_{C} omitted), respectively. For a strategy which assumes random choices (RANDOM), є_{k} is omitted from estimation as well.
The MMML method is not limited to the measures discussed. Any measure (for further measures, see Payne et al., 1988; Glöckner & Witteman, 2010b) can easily be added, as long as (1) the distribution of the measure is known and (2) predictions for the measure can be derived from each strategy, and thus contrasts can be formulated.
Types of decision tasks 1 2 3 4 5 6 A B A B A B A B A B A B Cue 1 (v = .80) + – + – + – + – + – – – Cue 2 (v = .70) + – + – – + – – – + – – Cue 3 (v = .60) + – – + – + – – + – + – Cue 4 (v = .55) – + – + – + – + – + – +Choice Predictions TTB A A A A A A EQW A A:B B A:B A:B A:B WADD_{corrected} A A B A A A PCS A A B A A A RANDOM A:B A:B A:B A:B A:B A:BTime Predictions (contrasts t_{T}) TTB −0.167 −0.167 −0.167 −0.167 −0.167 0.833 EQW 0 0 0 0 0 0 WADD_{corrected} 0 0 0 0 0 0 PCS −0.444 −0.354 0.556 −0.157 0.071 0.328 RANDOM 0 0 0 0 0 0Confidence Predictions (contrasts t_{C}) TTB 0.167 0.167 0.167 0.167 0.167 −0.833 EQW 0.667 −0.330 0.667 −0.330 −0.330 −0.330 WADD_{corrected} 0.630 0.230 −0.370 0.030 −0.170 −0.370 PCS 0.621 0.278 −0.326 −0.005 −0.189 −0.378 RANDOM 0 0 0 0 0 0Note. In the upper part of the table, the item types are presented. The cue validities v are provided beside each cue. The cue values are “+” for “cue is present” and “−” for “cue is absent”. Below, the predictions for choices are shown. A and B stand for the predicted option. “A:B” indicates random choices between A and B. The lower part of the table shows predictions for decision times and confidences expressed in contrast weights that add up to zero and have a range of 1. Contrast values represent relative weights comparing different cue patterns for one strategy (modified after Glöckner, 2009; 2010).
The MMML method is not limited to a specific set of strategies; it is applicable to any set of strategies as long as predictions for the measures can be derived from the strategy. In the current example, we use five strategies. All but one (i.e., RANDOM) can be easily replaced by other strategies.
The default strategies we use in the MMML method are “Take The Best” (TTB), “Equal Weight” (EQW), “Weighted Additive Corrected” (WADD_{corrected}) (Payne et al., 1993; Gigerenzer & Todd, 1999; Glöckner & Betsch, 2008a), “Parallel Constraint Satisfaction” (PCS) (Glöckner, 2006; Glöckner & Betsch, 2008b), and the “Random Model” (RANDOM), which is tantamount to guessing. Table 2 summarizes predictions of these strategies for six task types which are used for illustration. These tasks are probabilistic inferences in which decision makers choose which option is superior, based on dichotomous predictions of four different cues with certain predictive power (cue validity).
For example, a participant strictly following TTB chooses option A for all tasks; for each type of task, the first cue that discriminates between options always points to option A.
Predictions of decision times are derived from the number of computational steps needed to apply the respective strategy (TTB, EQW, WADD_{corrected}) and the number of iterations necessary to find a consistent solution of the PCS network (Glöckner & Betsch, 2008b). Predictions of confidence judgments are based on differences between the weighted (WADD_{corrected}) and unweighted (EQW) sum of cues, the validity of the differentiating cue (TTB), and the difference of activation between options (PCS). Predictions are transformed into contrasts with a range of 1 and a sum of values of 0. For RANDOM, we expect strategy consistent choice behavior to be at chance level (fixed є_{k}=0.5) and no differences in decision times and confidence judgments between the six types of decision tasks (thus R_{T} and R_{C} are set to 0).
The lower part of Table 2 shows the contrasts for decision times and confidence judgments for all strategies and six task types. For example, a participant strictly following TTB investigates only one cue for the first five types of task and three cues for the sixth type of task. Hence, more computational steps were necessary for applying TTB to the latter tasks. Specifically, 4 computational steps for the first five types of task (investigate cue 1 option A, investigate cue 1 option B, compare cues, choose option) and 10 computational steps for the sixth type of task, and therefore decision times should be longer (e.g., Bröder & Gaissmaier, 2007; Payne, Bettman, & Johnson, 1988). Furthermore, a decision for option A is based on a cue with a validity of .80 for the first five types of task and a validity of .60 for the sixth type of task. For TTB, we use the validity of the cue on which the decision is based as an indicator of judgment confidence (Gigerenzer, Hoffrage, & Kleinbölting, 1991). In order finally to derive the contrast vectors for TTB displayed in Table 2, we rescaled the prediction vectors for decision time [4 4 4 4 4 10] and for judgment confidence [.8 .8 .8 .8 .8 .6] into vectors of a range of values of 1 and a sum of values of 0.
R (2010) is software for statistical analysis under the GNU general public license, e.g., it is free of any charge. R is available for Windows, Mac, and UNIX systems. To download R, visit the “Comprehensive R Archive Network” (http://cran.rproject.org/). To learn more about R, we propose the free introduction to R by Paradis (2005); however, to apply the MMML method in R, no sophisticated prior experience with the R syntax is required. In this paper, we provide two different implementations of MMML in R.^{1} First, we describe a detailed implementation of MMML as syntax code that is similar to the implementation in STATA described by Glöckner (2009), and second, we discuss an alternative implementation as easy to use Rfunction. The former should provide insight in how MMML works; the latter should make MMML easy to apply.
First, for the more complex syntax version, we explain how to prepare the matrix of raw data (see 3.1), to change, if necessary, the values of the defaults, and to call the output (3.2). Following, we demonstrate the method with a data example (3.3). We conclude with a short description on how to estimate the parameters and to obtain the fit of further strategies (3.4). For the interested R user, we commented elements of this implementation of the MMML method in the code directly. In the last section (3.5), we explain how to apply the implementation of MMML as simple Rfunction. For users that are less familiar with R, we recommend concentrating on section 3.5.
The structure of the data file is identical to the file described in
Glöckner (2009). You will find an example of a data file —
data.csv
— in the supplementary material. The name tags,
descriptions, and valid values of the variables in the data file are
listed in Table 3.
Variable Name Description Valid Values PARTICIPANT number of participant integer, value >0 DEC number/marker of decision task any value STRAT type of strategy 1 = TTB, 2 = EQW, 3 = WADD_{corrected}, 4 = PCS, 5 = RANDOM TYPE type of task 1 = type 1, 2 = type 2, 3 = type 3, 4 = type 4, 5 = type 5, 6 = type 6 INDEX type of measure 1 = choices, 2 = decision times, 3 = confidence judgments TOTAL_PRED expected data choices: number of tasks of type j, decision times and confidence judgments: contrast weight for task i MISS random choice if a random choice is expected for task i, insert value = 1, else value = 0 DV observed data choices: number of strategyincongruent choices (if all number = 0 set value = 1.1 for one type of tasks), decision times: logtransformed data (with order effects partialed out), confidence judgments: raw data
The variable “PARTICIPANT” codes the number of the participant. The variable “DEC” codes the position of the decision task in the sequence of all tasks/trials. The variable “STRAT” codes the strategy: 1 = TTB, 2 = EQW, 3 = WADD_{corrected}, 4 = PCS. It is not necessary to input values for RANDOM because the data vector is generated based on the data from the other strategies. The variable “TYPE” codes the type of tasks. The types differ in the configurations of the cue values (Glöckner, 2009). The variable “INDEX” codes the type of measure: 1 = choice, 2 = decision time, 3 = confidence judgment. The variable “TOTAL_PRED” codes the total number of observations per type and the contrast weight for measures of decision times and confidence judgments. The variable “MISS” is used for choice data only: random choice for the specific task expected (= 1) vs. not expected (= 0). The final variable “DV” codes the observed data point of measure.
For choices, the number of strategyincongruent choices is coded. Hence, 0 indicates that all choices for tasks of the respective task type were in line with the prediction of the strategy. In case a participant shows strategycongruent choices for all tasks of all types, the input for “DV” should be coded as 1.1 for one type of tasks due to problems of convergence in the process of maximum likelihood estimation if the error is zero. 1.1 is used to indicate data points that were changed. The code of the MMML method will automatically change values of 1.1 to 1 (i.e., the maximum value of congruent choices is set to the total number of observations minus 1). Because decision times are usually highly skewed, logtransformed decision times should be coded. To account for learning effects over time it is recommended to use residuals after partialing out the order in presentation of choice tasks (which should, of course, be randomized in the experiment; logtransformations should be done before partialing out learning effects). Confidence judgments can be used without recoding.
Before you execute the code, save your data file under the directory
C:\
in csvformat; the directory can be changed and modified
for systems running Mac or Linux (see 3.2 for details).
For decision times and confidence judgments, a single line of the data matrix is reserved for task i, each participant, and strategy k. For choices, a single line of the data matrix is only needed for tasks of type j, each participant, and strategy k. Thus, in the example with 6 types of task and 10 tasks per type of task, there are two times sixty lines reserved for decision times and confidence judgments and only six lines reserved for choices for each participant and strategy k.
To illustrate the structure of the data file, we conclude with a short example. Assume you want to code the input for each measure (i.e., choices, decision times, and confidence judgments) for participant 6, type of tasks 1, and strategy 4 (= PCS). For the 10 tasks of type 1, participant 6 chose 10 times option A. In reference to the choices expected for type of tasks 1 and PCS (see Table 2), participant 6 made 0 strategyincongruent choices.
In the example, there are 10 tasks of type 1. Therefore, there are two times ten lines reserved for decision times and confidence judgments for participant 6 and PCS. As a matter of simplification, we only demonstrate the input for task 1 of type of tasks 1. Participant 6 needed 3001 ms before she decided to choose one of the options. Due to the skewed distribution of decision times, the logtransformation of 3001 ms = 8.007 is the input for the data file (for simplicity we do not consider partialing out time effects here). Furthermore, participant 6 selected a confidence rating of 29 (on a confidence scale ranging from 0 to 100) that she picked the option with the higher criterion value. Therefore, 29 serves as the input for the confidence judgment of task 1 in the data file.
The coding of the three lines of the input described in the example can be found in Table 4.
PARTICIPANT DEC STRAT TYPE INDEX TOTAL_PRED MISS DV 6 1 4 1 1 10 0 1.1 6 1 4 1 2 −0.444 0 8.007 6 1 4 1 3 0.621 0 29
For all three measures, we insert a 6 for participant 6 (PARTICIPANT), a 4 for PCS (STRAT), and a 1 for type of tasks 1 (TYPE).
In the first line of Table 4, the choices are coded. We insert a 1 to set choices as the type of measure (INDEX). We expect 10 choices congruent to PCS (TOTAL_PRED). Participant 6 made no strategyincongruent choices. Thus, we insert 1.1 for the observed value (DV). We did not expect random choices for PCS and type of tasks 1; therefore we insert a 0 for the random choice indicator (MISS).
In the second line of Table 4, the decision time is coded. We insert a 2 to set decision times as the type of measure (INDEX). The contrast weight for type of task 1 is −0.444 (TOTAL_PRED). We have observed a logtransformed decision time of 8.007 (DV). For decision times, the coding for random choices is not relevant. We therefore insert a 0 for random choices (MISS).
In the third line of Table 4, the confidence judgment is coded. We insert a 3 to set confidence judgments as the type of measure (INDEX). The contrast weight for type of task 1 is 0.621 (TOTAL_PRED). We have observed a confidence judgment of 29 (DV). For confidence judgments, the coding for random choices is not relevant. We therefore insert a 0 for random choices (MISS).
We can further insert a marker for each line in the data file (DEC). Entries in the DEC vector are not processed during the maximumlikelihood estimation in R. Nevertheless, it makes sense to code the order of appearance of the task in the experiment to investigate order effects for decision times and confidence judgments before applying the MMML method. Due to the coding of choices, you can insert a marker only for each type of task for choices.
To modify the MMML code, just open and change values in the
MMML.R
file with your preferred texteditor. The user
input is at the beginning of the file, perceptually segregated from
the program code. To run the code, just copy the code of the
MMML.R
file in the open R Console, or submit it with
source('MMML.R')
from the R command line.
In the “user input”, you can set the directory where the data file is located.
The program produces two outcome variables: “output” and “likbic”
(see 3.2). Both variables are printed in the R Console and saved in
csv files by default under the directory C:\
. (We use Windows
conventions in this exposition. In all cases, users of Linux, Unix,
or OSX can replace the working directory without the C:\
prefix.) The variable “output” stores estimations of coefficients,
corresponding standard errors, zvalues, probabilities for absolute
zvalues, and confidence intervals for each participant and
strategy. The variable “likbic” stores the BIC and loglikelihoods
for each participant and strategy. The output display is similar to
the STATA output described in Glöckner (2009, p. 195).
Furthermore, you can easily inactivate/activate code sections, e.g., whether to read in raw data, run maximum likelihood estimations, print output, and save output; see “inactivate/activate code sections” in the code for details. This enables you to print the output for further participants without having to rerun the entire code.
By default, R will print the output for all participants and strategies. For purposes of clarity, you can also print the output for a specified participant and strategy; see “output: print selection of coefficients …”.
Finally, you can specify the maximum number of iterations and the relative criterion of convergence^{2} for the BFGS maximum likelihood estimation algorithm^{3} (Broyden, 1970, Fletcher, 1970, Goldfarb, 1970, Shanno, 1970) in “configure the properties of maximum likelihood algorithm (mle)”. Defaults should be fine for most applications. For the unlikely case that the maximum likelihood estimation algorithm does not converge for a strategy of a participant, you can easily increase the maximum number of iterations (see comments in the code).
In the supplementary material, you will find the file
data.csv
. Please copy this file into the directory C:\
.
In the data file, there are codings for 10 participants, 6 task types,
and 10 tasks for each type of task; see Glöckner (2009; 2010) for
details. First, we suggest you run the MMML method for all
participants and strategies. You need to open the file MMML.R
with a text editor, set the variable “totalprint” in the section
“inactivate/activate code sections” to a value of 1 (= default
value), and copy/paste the entire code into the open R Console, or
submit it from the command line.
If you require individual predictions for a specific person and strategy, you can modify the variables “participantOUT” and “strategyOUT” in the section “output: print selection of coefficients …” as in the following example. Assume one wants to print the loglikelihoods and BIC values for all strategies for participant 6. Simply set “participantOUT” to a value of 6. Next, select all text, copy it, and paste it into the open R Console (or submit from the command line).
Participant Lik/Bic TTB EQW WADD_{corrected} PCS Random logLik 6 1 −327.83 −353.09 −319.03 −313.22 −361.30 BIC 6 2 675.90 723.53 655.40 646.68 734.16 Participant Strategy Coef. Std.Err. z P >z CI 2.5% CI 97.5% Epsilon 6 4 0.11 0.04 2.81 0.004 0.03 0.19 mu_Time 6 4 8.19 0.05 140.74 0.000 8.07 8.30 sigma_Time 6 4 0.45 0.04 10.95 0.000 0.38 0.54 R_Time 6 4 0.52 0.16 3.23 0.001 0.20 0.84 mu_Conf 6 4 17.20 2.45 7.00 0.000 12.31 22.10 sigma_Conf 6 4 19.03 1.73 10.95 0.000 16.07 23.02 R_Conf 6 4 58.40 6.96 8.39 0.000 44.53 72.26Note. The output of the loglikelihoods and BIC values for participant 6 and all strategies (top) and the coefficients for participant 6 and strategy 4 (= PCS) (bottom) are shown.
Based on the BIC values of the output (see Table 5, top), participant 6 most likely followed the PCS strategy (in comparison to all other tested strategies).
To print out the coefficients for participant 6 and PCS, set “strategyOUT” to a value of 4. To prevent R from rereading the entire raw data and repeating the maximum likelihood estimation, disable these code sections by setting “readdata” and “mml” in “inactivate/activate code sections” to a value of 0. Again, select all text, copy it, and paste it into the open R Console (or submit). This produces the output (see Table 5, bottom) for all coefficients, e.g., є_{k},µ_{T}, σ_{T}, R_{T}, µ_{C}, σ_{C}, and R_{C} along with the corresponding test statistics. In the example, all coefficients are significantly (p<.05) different from 0.
The provided R code cannot be applied to just the default strategies. It is flexible enough to enable you to estimate the parameters and obtain the fit for most strategies you would like to test. The only constraint is that your strategy needs to match the number of parameters estimated for one of the strategies described in the article. This is the case if (a) the strategy to be considered makes clear predictions concerning choices (i.e., option A, option B, or guessing) and (b) if the data set contains task types for which the strategy predicts differences in decision times and confidences. For such a strategy, all parameters described in Table 1 are estimated. To analyse such a strategy, you generate the expected choices and contrast weights for decision time and confidence in accordance with the predictions of your strategy and set STRAT = 1 or 4 (currently used for TTB or PCS) in the raw data file. Alternatively, if the additional strategy predicts equal decision times for all task types, it includes all parameters except for R_{T}. In this case, you proceed as described above, but you set STRAT = 2 or 3 (currently used for EQW or WADD_{corrected}). Finally, you should adjust strategy labels that are displayed in the output in “set strategy labels” accordingly. Note that the MMML estimations for strategies are independent of each other. It is therefore theoretically possible to compare as many strategies as one needs by rerunning MMML with additional strategies. Finally, the code does not only allow testing the specific number of tasks and type of tasks used in the example. It is possible to change the number of task types and the number of tasks for each task type without having to change code. The number of free parameters for the BIC value is adjusted automatically. Therefore, MMML users are by no means limited to relying on six task types and ten tasks of each type. We use them only as one example.
The generalized version of the MMML method is implemented as an easytouse R function. To improve usability, the function uses a more convenient format of the raw data file.
The raw data file consists of 6 columns. The first three indicate the
number of the participant (“PARTICIPANT”), the
number of the decision task (“DEC”), and the type of
the task (“TYPE”). The fourth column
“ACHOICES” codes whether the participant chose
option A (coded as 1) or option B (coded as 0) in this task. In the
fifth column, the decision time of the participant for the task is
indicated (“DECTIMES”). In the sixth column, the
confidence judgment for the task is coded
(“CONFJUDGMENTS”). Hence, all data concerning one
choice task is now coded in one line. Furthermore, choices do not need
to be aggregated by the user, and expected choices and contrasts do
not need to be specified for every single strategy. If you did not
assess decision times and/or confidence judgments, just delete the
respective columns in the data file. In the supplementary material you
find a data file in the respective simplified format
(datafunction.csv
; which is a reformatted version of the
original data file data.csv
).
To use the MMML method function, you need to copy and paste (or
submit) the code provided in the file FunctionMMML.R
. To call
the function afterward, type the command:
MMML(partic, stratname, expectedchoice, contrasttime, contrastconfidence, saveoutput, directoryData, directoryOutput, separator, numberOFiterations, relconvergencefactor)
in the open R console and hit enter. If an argument of the function is left blank, the default is applied. Arguments, descriptions, valid values, examples and defaults are listed in the Appendix.
For example, to estimate the parameters and assess the fit for the TTB strategy described in section 2.2 for all participants in your dataset and keep the defaults for all other arguments of the function, type:
MMML(,“TTB”,c(10,10,10,10,10,10), c(−0.167,−0.167,−0.167,−0.167,−0.167,0.833), c(0.167,0.167,0.167,0.167,0.167,−0.833))
in the open R Console and hit enter. Because partic was not
specified, estimates for all participants are generated. Estimates
of the parameters, loglikelihoods and BICs are prompted in the R
Console and are saved in the file output.csv
under directory
C:\
. In case you did not assess decision times in your study
and do not want to save the output, you can leave the fourth
argument of the function blank and input a 0 for
saveoutput, i.e, you type:
MMML(,“TTB”,c(10,10,10,10,10,10), , c(0.167,0.167,0.167,0.167,0.167,−0.833),0).
It should be clear now that you can test further strategies by simply changing the expected choices and contrast weights in the MMML function. You can exclude measures from the MMML method by leaving the argument expectedchoice and/or contrasttime and/or contrastconfidence in the function blank. Again, the number of task types and the number of tasks per type can be altered without the need to change code.
Finally, we included the following features that will further simplify usability. First, it is unnecessary to input contrast weights that meet the scaling properties discussed in section 2.2, i.e., sum of contrast weights = 0 and range of contrast weights = 1. The user can input the “raw” contrast weights, i.e., c(4,4,4,4,4,10) for TTB contrast weights. The function rescales the contrast weights automatically. Second, the function automatically adds or subtracts one strategy congruent or incongruent choice if a participant shows strategy congruent or incongruent choices (or mixed) for all task types (see section 3.1). Automatic addition or subtraction of a choice is prompted in the output in the R Console.
The code of the MMML method in R should enable researchers easily to identify participants’ decision strategy in complex decision tasks. Beyond the benefit of strategy classification, the MMML method facilitates thinking about strategies on a detailed process level. To apply the MMML method, researchers have to specify the process and outcome characteristics of a strategy. The MMML method can therefore be used as a tool for constructing new strategies and improving existing strategies of decision making. All it necessitates is clearly specified models. Besides estimating the overall fit of observed data to the predictions of the different strategies, the method allows the investigation of process properties in more depth. In particular, you can ask whether the scaling parameters for time R_{T} and R_{C} confidence contribute significantly to predicting the data per individual. If this is not the case, predictions for the respective dependent measure and possibly also assumptions about underlying processes should be rethought.
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Arguments, descriptions, valid values, examples, and defaults.
Argument  Description  Valid Values  Example  Default 
partic  input the number of the participant you want to
apply the MMML method to  1, 2, ..., n  1  the MMML method is applied to all participants in the raw data file 
stratname  input the name of the strategy  any value  “EQW” (be aware of “”)  “NONAME” 
expectedchoice  data vector: set the number of A choices expected for each type of task  set value = number
of tasks if the strategy predicts A choices for the type of task,
set value = 0 if the strategy predicts B choices for the type of task, set value = 0.5 if the strategy predicts guessing for the type of task  c(10,0.5,0,0.5,0.5,0.5) (be aware of c(); the first position in the vector is the prediction for type of tasks 1, the second position in the
vector is the prediction for type of tasks 2, ...)  choices are excluded from the MMML method 
contrasttime  data vector: set the contrast weights for decision times for each type of task  any numeric value  c(0,0,0,0,0,0) (be aware of c())  decision times are excluded from the MMML method 
contrastconfidence  data vector: input the contrast weights for confidence judgments for each type of task  any numeric value  c(0.667,−0.33,0.667, −0.33, −0.33, −0.33) (be aware of c())  confidence judgments are excluded from the MMML method 
saveoutput  indicate if you want to save the output in a file  save output?
1 = yes, 0 = no  1  1 
directoryData  indicate the directory of the raw data file
datafunction. csv  platform specific requirements  “ C:/datafunction .csv ” (be aware of “”)  “ C:/datafunction .csv ” 
directoryOutput  set the name and directory of the output file  platform specific requirements  “ C:/output.csv ” (be aware of “”)  “ C:/output.csv ” 
separator  indicate the column separator of the input file  “;”, “,”, “ ”  “,”  “,” 
numberOFiterations  set the maximum number of iterations for the mle algorithm  integer > 0  10^{9}  10^{9} (the default should be fine) 
relconvergencefactor  set the relative criterion of convergence for the mle algorithm  real number > 0  10^{−15}  10^{−15} (the default should be fine) 
This document was translated from L^{A}T_{E}X by H^{E}V^{E}A.