# Withdrawal Design Interactive Model Expanded

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## WHAT IS IT?

This model is an expansion of the Withdrawal Design Interactive Tutorial model. This model adds facsimiles of random ratio, fixed interval, and random interval schedules as reinforcement options.

From the Withdrawal Design Intervactive Tutorial model:

This model is designed to be used as a "hands on" instructional supplement for teaching students to analyze the effects of an independent variable using a withdrawal design. In the model, the agent engages in two behaviors according to separate schedules of reinforcement. Behaviors are plotted session by session, allowing students to use visual inpsection to determine when to move to the next condition (set of reinforcement schedules).

For a comprehnsive set of instructions on how to use to use the model, see https://app.box.com/s/wmtp0hs41st2jb5sp4dohq0wdtn2x2jl

## REINFORCEMENT

This model includes only one type of reinforcement schedule - the fixed ratio schedule.
In fixed-ratio schedules, a reinforcer is delivered after a specific number of responses. For example, a vending machine that only accepts quarters and vends items for 1 dollar could be said to reinforce inserting quarters on a fixed-ratio 4 schedule. In the simulation, setting *ratio1* to 4 means that every fourth time the agent engages in behavior 1, reinforcement will be delivered.

In the simulation, behavior 1 is represented by drawing an orange square, and behavior 2 is represented by drawing a violet circle. Reinforcement is represnted by the shape being filled in and (if the SOUND? switch is available and on) an audible tone (a note from a grand acoustic piano for behavior 1, and a note from a glockenspiel for behavior 2).

## HOW IT WORKS

An agent is randomly seeded on the screen and given the following properties:

behavior1 - a running tally of the number of times the agent draws a square

behavior2 - a running tally of the number of times the agent draws a circle

reinforcement1 - a running tally of the number of reinforcements that have followed behavior1

reinforcement2 - a running tally of the number of reinforcements that have followed behavior2

b1set - a tally of behavior1 that resets each new session

b2set - a tally of behavior2 that resets each new session

After the investigator adjusts the sliders to select the session-length, the ratio schedules, and the extinction settings, the investigator is ready to click the SETUP button and GO.

Each tick, the agent engages in behavior1 or behavior2. Which behavior the agent engages in is based upon the ratio of reinforcement for engaging in each of the behaviors (see NetLogo Features below). If both extinction switches are switched on, neither behavior is engaged in.

When an agent draws one of the shapes, it's behavior is reinforced based upon the selected schedule. Reinforcement is increased by 1 if the count of the behavior is divisable by the ratio.

At the beginning of each new session, b1set and b2set are reset to 0, and reinforcement1 and reinforcement2 are both set to 1.

## HOW TO USE IT

SESSION-LENGTH: Use this slider to set the session-length (how many ticks the session will last).

RATIO sliders: Set these sliders to determine the schedule of reinforcement for behavior1 and behavior2. Remember, the lower the number of the ratio, the more often the behavior will be followed by reinforcement. A ratio of 1 means every behavior will be reinforced.

EXTINCTION switches: Setting these to "ON" will prevent reinforcement from being delivered, regardless of the RATIO slider setting.

SETUP: resets the simulation.

GO: advances the simulation one session at a time.

EVER-RUN?: setting this switch to on keeps the simulation moving right along until the switch is turned off or "GO" is clicked again.

SOUND?: If available, this switch allows you to turn sound on or off.

## WHAT TO LOOK FOR AND TO TRY

There are two main ways to use the model.

**Point by point analysis.** To use the model this way, make sure the EVER-RUN? switch is set to off. Clicking GO will advance the simulation one session. The top plot shows the proportion of selections for behavior1 per session. The smaller plots show overall frequency and both behavior1 and behavior2 by session. Decisons can be made as to whether to continue with the same schedules of reinforcement or not using visual inspection.

**Running multiple sessions at once.** To use the model this way, turn the EVER-RUN? switch on and let the simulation continue to run until you are ready to make a change. Then click the EVER-RUN? switch off.

To create an ABAB withdrawal design, try the following:

- Set RATIO1 and RATIO2 to 1.
- Set EXTINCTION1 to OFF and EXTINCTION 2 to on.
This is Condition A.- Set EVER-RUN to OFF.
- Click SETUP
- Click GO at least three times.
- Determine if responding is stable enough to change schedules. If not, continue clicking go until it is.
- Once responding is stable, change the schedule by turning EXTINCTION1? ON and EXTINCTION2? OFF.
This is Condition B.- Click GO at least three times. Analyze. Keep clicking GO unitl you are ready to move on.
- Reset the schedule to Condition A (EXTINCTION1? OFF, EXTINCTION2? ON).
- Click GO until responding is steady.
- Reset the schedule to Condition B. (EXTINCTION1? ON, EXTINCTION2? OFF).
- Click GO until stable.

Following the instructions above should result in an ABAB withdrawal design that is easy to see in the top plot.

Setting the RATIOs to 1 and adjusting the schedules by turning the EXTINCTION? switches on and off results in the most stable and differentiated levels of behavior. If you wish to investigate more variable behavior, keep the EXTINCTION? switches off and try different ratio values. Keep in mind that if you set the ratios very high there will be few opporunities for reinforcement and responding will be fairly random. For this reason, the ratio sliders are set to range from 1 to 10.

## EXTENDING THE MODEL

Some suggestions for extending the model include the following:

adding in additional schedules of reinforcement

allowing more precise user-control over variability, level, and trend

simulating other types of single-subject designs

adding in confounds that can be manipulated

simulating different types of interventions in addition to reinforcement

## NETLOGO FEATURES

The logic for determining which behavior is engaged in is determined as follows:

...

ask turtles [

ifelse extinction1? and extinction2? [set b1set b1set set b2set b2set]

```
[
ifelse random-float 1 < reinforcement-ratio
[
behave1
if behavior1 mod ratio1 = 0 [if not extinction1? [reinforce1]]
]
[
behave2
if behavior2 mod ratio2 = 0 [if not extinction2? [reinforce2]]
]
]
```

]

...

where the "reinforcement-ratio" is determined by dividing reinforcement1 by the sum of reinforcement1 and reinforcement2.

## RELATED MODELS

Subsequent models for use in interactive exercises exploring single-subject experimental designs will be linked to here as they are developed.

## CREDITS AND REFERENCES

This model can be downloaded from the web at https://app.box.com/s/y8z1yp9a6z9cbushw0un4z0hvlys4x02

It is also available from the NetLogo Commons at http://modelingcommons.org/browse/one*model/5954#model*tabs*browse*info

## COPYRIGHT AND LICENSE

Copyright 2019 Allen Karsina

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of the license, visit https://creativecommons.org/licenses/by-nc-sa/3.0.

## Comments and Questions

turtles-own [ ;; these variables reflect selection and reinforcement behavior1 ;; counts all moves to black patches from any patch behavior2 ;; tcounts all moves to white patches from any patch reinforcement1 ;; tracks all reinforcement for moves to black patches reinforcement2 ;; tracks all reinforcement for moves to white patches b1set ;; depicts sets of 10 trials/time units b2set ;; depicts sets of 10 trials/time units reinforcement-ratio ;; this represents reinforcement1/(reinforcement1 + reinforcement2) interval1-check ;; temporary value for use with the random interval schedule interval2-check randomratio1-check ;; temporary values for use with the random ratio schedule randomratio2-check countint ;; keeps track of intervals within a session ] to setup clear-all setup-turtles reset-ticks end to setup-turtles create-turtles 1 ;; only 1 agent in the base model ask turtles [ setxy random-xcor random-ycor ;;each turtle starts on a random patch set shape "face neutral" set size 6 set color yellow ;; set initial parameters set behavior1 0 set reinforcement1 1 set behavior2 0 set reinforcement2 1 set reinforcement-ratio (reinforcement1 / (reinforcement1 + reinforcement2)) set interval1-check interval1 set interval2-check interval2 set randomratio1-check ratio1 set randomratio2-check ratio2 ] end to go ask turtles [ set b1set 0 set b2set 0 ] repeat session-length [ cd if schedule-type = "Fixed Ratio" [ ask turtles [ set shape "face neutral" ifelse extinction1? and extinction2? [set b1set b1set set b2set b2set] [ ifelse random-float 1 < reinforcement-ratio [ behave1 if behavior1 mod ratio1 = 0 [if not extinction1? [reinforce1]] if confound1? and behavior1 mod ratio1 != 0 [reinforce1] ] [ behave2 if behavior2 mod ratio2 = 0 [if not extinction2? [reinforce2]] if confound2? and behavior2 mod ratio2 != 0 [reinforce2] ] ] ] ] if schedule-type = "Random Ratio" [ ask turtles [ set shape "face neutral" ifelse extinction1? and extinction2? [set b1set b1set set b2set b2set] [ ifelse random-float 1 < reinforcement-ratio [ behave1 if behavior1 mod randomratio1-check = 0 [if not extinction1? [ reinforce1 set randomratio1-check (2 * random ratio1) + 1 ] ] ] [ behave2 if behavior2 mod randomratio2-check = 0 [if not extinction2? [ reinforce2 set randomratio2-check (2 * random ratio2) + 1 ] ] ] ] ] ] if schedule-type = "Fixed Interval" [ ask turtles [ set shape "face neutral" ifelse extinction1? and extinction2? [set b1set b1set set b2set b2set] [ ifelse random-float 1 < reinforcement-ratio [ behave1 if interval1-check < countint [if not extinction1? [ reinforce1 set interval1-check interval1 + countint ] ] ] [ behave2 if interval2-check < countint [if not extinction2? [ reinforce2 set interval2-check interval2 + countint ] ] ] ] ] ] if schedule-type = "Random Interval" [ ask turtles [ set shape "face neutral" ifelse extinction1? and extinction2? [set b1set b1set set b2set b2set] [ ifelse random-float 1 < reinforcement-ratio [ behave1 if interval1-check < countint [if not extinction1? [ reinforce1 set interval1-check (2 * random interval1) + 1 + countint ] ] ] [ behave2 if interval2-check < countint [if not extinction2? [ reinforce2 set interval2-check (2 * random interval2) + 1 + countint ] ] ] ] ] ] ask turtles [ set countint countint + 1 ;; if R1 + R2 do not equal 0, then ifelse reinforcement1 + reinforcement2 != 0 ;; set reinforcement-ratio equal to R1/(R1+R2) adjusted for history [set reinforcement-ratio (reinforcement1) / (reinforcement1 + reinforcement2)] ;; otherwise set reinforcement-ratio to chance [set reinforcement-ratio 0.5] ] tick ] ;;reset reinforcement ratios at end of session to help "discriminate" new schedules ask turtles [ set reinforcement1 1 set reinforcement2 1 ] if not ever-run? [stop] ;; stops simulation at intervals specified by session-length ;;if ever-run? = false and ticks mod session-length = 0 [stop] end to behave1 ;; executes behavior1 and updates settings for behavior1 and b1set pu set color orange rt random 360 fd random 20 pd repeat 4 [ fd 10 rt 90 ] set behavior1 behavior1 + 1 set b1set b1set + 1 end to behave2 ;; executes behavior2 and updates settings for behavior2 and b2set pu set color violet rt random 360 fd random 20 pd repeat 9 [ fd 12 left 40 ] set behavior2 behavior2 + 1 set b2set b2set + 1 end to reinforce1 set reinforcement1 reinforcement1 + 1 set shape "face happy" let n 10 loop [ set n n - 0.25 repeat 4 [ fd n rt 90 ] if n = 0.25 [stop] ] end to reinforce2 set reinforcement2 reinforcement2 + 1 set shape "face happy" pd let n 12 loop [ set n n - 0.25 repeat 9 [ fd n left 40 ] if n = 0.25 [stop] ] end

There is only one version of this model, created 13 days ago by Allen Karsina.

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**Parent:** Withdrawal Design Interactive Model

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