ArticlePublisher preview available

Discounting and the Portfolio of Desires

Psychological Review
Authors:
Peter R Killeen at Arizona State University Tempe
Peter R Killeen
  • Arizona State University Tempe
Read publisher preview
Download citation
To read the full-text of this research, you can request a copy directly from the author.

Abstract

The additive utility theory of discounting is extended to probability and commodity discounting. Because the utility of a good and the disutility of its delay combine additively, increases in the utility of a good offset the disutility of its delay: Increasing the former slows the apparent discount even with the latter, time-disutility, remaining invariant, giving the magnitude effect. Conjoint measurement showed the subjective value of money to be a logarithmic function of its amount, and subjective probability—the probability weighting function—to be Prelec’s (1998). This general theory of discounting (GTD) explains why large amounts are probability discounted more quickly, giving the negative magnitude effect. Whatever enhances the value of a delayed asset, such as its ability to satisfy diverse desires, offsets its delay and reduces discounting. Money’s liquidity permits optimization of the portfolio of desired goods, providing added value that accounts for its shallow temporal discount gradient. GTD predicts diversification effects for delay but none for probability discounting. Operations such as episodic future thinking that increase the larder of potential expenditures—the portfolio of desirable goods—increase the value of the asset, flattening the discount gradient. States that decrease the larder, such as stress, depression, and overweening focus on a single substance like a drug, constrict the portfolio, decreasing its utility and thereby steepening the gradient. GTD provides a unified account of delay, probability, and cross-commodity discounting. It explains the effects of motivational states, dispositions, and cognitive manipulations on discount gradients.
A preview of this full-text is provided by American Psychological Association.
Learn more
Content available from Psychological Review 
This content is subject to copyright. Terms and conditions apply.
Discounting and the Portfolio of Desires
Peter R. Killeen
Department of Psychology, Arizona State University
The additive utility theory of discounting is extended to probability and commodity discounting. Because
the utility of a good and the disutility of its delay combine additively, increases in the utility of a good offset
the disutility of its delay: Increasing the former slows the apparent discount even with the latter, time-
disutility, remaining invariant, giving the magnitude effect. Conjoint measurement showed the subjective
value of money to be a logarithmic function of its amount, and subjective probability—the probability
weighting function—to be Prelec’s (1998). This general theory of discounting (GTD) explains why large
amounts are probability discounted more quickly, giving the negative magnitude effect. Whatever enhances
the value of a delayed asset, such as its ability to satisfy diverse desires, offsets its delay and reduces
discounting. Money’s liquidity permits optimization of the portfolio of desired goods, providing added
value that accounts for its shallow temporal discount gradient. GTD predicts diversification effects for delay
but none for probability discounting. Operations such as episodic future thinking that increase the larder of
potential expenditures—the portfolio of desirable goods—increase the value of the asset, flattening the
discount gradient. States that decrease the larder, such as stress, depression, and overweening focus on a
single substance like a drug, constrict the portfolio, decreasing its utility and thereby steepening the gradient.
GTD provides a unified account of delay, probability, and cross-commodity discounting. It explains the
effects of motivational states, dispositions, and cognitive manipulations on discount gradients.
Keywords: additive utility theory, general theory of discounting, probability and delay discounting,
portfolio diversification, liquidity
When the receipt of a good is delayed money is discounted much
more gradually than other goods such as food, entertainment,
alcohol, drugs, sex, and so forth. But when the receipt of money
is probabilistic, it is discounted at about the same rate as other
goods. These are just two of the many perplexities in the extensive
discounting literature. Another layer of complexity is that large
magnitudes are discounted over delays in their receipt more slowly
than small ones—the positive magnitude effect—but are discounted
more quickly in probability discounting—the negative magnitude
effect. Figure 1, after Estle et al. (2007), offers a paradigmatic
representation of these central issues. Their experimental procedure,
typical of discounting tasks, was:
Participants were told that on each trial, two amounts of a hypothetical
reward (money, beer, candy, or soda) would appear on the screen. For
the temporal-discounting task, they were instructed that one amount
could be received right now, whereas the other amount could be
received after some specified period of time. For the probability-
discounting task, they were instructed that one amount could be
received for sure, whereas the other amount could be received with
some specified probability. (p. 59)
After being asked to choose, the immediate or sure thing was
adjusted to achieve indifference between it and the delayed or
probabilistic one. The relative discount, the value of the immediate
sure thing divided by the value of the delayed or probabilistic one, is
then plotted as a discount function (e.g., Figure 1).
Why are money delay functions shallower than commodity
functions, why are there magnitude effects, and why are those for
delay and probability discordant? This article resolves these
questions with an existing theoretical model (additive utility theory
[AUT]; Killeen, 2009,2023). AUT is then extended to probability
discounting and to the many interesting effects of cognitive and
emotional manipulations and demographic correlates on the rate of
delay discounting, and why these variables play the roles that they
do. To set the stage, it is necessary to reconstruct the AUT of delay
discounting, as it forms the necessary foundation for this solution.
A General Frame
The utility of a package of goods, U(G), is given by some
concatenation of the variables considered in this article:
UðGa,d,p,nÞ=F½faðaÞ,fdðdÞ,fpðpÞ,fnðnÞ:(1)
Here, ais its amount, dis the delay of its receipt, pis the
probability of receiving it, and nis the diversification it affords.
The functions within the brackets, f
x
, are psychophysical value
functions (Stevens, 1986/1975), transforming the numbers on
which they operate into their psychological counterparts. F[]
concatenates those attributes and converts that combination into
the quantity on the left-hand side (lhs), the utility of the package.
This utility adds to that of the existing portfolio of goods, which
constitutes their reference level (Thaler, 1999). For the experiments
covered in this article, it is not necessary to determine the form of
the utility transformation F.
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
This article was published Online First September 14, 2023.
Peter R. Killeen https://orcid.org/0000-0002-0889-4040
The author thanks Junyi Dai and Jonathan Friedel for their most helpful
comments on earlier drafts.
Correspondence concerning this article should be addressed to Peter R.
Killeen, Department of Psychology, Arizona State University, 405 Marcus
Drive, Prescott, AZ 86303, United States. Email: killeen@asu.edu
Psychological Review
© 2023 American Psychological Association 2023, Vol. 130, No. 5, 1310–1325
ISSN: 0033-295X https://doi.org/10.1037/rev0000447
1310
... delay discounting was indexed in multiple ways including fitting a hyperbolic and an exponential function to the indifference points. The hyperbolic equation, and variants of this equation family, has been suggested as a conceptually more attractive way to describe delay discounting than the exponential function, though that is a discussion beyond the scope of this manuscript.[76][77][78] Because the appropriate summary measures for delay discounting is not settled science, the area under the indifference points (AUC) was calculated. ...
Genome‐wide association study of delay discounting in Heterogeneous Stock rats
Article
Full-text available
Delay discounting refers to the behavioral tendency to devalue rewards as a function of their delay in receipt. Heightened delay discounting has been associated with substance use disorders and multiple co‐occurring psychopathologies. Human and animal genetic studies have established that delay discounting is heritable, but only a few associated genes have been identified. We aimed to identify novel genetic loci associated with delay discounting through a genome‐wide association study (GWAS) using Heterogeneous Stock (HS) rats, a genetically diverse outbred population derived from eight inbred founder strains. We assessed delay discounting in 650 male and female HS rats using an adjusting amount procedure in which rats chose between smaller immediate sucrose rewards or a larger reward at various delays. Preference switch points were calculated and both exponential and hyperbolic functions were fitted to these indifference points. Area under the curve (AUC) and the discounting parameter k of both functions were used as delay discounting measures. GWAS for AUC, exponential k, and one indifference point identified significant loci on chromosomes 20 and 14. The gene Slc35f1, which encodes a member of the solute carrier family, was the sole gene within the chromosome 20 locus. That locus also contained an eQTL for Slc35f1, suggesting that heritable differences in the expression might be responsible for the association with behavior. Adgrl3, which encodes a latrophilin subfamily G‐protein coupled receptor, was the sole gene within the chromosome 14 locus. These findings implicate novel genes in delay discounting and highlight the need for further exploration.
View
... This finding may underlie the lack of amount-dependent discounting in many studies with nonhumans, as testing most often does not include the two delayed amounts in the same context (Grace et al., 2012; but see Holt & Wolf, 2019). Killeen's (2023) extension of the Additive Utility Theory (AUT; Killeen, 2009) offers an account of the magnitude effect. In Killeen's Equation 6, the rate constant λ is divided by the amount of the delayed outcome, which results directly in an amount effect, without parameter adjustment. ...
Recent Experience Affects Delay Discounting: Evidence across Temporal Framing, Signs, and Magnitudes
Article
  • Jul 2024
Delay discounting, the decrease in outcome value as a function of delay to receipt, is an extensive area of research. How delays are framed (i.e., temporal framing), as well as the sign and magnitude of an outcome, produce important effects on the degree to which outcomes are discounted. Here, we examined how recent experience (i.e., order of presentation) modifies these well-known findings. Experiment 1 examined the effects of temporal framing across gains and losses. Regardless of outcome sign, the order of task presentation affected the effect of temporal framing. In particular, when typical delay frames (e.g., 1 week) preceded delays framed as actual dates (e.g., February 15), discounting was less in the date-framed task. However, when dates were followed by the delay frame, there was no difference in the degree of discounting. The experience of date-framed delays persisted or carried over to the delay-framed task. Experiment 2 examined recent experience and the magnitude effect. In particular, 10and10 and 100 were discounted similarly between-subjects when it was the first task completed. However, once participants completed the second magnitude task, the magnitude effect was present both within-subjects and across subjects. Furthermore, 10wasdiscountedmoresteeplywhenitfollowed10 was discounted more steeply when it followed 100, and 100wasdiscountedlesssteeplywhenitfollowed100 was discounted less steeply when it followed 10. The impact of recent experience on delay discounting has important implications for understanding mechanisms that may contribute to delay discounting. Recent experience should be considered when designing delay discounting experiments as well as when implementing interventions to reduce steep delay discounting.
View
... Equation 7 has another family line in Killeen's (2009Killeen's ( , 2023b additive utility theory of delay discounting. In it, the disutility of the delay, (kd) s , is subtracted from the utility of the delayed amount a α , (rather than multiplying it, as in all of the above models), yielding Equation 8: ...
Hyperbolae
Article
  • May 2024
Hyperbolic relations between independent and dependent variables are ubiquitous in the experimental analysis of behavior, mentioned in over 150 articles in the Journal of the Experimental Analysis of Behavior . There are two principal forms of hyperbolae: The first describes the relation between response rate and reinforcement rate on variable‐interval schedules of reinforcement; it rises asymptotically toward a maximum. The second describes the relation between the current equivalent value of an incentive and its delay or (im)probability; it falls from a maximum toward an asymptote of 0. Where do these come from? What do their parameters mean? How are they related? This article answers the first two questions and addresses the last.
View
... How to cite this article: Killeen, P. R. (2023). From data through discount rates to the area under the curve. ...
From data through discount rates to the area under the curve
Article
Full-text available
  • Nov 2023
The rate of discounting future goods is a crucial factor in intertemporal trade‐offs, upon which depends not only individual well‐being but also that of our planet: How much privation now for a temperate future for our grandchildren? What is the best way to measure how the value of future goods decreases with its delay? The most accurate discount functions involve several covarying parameters, making interpretation equivocal. A universal and robust measure is the area under the discount curve, the AuC . The AuC of a hyperbolic discount function is a logarithmic function of the discount rate, k . The same integral also approximates the area under a hyperboloid function. A simple technique converts each datum into estimates of the discount rate, eliminating rogue data points in the process. These trimmed estimates are converted into areas and tested against data, where they succeed at predicting the AuC and its relation to log( k ).
View
View
Modular Maximization Theory: A Functional Account of Economic Behavior in Laboratory Animal Models, with Applications to Drug-Seeking Behavior
Preprint
Full-text available
  • Sep 2024
Substance abuse research depends on precise and sensitive assessments of reinforcer efficacy in animal models. However, conventional methods often lack theoretical rigor and specificity. To address these gaps, the Modular Maximization Theory (MMT) is introduced as a comprehensive framework for understanding instrumental behavior. Like earlier maximization theories, MMT posits that behavior is distributed across alternatives to maximize utility over time. This concept is structured through five foundational postulates that define alternatives (e.g., leisure and work) and choice rules as budget constraints and utility functions. A key innovation of MMT is its incorporation of reinforcer utilization—encompassing both consummatory and post-consummatory activities—into the budget-constraint function. A model of ratio-schedule performance is developed under the assumption that utilization is proportional to demand, with utility represented as an additive power function of reinforcer magnitude. This model, termed PURSPU (Proportional Utilization, Ratio Schedule, Power Utility), effectively explains how reinforcer magnitude, response effort, non-contingent reinforcement, and income influence demand curves, behavior-output functions, dose-response relationships, and progressive-ratio breakpoints, while accounting for rate-dependent effects. The PURSPU model is contrasted with two prominent alternatives: the Exponential Demand Equation and the Mathematical Principles of Reinforcement, highlighting key differences. The model also offers novel insights into choice behavior, including concurrent-schedule performance, income dependency, and delay discounting, as well as post-reinforcement pauses and run rates. Variations in budget constraints and utility functions are proposed as alternative models. Potential theoretical advancements, more targeted assessments of drug abuse liability, and the broader role of MMT in understanding human drug abuse are explored.
View
Individual differences in the discounting of combination outcomes in which immediate gains are followed by delayed losses
Article
  • Jun 2024
The vast majority of studies on discounting have focused on simple delayed outcomes, but most everyday decisions are more complicated. The present experiment focused on one such scenario, an iconic self‐control situation in which immediate gains are followed by delayed losses. The same participants were studied in all conditions to permit examination of individual differences in choice behavior using intercorrelations and factor analysis. Consistent with previous research, the hyperboloid model accurately described the form of the discounting function and discounting was not affected by the amount of the delayed loss when it was presented alone. However, replicating other studies, smaller delayed losses were discounted more steeply than larger ones when presented in combination with immediate gains. Exploratory factor analysis revealed two factors, one loading primarily on loss‐only conditions and the other loading primarily on conditions involving outcomes that combined gains and losses. These results imply that there are individual differences in how one combines gains and losses and that this characteristic of individual decision making might be an important predictor of decisions in the many everyday choice situations that involve complex outcomes.
View
Variations on a theme by Rachlin: Probability discounting
Article
Full-text available
  • Dec 2022
  • J EXP ANAL BEHAV
Rachlin and colleagues laid the groundwork for treating the discounting of probabilistic goods as a variant of the discounting of delayed goods. This approach was seminal for a large body of subsequent research. The present paper finds the original development problematic: In converting probability to delay, the authors incorrectly dropped trial duration. The subsumption of probability by delay is also empirically questionable, as those are different functions of variables such as magnitude of outcome and commodity versus money. A variant of Rachlin's theme treats human discounting studies as psychophysical matching experiments, in which one compound stimulus is adjusted to equal another. It is assumed that a function of amount (its utility) is multiplied by a function of probability (its weight). Conjoint measurement establishes the nature of these functions, yielding a logarithmic transform on amount, and a Prelec function on probability. This model provides a good and parsimonious account of probability discounting in diverse data sets. Variant representations of the data are explored. By inserting the probabilistically discounted utility into the additive utility theory of delay discounting, a general theory of probabilistic intertemporal choice is achieved.
View
Impulsive and Self-Control Choices in Opioid-Dependent Patients and Non-Drug-Using Control Participants: Drug and Monetary Rewards
Article
Full-text available
  • Aug 1997
Delay discounting was investigated in opioid-dependent and non-drug-using control participants. The latter participants were matched to the former on age, gender, education, and IQ. Participants in both groups chose between hypothetical monetary rewards available either immediately or after a delay. Delayed rewards were 1,000,andtheimmediate−rewardamountwasadjusteduntilchoicesreflectedindifference.Thisprocedurewasrepeatedateachof7delays(1weekto25years).Opioid−dependentparticipantsweregivenasecondseriesofchoicesbetweenimmediateanddelayedheroin,usingthesameprocedures(i.e.,theamountofdelayedheroinwasthatwhichcouldbepurchasedwith1, 000, and the immediate-reward amount was adjusted until choices reflected indifference. This procedure was repeated at each of 7 delays (1 week to 25 years). Opioid-dependent participants were given a second series of choices between immediate and delayed heroin, using the same procedures (i.e., the amount of delayed heroin was that which could be purchased with 1, 000). Opioid-dependent participants discounted delayed monetary rewards significantly more than did non-drug-using participants. Furthermore opioid-dependent participants discounted delayed heroin significantly more than delayed money.
View
Variations on a theme by Rachlin: Probability discounting
Article
Full-text available
  • Dec 2022
  • J EXP ANAL BEHAV
Rachlin and colleagues laid the groundwork for treating the discounting of probabilistic goods as a variant of the discounting of delayed goods. This approach was seminal for a large body of subsequent research. The present paper finds the original development problematic: In converting probability to delay, the authors incorrectly dropped trial duration. The subsumption of probability by delay is also empirically questionable, as those are different functions of variables such as magnitude of outcome and commodity versus money. A variant of Rachlin's theme treats human discounting studies as psychophysical matching experiments, in which one compound stimulus is adjusted to equal another. It is assumed that a function of amount (its utility) is multiplied by a function of probability (its weight). Conjoint measurement establishes the nature of these functions, yielding a logarithmic transform on amount, and a Prelec function on probability. This model provides a good and parsimonious account of probability discounting in diverse data sets. Variant representations of the data are explored. By inserting the probabilistically discounted utility into the additive utility theory of delay discounting, a general theory of probabilistic intertemporal choice is achieved.
View
Commodity Discounting: Obstacles and Solutions
Article
Full-text available
  • Sep 2022
Addictive behaviors involve patterns of impulsive choices. Discount functions are a useful means of describing the behavioral contingencies involved in those impulsive choices. Although monetary discounting tasks have proven useful, most impulsive behaviors of interest involve nonmonetary consequences. Objective: Developing effective commodity discounting tasks is critical for assessing how delay (and other variables) influences choice with respect to meaningful real-world commodities (e.g., high-calorie foods, alcohol, opioids, and other drugs). Method: Identifying the obstacles specific to nonmonetary commodity discounting and evaluating solutions to those obstacles. Results: Those obstacles include (1) real versus hypothetical commodities, (2) framing, (3) commodity indivisibility, (4) diminishing marginal utility, and (5) variations in economic context. Conclusions: Solutions are presented and evaluated for each of these five obstacles, including the following: (1) assessing relevant experiences and explicitly stipulating transportation and storage issues, (2) systematic analyses across various wordings and holding wording constant across commodities, (3) using an adjusting delay procedure with only whole commodities, (4) assessing value for different commodity amounts (without delay) and adopting quantitative models of discounting that include marginal utility, and (5) controlling for motivating operations, accounting for individual histories, and using closed economies. (PsycInfo Database Record (c) 2022 APA, all rights reserved).
View
Qualitative Variations in Delay Discounting: A Brief Review and Future Directions
Article
Full-text available
  • Jun 2022
  • BEHAV PROCESS
The discounting paradigm has been challenged by an increasing number of studies presenting qualitative variations in the individual discount function. Particularly, the subjective value of a loss does not necessarily systematically decrease with delay to the outcome. Qualitative variation refers to variations in shape rather than steepness of the discount function, such as positive discounting, zero discounting, unsystematic discounting, and negative discounting. Data from three previous studies were analysed in terms of qualitative variations observed in delay discounting patterns. Attention was also given to methods used and to the relationship between the results from the various levels of investigation. We found qualitative differences between discounting of monetary gains and losses on an individual level. While discounting of gains mainly took the form of conventional positive discounting, discounting of losses often took the form of zero discounting or unsystematic discounting. Further, there were more qualitative variations in discounting of both gains and losses among adolescents compared to adults. By examining verbal reports and single choices, we identified some of the rules and consequences involved in these delay discounting patterns. The different rules and consequences observed for the gain and loss scenarios, support that discounting of gains and losses may involve different combinations of reinforcing contingencies. These results point towards a possible way to explain the influences of qualitative variations in delay discounting.
View
View
Deprivation Has Inconsistent Effects on Delay Discounting: A Review
Article
Full-text available
  • Feb 2022
Delay discounting, the tendency for outcomes to be devalued as they are more temporally remote, has implications as a target for behavioral interventions. Because of these implications, it is important to understand how different states individuals may face, such as deprivation, influence the degree of delay discounting. Both dual systems models and state-trait views of delay discounting assume that deprivation may result in steeper delay discounting. Despite early inconsistencies and mixed results, researchers have sometimes asserted that deprivation increases delay discounting, with few qualifications. The aim of this review was to determine what empirical effect, if any, deprivation has on delay discounting. We considered many kinds of deprivation, such as deprivation from sleep, drugs, and food in humans and non-human animals. For 23 studies, we analyzed the effect of deprivation on delay discounting by computing effect sizes for the difference between delay discounting in a control, or baseline, condition and delay discounting in a deprived state. We discuss these 23 studies and other relevant studies found in our search in a narrative review. Overall, we found mixed effects of deprivation on delay discounting. The effect may depend on what type of deprivation participants faced. Effect sizes for deprivation types ranged from small for sleep deprivation (Hedge's g s between −0.21 and 0.07) to large for opiate deprivation (Hedge's g s between 0.42 and 1.72). We discuss possible reasons why the effect of deprivation on delay discounting may depend on deprivation type, including the use of imagined manipulations and deprivation intensity. The inconsistency in results across studies, even when comparing within the same type of deprivation, indicates that more experiments are needed to reach a consensus on the effects of deprivation on delay discounting. A basic understanding of how states affect delay discounting may inform translational efforts.
View
Promoting Farsighted Decisions Via Episodic Future Thinking: A Meta-Analysis
Article
Full-text available
  • Nov 2021
Episodic future thinking (EFT) denotes our capacity to imagine prospective events. It has been suggested to promote farsighted decisions that entail a trade-off between short-term versus long-term gains. Here, we meta-analyze the evidence for the impact of EFT on such intertemporal choices that have monetary or health-relevant consequences. Across 174 effect sizes from 48 articles, a three-level model yielded a medium-sized effect of g = .44, 95% (CI) [.33, .55]. Notably, this analysis included a substantial number of unpublished experiments, and the effect remained significant following further adjustments for remaining publication bias. We exploited the observed heterogeneity to determine critical core components that moderate the impact of EFT. Specifically, the effect was stronger when the imagined events were positive, more vivid, and related to the delayed choice. We further obtained evidence for the contribution of the episodicity and future-orientedness of EFT. These results indicate that the impact of EFT cannot simply be accounted for by other modes of prospection (e.g., semantic future thinking). Of note, EFT had a greater impact in samples characterized by choice impulsivity (e.g., in obesity), suggesting that EFT can ameliorate maladaptive decision making. It may accordingly constitute a beneficial intervention for individuals who tend to make myopic decisions. Our analyses moreover indicated that the effect is unlikely to merely reflect demand characteristics. This meta-analysis highlights the potential of EFT in promoting long-term goals, a finding that extends from the laboratory to real-life decisions. (PsycInfo Database Record (c) 2021 APA, all rights reserved).
View
Consumer choices with variations in item price, delay, and opportunity cost
Article
  • Nov 2022
Tversky and Kahneman (1981) told participants to imagine they were at a store about to purchase an item. They were asked if they would be willing to drive 20 min to another store to receive a 5discountontheitem′sprice.Mostparticipantswerewilling,butonlywhentheoriginalpriceoftheitemwassmall(5 discount on the item's price. Most participants were willing, but only when the original price of the item was small (15); when the original price was relatively large (125),mostsaidtheywouldnotdrive20minfora125), most said they would not drive 20 min for a 5 discount. We examined this framing effect in 296 participants, but instead used a psychophysical-adjustment procedure to obtain quantitative estimates of the discount required with different (a) item prices, (b) delays until the item's receipt, and (c) opportunity costs (in "driving" vs. "delivery" tasks). We systematically replicated Tversky and Kahneman's results, but also extended them by showing a substantial influence of opportunity costs on the consumer discounts required. A behavioral model of delay discounting-additive-utility theory-accounted for 97% of the variance in these consumer discounts.
View
View
Measures and modalities in restorative virtual natural environments: An integrative narrative review
Article
  • Sep 2021
  • COMPUT HUM BEHAV
Decades of research in environmental psychology have shown that contact with natural environments has restorative, stress-ameliorating effects. At present, researchers in the emerging field of virtual natural environments are studying whether these restorative health effects can be reproduced with simulated environments, raising new possibilities for preventive healthcare and therapy. This paper aims to synthesize earlier research on restoration and virtual nature, including theory, measurement, and modalities. Restoration theories were reviewed regarding their connection to measures and modalities, identifying possible research gaps in the current approaches. Furthermore, we performed a descriptive analysis of empirical studies utilizing virtual nature for restoration, exploring the commonalities and differences between the studies, emphasizing measured outcomes and modalities. Based on a thematic analysis of the theoretical and empirical review, we also introduce a new conceptual model named the Multidimensional Model of Restoration Measurement. This model connects different aspects of restoration measurement and theories. We conclude the review by discussing current measurement practices and envision multiple paths for future research.
View