Entropy as a Measure of Auditory Environment Diversity: An Ecological Momentary Assessment (EMA) Approach

Abstract

Objectives:

To determine validity and usefulness of entropy computed using ecological momentary assessment (EMA) data as a measure of auditory environment diversity.

Design:

We conducted two secondary analyses on existing EMA datasets. The first determined the construct validity of auditory environment entropy by examining the effect of COVID-19 on entropy. To demonstrate entropy’s usefulness, the second examined if entropy could predict benefit from hearing aid (HA) noise reduction features.

Results:

Consistent with the known effect of COVID-19 on social lifestyle, COVID-19 significantly reduced auditory environment diversity, supporting entropy’s construct validity. HA users with higher entropy reported poorer outcomes and perceived more benefit from HA features, supporting the feasibility of using entropy to predict communication performance and feature benefit.

Conclusions:

Entropy derived from EMA data is a valid and useful auditory environment diversity measure. This measure could allow researchers to better understand communication needs of people with hearing loss.

INTRODUCTION

It has been recognized that the characteristics of auditory environments could influence the communication performance of people with hearing loss (e.g., Demorest & Erdman 1989). One of these characteristics is the type, range, and diversity of auditory environments that an individual experiences in daily life. Terms used to describe this construct include auditory lifestyle (Gatehouse et al. 1999) and auditory reality (Noble 2008).

Individuals with more active lifestyles could experience a wider range of listening situations, which could place higher demands on listening and result in poorer communication performance. For example, Wu and Bentler (2012) used noise dosimeter sampling to quantify auditory lifestyle and found that individuals with smaller social networks were more likely to experience quieter environments that place lower demands on listening. Auditory lifestyle could also moderate hearing aid (HA) outcomes. For example, Gatehouse et al. (2006) used the Auditory Lifestyle and Demand Questionnaire (ALDQ) (Gatehouse et al. 1999) to assess auditory environments and found that HA users with more diverse auditory lifestyles (higher ALDQ scores) reported better outcomes with fast-acting compression relative to slow-acting compression. However, Cox et al. (2011) illustrated that preference for use of one versus two HAs could not be predicted from ALDQ scores despite that, theoretically, HA users with wider ranging listening environments would be expected to prefer bilateral fittings. More recently, Plyler et al. (2021) divided research participants into two lifestyle groups (high vs. low listening demand) based on HAs’ environment classification data. Although participants in the high demand group tended to prefer premium-level HAs over basic-level HAs (possibly due to the more advance noise reduction features), the real-world outcome differences between the two types of HAs were quite similar for both groups.

In addition to retrospective questionnaires (e.g., the ALDQ) and objective sensor data (e.g., dosimeter and HA datalogging), ecological momentary assessment (EMA) has been used to assess auditory lifestyle. EMA entails asking respondents to continually report their present or very recent experiences and related contexts as they go about their normal daily activities. EMA data can deliver an abundance of information from an individual’s life without biases imposed by the mistaken recollection of memories and delay in experience assessments that accompany retrospective self-reports. EMA can also provide detailed information (e.g., frequency of occurrence and range) of auditory environments. For example, Wu and Bentler (2012) asked research participants to answer a series of questions about the auditory environment (e.g., listening activity and location) using paper-and-pencil EMA journals. These researchers then reported the frequency of occurrence of 30 listening scenarios (e.g., small-group conversations at home) of younger and older participants. More recently, Smeds et al. (2020) used smartphone-based EMA to describe HA users’ auditory lifestyle using the Common Sound Scenarios framework (Wolters et al. 2016), which has 3 intention (e.g., speech communication) and 7 task (e.g., two-person conversation) categories. These researchers reported the frequency of occurrence of each category and the corresponding hearing difficulty and importance ratings.

Although EMA can provide rich information about the auditory environment, EMA often uses multiple survey questions to describe the environment. To date, there is no measure or index that integrates information from multiple EMA survey questions to quantify an individual’s auditory lifestyle. This index could facilitate data analysis and data visualization. This index also has the potential for clinical use to assess a patient’s communication needs if EMA could be implemented in clinical settings.

Auditory environment entropy

In the present paper we propose using entropy, which is derived from EMA self-reports, to quantify the diversity of auditory environments. Entropy was selected because it measures the diversity of a system by quantifying its predictability. For listeners who encounter many different listening situations, their auditory environments would be less predictable and the entropy values would be higher. For listeners who always experience the same listening situations, their environments would be more predictable and the entropy values would be lower. We termed this measure auditory environment entropy.

Below we use the EMA dataset from Dunn et al. (2021) to illustrate how we computed auditory environment entropy. The left column of Table 1 shows the 11 EMA questions used in Dunn et al. (2021). The 11 questions have a total of 47 response options. To calculate entropy, we use a network approach (Li et al. 2015). We first treat the 47 response options of the 11 EMA questions as the nodes of a network. We then establish links between nodes. Specifically, when two responses are selected together in a survey (e.g., Location=LC1 and Signal Type=ST1, see Table 1), a link between these two responses is created. Because 11 questions are used to establish the network, a single survey could generate up to 55 undirected links (55=10+9+8+…+1). We repeat this procedure on the EMA surveys completed by a given respondent and determine the number of links between nodes to create a network. See Figure 1 for the example. In the figure the size of the node and thickness of the line reflects how often a response is selected and how often two responses are selected together in a survey, respectively. Note that in the network a link between two nodes is independent of how these two nodes connect to other nodes. For example, two sets of survey responses {LC1, ST1, SA1} and {LC1, ST1, SA5} would generate the same LC1-ST1 link twice. Also note that a node is not expected to be able to connect to all other nodes in the network. For example, nodes belonging to the same survey question cannot connect to each other because all questions were single-select questions.

Table 1.

EMA survey questions and response options used to compute auditory environment entropy. Square brackets show the question topic/category.

Dunn et al. (2021) #	Wu et al. (2019) and Wu et al. (2020)
[Location] Where were you?	[Activity] What were you listening to?
LC1: Indoors at home	AC1: Conversation, 3 or fewer
LC2: Indoors other than home	AC2: Conversation, 4 or more
LC3: Car	AC3: Speech listening, live
LC4: Outdoors	AC4: Speech listening, media
[Signal Type] What kind of sounds were you listening to?	AC5: Conversation, phone
	AC6: Non-speech sound listening
ST1: Speech	AC7: Not actively listening
ST2: Music	[Location] Where were you?
ST3: Other sounds or more than one sound	LCN1: Outdoor, moving traffic
[Speech Activity] What kind of speech listening activity were you engaged in?	LCN2: Outdoor, other than traffic
	LCN3: Home, 10 or fewer
SA1: Live conv. with one person	LCN4: Other than home, 10 or fewer
SA2: Live conv. with more than one	LCN5: Crowd of people, 11 or more
SA3: Conv. on electronic device	[Talker Familiarity] Were you familiar with the talker(s)?
SA4: Speech listening, live
SA5: Speech listening on electronic device (TV, radio, etc.)	TF1: Unfamiliar
	TF2: Somewhat unfamiliar
[Visual Cues] Could you see the talker’s face?	TF3: Somewhat familiar
VC1: No	TF4: Familiar
VC2: Yes, but only sometimes	[Visual Cues] Could you see the talker’s face?
VC3: Almost always	VC1: No
[Talker Familiarity] Were you familiar with the talker(s)?	VC2: Yes, but only sometimes
	VC3: Almost always
TF1: Unfamiliar	[Talker Location] Where was the talker most of the time?
TF2: Somewhat unfamiliar
TF3: Somewhat familiar	TL1: Front
TF4: Familiar	TL2: Side
[Talker Characteristics] Who were you listening to?	TL3: Back
	[Noisiness] On average, how noisy was it during the listening event?
TC1: Male adult
TC2: Female adult	NZS1: Quiet
TC3: Kid	NZS2: Somewhat noisy
TC4: Other or more than one	NZS3: Noisy
[Signal Distance] How far away was the sound you were trying to listen to?	NZS4: Very noisy
	[Noise Location] Where was the noise most of the time?
SD1: No distance (e.g., streaming)
SD2: 3 feet or less	NLN1: Front
SD3: 4 to 10 feet	NLN2: Side
SD4: More than 10 feet	NLN3: Back
[Signal Location] Where was the sound you were trying to listen to? (relative to your head)	NLN4: All around
	[Reverberation] (a variable derived from the Location question and two survey questions about carpeting and room size*)
SL1: In front
SL2: In back	RV1: High
SL3: To the right	RV2: Low
SL4: To the left
SL5: All around
[Noise Type] What were the environmental or background sounds?
NT1: Other talkers
NT2: Music
NT3: Noise (cars, wind, fans, dishes)
NT4: No environmental sounds
NT5: Other or more than one sound
[Noisiness] Overall, how loud were the background/ environmental sounds?
NZ1: Very loud
NZ2: Loud
NZ3: Medium
NZ4: Soft
NZ5: Very soft
[Noise Location] Where were the background sounds?
NL1: In front
NL2: In back
NL3: To the right
NL4: To the left
NL5: All around

^#: The original multi-select questions used in Dunn et al. (2021) were re-coded to become single-select questions. For example, the original Signal Type question used in Dunn et al. was a multi-select question (i.e., “select all that apply”) and had three response options: Speech, Music, and Other. In the present paper, a new response “Other sounds or more than one sound” (ST3 in the table) was created to include the situations that participants selected Other or selected more than one response in the original survey.

^*: The Reverberation question was derived using the Location question and two questions about carpeting (“Was there carpeting?”, yes/no) and room size (“Compared to an average living room, how large was the room?”, smaller/about average/larger) in the original survey. Outdoor locations and indoor locations that were carpeted and were equal in size or smaller than an average living room were coded as low reverberation. The remaining indoor locations were coded as high reverberation.

Figure 1.

Networks that represent the auditory environment of two participants with high (1A) and low (1B) auditory environment entropy. Nodes represent the response options of EMA surveys. See Table 1 for the labels of response options. Size of the node and thickness of the line reflects how often a response is selected and how often two responses are selected together in a survey, respectively. Nodes with the same color belong to the same survey question.

Next, we calculate Shannon entropy (Shannon 1948) of a given node i by

$$H(i)=-{\sum }_{j=1}^n{p}_{ij}\text{log}(p_{ij}),$$ (1)

where n is the total number of nodes included in the network, p_ij is the proportion of the links between nodes i and j to the total links that involve node i. Based on the work by Li et al. (2015), we define auditory environment entropy H as the sum of the entropy values of all nodes included in the network normalized by the logarithm of the number of EMA surveys used to calculate entropy (k), namely

$$H=\frac{{\sum }_{i=1}^{n}H(i)}{\text{log}\left(k\right)}=\frac{-{\sum }_{i=1}^n{\sum }_{j=1}^n{p}_{ij}\text{log}(p_{ij})}{\text{log}\left(k\right)}.$$ (2)

Entropy is normalized by log(k) because more EMA surveys completed provide more opportunities for connections between nodes and therefore are more likely to yield higher diversity (higher entropy).

It should be noted that there are other ways to compute entropy. For example, we could code each combination of potential response options as a unique situation (e.g., LC3+ST1+SA5+…+NL5). We could then use the probability of each unique situation to compute Shannon entropy. We chose to use the network approach because it provides a great way to visualize the EMA data. For example, Figure 1 shows networks from two individuals who have high and low entropy, respectively.

Although the number of EMA surveys completed is controlled for in the entropy calculation by standardizing by log(k), there is another theoretical consideration regarding the number of surveys an individual responds to. Specifically, the entropy calculation is based upon the links between nodes (i.e., survey responses). Between two survey questions, the minimum number of EMA surveys required to generate all possible links that connect the response options would be the multiplication of the number of response options of each question (e.g., Location and Signal Type, 4×3=12, see Table 1). Therefore, if the number of EMA surveys used to compute entropy is fewer than the maximum number of possible connections between the responses of any two questions in the survey, there is always a possibility that the entropy is underestimated. To prevent this issue, we would exclude respondents who complete fewer than the largest number of possible connections between two questions’ responses from analysis.

Objective of the present paper

The purpose of the present paper is to examine the validity and usefulness of auditory environment entropy. To achieve this goal, we conducted two secondary analyses on existing EMA datasets. In the first analysis, we took advantage of a natural experiment—the COVID-19 pandemic, whose lockdowns and social distancing substantially changed people’s lifestyles—to validate entropy as a measure of auditory environment diversity. To examine the usefulness of entropy, in the second analysis we investigated if entropy could be used to predict the benefit from HA noise reduction features.

ANALYSIS 1: CONSTRUCT VALIDITY OF ENTROPY

The purpose of this analysis was to determine the construct validity—the degree to which a measurement reflects what it is intended to measure—of entropy as a measure of auditory environment diversity. A result showing that COVID-19 social distancing, which has a known effect on reducing social interactions, could decrease auditory environment entropy would support the construct validity of this measure.

Methods

The dataset from Dunn et al. (2021) was used. The purpose of Dunn et al. was to examine the effect of COVID-19 social distancing on auditory environment, communication functions, and psychosocial well-being for 48 adult cochlear implant (CI) users. Data from EMA and retrospective questionnaires (including the ALDQ) were collected in two conditions: Pre-COVID (8/17/2018 to 2/1/2020) and During-COVID (4/20/2020 to 5/8/2020). Time between the pre- and during-COVID conditions ranged between 2 and 20 months (mean=10.2, SD=4.18). EMA results showed that the CI users were more likely to engage in media listening (e.g., TV) while staying at home During-COVID compared to Pre-COVID. Additionally, participants spent less time listening actively and participating in group conversations During-COVID. The ALDQ scores revealed less diverse listening experiences During-COVID. See Dunn et al. for detailed information.

In Dunn et al. (2021), EMA data were collected using a smartphone application for 7 days in each condition. The entire survey consisted of 32 questions. Among them, 11 questions relevant to auditory environment were used in the present study (Table 1). The method described previously was used to compute entropy. Because the largest number of possible connections between two questions’ responses is 25 (Signal Location and Noise Location, 5×5=25, see Table 1), we excluded participants who completed fewer than 25 surveys from analysis.

To compare the auditory lifestyle quantified using entropy and retrospective questionnaires, we included the ALDQ in the analysis. The ALDQ lists 24 different listening scenarios and asks the respondents to rate how often and how important the scenarios are in their daily lives using a three-point scale. The ALDQ generates two scores and the score that indicates the frequency in which a respondent encountered different scenarios was used in the present study. Higher scores represent a wider range set of auditory environments.

Results

After excluding 18 participants who completed fewer than 25 surveys in either COVID condition, a total of 2190 EMA surveys (self-initiated and prompted surveys combined) from 30 participants were analyzed (age: mean=61.5 years, SD=12.4). On average each participant completed 34.6 surveys (SD=11.2) and 38.4 surveys (SD=14.7) in the Pre- and During-COVID conditions, respectively. The number of EMA surveys responded to did not significantly differ between the Pre-and During-COVID conditions (t=−1.32, p=.197). Entropy was not significantly correlated with the number of surveys completed (Pre-COVID: r=−.018, p=.927; During-COVID: r=−.10, p=.589). Entropy ranged from 12.24 to 35.89.

To compare the mean entropy of the two COVID conditions (Figure 2), we conducted a paired t-test. The result indicated that Pre-COVID entropy (mean=28.59, SD=4.37) was significantly higher than During-COVID entropy (mean=25.87, SD=4.27) (t=4.03, p<.001, Cohen’s d=.74). Among the 30 participants, 28 had ALDQ data. A paired t-test indicated that the ALDQ scores in the Pre-COVID (mean=24.7, SD=6.6) and During-COVID (mean=23.1, SD=5.6) conditions did not significantly differ (t=2.02, p=.054, Cohen’s d=.38). Entropy and ALDQ scores were moderately correlated (Pre-COVID: r=.59, p=.001; During-COVID: r=.49, p=.009).

Figure 2.

Boxplots of auditory environment entropy as a function of COVID condition. Boundaries of the boxes represent the 25th and 75th percentile and error bars indicate the 10th and 90th percentiles. Circles represent individual data points.

ANALYSIS 2: USEFULNESS OF ENTROPY

The purpose of this analysis was to demonstrate the usefulness of auditory environment entropy. It has been suggested that HA users with more active lifestyles would experience more diverse acoustic environments and therefore would have higher listening demands and could perceive more benefit from HA features (e.g., Plyler et al. 2021). A result supporting this speculation would indicate that entropy could predict communication need and HA outcomes, demonstrating its usefulness.

Methods

The EMA data from Wu et al. (2019) and Wu et al. (2020) were used. Both studies were parts of a larger study. Wu et al. (2019) investigated real-world effectiveness of premium-level noise reduction features (directional microphones and digital noise reduction algorithms) relative to basic-level features. Fifty-four older HA users completed a cross-over trial. The trial consisted of four HA conditions, which were factorial combinations of HA model (premium vs. basic) and feature status (on vs. off). The purpose of Wu et al. (2020) was to examine the test-retest reliability of EMA. To this end, all participants but three from Wu et al. (2019) repeated one of the four HA conditions (randomly selected) after they completed the cross-over trial. In each condition, EMA data were collected using a smartphone application for 7 days. See Wu et al. (2019 & 2020) for detailed information. The results of Wu et al. (2019) indicate that participants were more satisfied when noise reduction features were turned on compared to when they were turned off. However, there was no evidence to support the benefit of premium HAs and features over basic HAs and features, respectively. Therefore, in the present study we combined the data from premium and basic HAs to create two conditions: Feature-On and Feature-Off.

The right column of Table 1 shows the 8 EMA questions, which had a total of 32 response options, used to compute Entropy. Because the initial analysis indicated that the mean entropy of the Feature-On and -Off conditions did not significantly differ (t=.93, p=.356), the EMA data of the two conditions were combined to calculate the participant’s auditory environment entropy across the entire field trial. Participants who completed fewer than 35 surveys were eliminated as the maximum number of possible connections between two questions’ responses was 35 (i.e., Activity and Location, 7×5=35, see Table 1).

To serve as dependent variables, five EMA questions about HA outcomes used by Wu et al. (2019 & 2020) were used: Speech Understanding (“How much speech did you understand?”), Listening Effort (“How much effort was required to listen effectively?”), Loudness Satisfaction (“Were you satisfied with the loudness?”), HA Satisfaction (“Were you satisfied with your hearing aids?”), and Participation Restriction (“How much have your hearing difficulties affected what you wanted to do?”). Participants used a visual analog scale with a sliding bar to indicate experience on the smartphone. The outcome score ranged from 0 to 100. For all outcomes except for Listening Effort and Participation Restriction, higher scores represent better outcomes.

Results

One participant who completed 29 surveys was eliminated. The remaining 53 participants (age: mean=73.6 years, SD=6.8) completed a total of 9368 surveys (self-initiated and prompted surveys combined). On average each participant completed 176.2 surveys (Feature-On: mean=88.0, SD=39.0; Feature-Off: mean=88.2, SD=38.0). Entropy was negatively correlated with the number of EMA surveys completed (r=−.29, p=.037). Entropy ranged from 11.71 to 17.65, with a median of 14.97.

To determine how entropy could impact HA outcomes and moderate the outcome difference between Feature-On and Feature-Off conditions, we conducted analyses using linear mixed models. To facilitate data interpretation, the participants were median split into two entropy groups (High vs. Low) based on their entropy. The dependent variables of the model are HA outcome variables (e.g., Speech Understanding). The models included a random intercept for subject to account for the repeated observations per participant, with fixed effects being HA condition (Feature-On vs. Feature-Off; within-subject factor), entropy group (High vs. Low; between-subject factor), and their interaction. We conducted separate analyses for each outcome variable.

The results indicated that, for all outcome variables, the interaction was significant (all p<.001), suggesting that the outcome difference between Feature-On and -Off conditions depended on entropy group. Because our primary research question was on the pair-wise comparisons, we examined those directly. Figure 3 shows the results. In the figure the scores for Listening Effort and Participation Restriction have been reversed so that higher scores represent better outcomes. The results indicated that the high entropy group reported poorer outcomes than the low entropy group in the Feature-Off condition (indicated by wide brackets in Figure 3; p=.049 to .007), while the outcome difference between the two entropy groups diminished in the Feature-On condition (all outcome variables except for Participation Restriction). Furthermore, the Feature-On condition had significantly better outcomes than the Feature-Off condition for the high entropy group (indicated by narrow brackets in Figure 3; all p<.001), while outcomes did not significantly differ between the Feature-On and -Off conditions for the low entropy group (all outcome variables expect for HA satisfaction). Note that to ensure figure readability Figure 3 does not show the significant differences that are not the focus of the analysis (i.e., Low-On vs. High-Off). Detailed statistical results are available in the tables in Supplemental Digital Content.

Figure 3.

Model estimated mean outcome scores are displayed for the combination of feature condition (Off vs. On) with entropy group (Low vs. High). The scores for Listening Effort and Participation Restriction have been reversed so that higher scores represent better outcomes. Brackets represent significant differences (p<.05). The significant differences that are not the focus of the study (e.g., Low-On vs. High-Off) are not shown in the figure. Error bars = 1 SE.

DISCUSSION

In the present paper, we propose using entropy computed from EMA self-reports to quantify the diversity of auditory environments. We re-analyzed data from two EMA datasets to validate this new measure and to demonstrate its usefulness. The first analysis shows that social distancing due to COVID-19 significantly reduced CI users’ auditory environment entropy. Because this result is consistent with the known effect of COVID-19 on social interaction, the construct validity of entropy is supported. This is also consistent with Dunn et al. (2021) which shows that During-COVID CI users had fewer social interactions and spent more time at home and in quiet environments compared with Pre-COVID. Note that although the ALDQ scores did not significantly differ across the two COVID conditions in the present paper (n=28), with the ALDQ data from 45 participants Dunn et al. found that the Pre-COVID ALDQ score was significantly higher (more diverse) than the During-COVID score. This may indicate that the retrospective questionnaire ALDQ requires a larger sample size to detect auditory lifestyle change.

In the second analysis, we demonstrated that the high entropy group tended to report poorer HA outcomes than the low entropy group and that HA noise reduction features could help eliminate the outcome difference between the two entropy groups. This is consistent with Wu and Bentler (2012) and indicates that more diverse auditory environments could place higher demands on listening and result in poorer communication performance. The results also showed that the high entropy group perceived benefit from HA features, while the low entropy group did not. This is consistent with Wu (2010), which shows that older HA users—who tend to have fewer social interactions—perceive less benefit from directional microphone features. Because the analysis result suggests that auditory environment entropy could predict communication performance and HA feature benefit, the usefulness of entropy as a measure of environment diversity is supported. The result also supports the best-practice guidance that clinicians should consider a person’s communication needs and auditory environments when selecting and configuring HA features.

Although auditory environment entropy computed from EMA data has advantages such as low memory bias, it has limitations. First, the absolute value of entropy is not meaningful because it depends on the design of EMA survey. As a result, auditory environment entropy of different studies cannot be directly compared. Further, it would be difficult to determine if a difference in entropy values (e.g., Pre- vs. During-COVID) is clinically relevant or not. Second, entropy is affected by the number of EMA surveys completed. When a respondent only completes a small number of surveys, the EMA data will never demonstrate highly diverse auditory environments, resulting in an underestimation of entropy. Although we have tried to take the number of surveys into account (Equation 2), the issue may remain. For example, in the second analysis entropy was negatively correlated with the number of surveys completed (r=−.29, p=.037), suggesting that Equation 2 may over-correct the effect of survey number when the number of surveys is small. To address this issue, reducing the number of survey questions or response options used in entropy calculation (i.e., reducing the size of the network) could be helpful. This is because a smaller network is inherently less diverse and therefore does not require lots of surveys to generate high entropy relative to its maximum possible entropy. Also, a fully Bayesian approach may provide a better solution than what is described in Equation 2. In the Bayesian approach, the number of surveys taken by each participant would be treated as a random variable to be estimated and the variability in number of EMA surveys would be directly estimated within the model. Finally, what we reported in the present paper should be viewed as preliminary because methodological factors that could impact entropy (e.g., duration and timing of EMA data collection and how to treat self-initiated vs. prompted surveys) have not been fully investigated. More research is warranted to optimize EMA study design from the perspective of auditory environment entropy.

CONCLUSIONS

The present paper suggests that entropy derived from EMA data is a valid and useful measure of auditory environment diversity. This measure, along with respective questionnaires and objective data collected by sensors, would allow researchers, and perhaps clinicians, to better understand the communication needs of people with hearing loss.