The feeling of comfort in residential settings II: a quantitative model

3.1 Modelling the immediate satisfaction with the room

The ‘immediate satisfaction with the occupied space’ can be defined as the outcome that occurs when people cognitively assign meaning to different aspects of a room, which is aggregated into a single state of satisfaction with the here and now. The factors that determine this satisfaction are all the perceptions and trade-offs. This includes all the commonly studied perceptions (e.g. glare and thermal sensation) and those less-commonly studied ones (e.g. the perception of bothering others, feeling of confinement). The immediate satisfaction with the occupied space is represented by the function $s(\overrightarrow{m})$, where $\overrightarrow{m}$ is the list containing the perceptions and the factors outside of the realm of building science that are relevant for people’s wellbeing (e.g. safety concerns, utility bills). Within the occupied space of a dwelling, people will change the indoor environment to try to improve their immediate satisfaction, e.g. make a room warmer or cooler.

Because $s(\overrightarrow{m})$ is different for everyone, this is the function that introduces most of the subjectivity to the model. The identification of this function requires careful consideration. A plausible way for doing so is to replicate the methods used by other comfort studies (Schweiker et al. 2020a), i.e. to correlate people’s self-reported perceptions and satisfaction. It should be noted that gathering all individuals in the same group—thus ignoring all their internal elements—is not advised. The recommendation is to group individuals who—due to their non-physical personal factors—are expected to share similar satisfaction functions (e.g. people whose household composition is similar). This would lead to a set of more precise and customised equations representing the ‘immediate satisfaction with the occupied space, $s(\overrightarrow{m})$’ for different individuals. Unfortunately, this process will lead to functions that are representative of an average individual within a larger population (O’Brien et al. 2017), meaning that using it for designing homes does not guarantee the satisfaction of every single person (ASHRAE 1999; de Dear & Brager 2002). Despite this, it would be expected that the increased customisation will lead to the satisfaction of a larger portion of the population.

The elements in vector $\overrightarrow{m}$ can be estimated based on the set of quantifiable elements of the physical world $\overrightarrow{q}$. (Note that, for simplicity, environmental cues—often impossible to quantify—are assumed to be irrelevant. Future research might help overcome this limitation.) $\overrightarrow{q}$ not only contains variables that can be sensed by organs in the human body—such as temperature and illuminance—but also other variables, such as the amount of clothing and the monetary cost of energy.

3.2 Perceptions and trade-offs

The commonly and less-commonly studied perceptions of the here and now—allocated in a vector $\overrightarrow{m}$—can be mathematically represented as has been done traditionally in building science. They can then be put together in a function $s(\overrightarrow{m})$ that represents the immediate satisfaction with the environment, as done in multi-domain comfort studies (Buratti et al. 2018; Franzitta et al. 2014; Ricciardi & Buratti 2018).

Since the function $s(\overrightarrow{m})$ includes all the relevant perceptions, it will automatically also account for trade-offs that relate to different domains of comfort. For instance, since the vector $\overrightarrow{m}$ already includes the perceptions of glare and thermal sensation, any software that can simultaneously model the lighting and thermal domains will account for the trade-offs between them. However, the feeling of comfort model is emphatic in that the comfort of people at home is not constrained to factors associated with indoor environmental quality. Consequently, it becomes relevant also to include in this vector $\overrightarrow{m}$ the other elements that people use to assess how comfortable a space is, even if these are not within the traditional scope of comfort research. For instance, it becomes necessary to account for the fact that (sometimes, in some socio-economic and cultural contexts) wearing too many layers of clothing might be considered a nuisance. This nuisance can probably be estimated by means of the ‘clo’ value, often used for representing the insulation value of clothing. While further research is required to account for these perceptions, nothing suggests that doing so is impossible.

3.3 Expected outcomes

As mentioned above, people care not only about their present comfort but also about their future comfort. In this regard, people often mentioned that the ideal dwelling might be ideally comfortable everywhere and all the time, but as that was likely impossible in a home, they would make choices that affect their comfort based on the chances of change by a certain time. For example:

The immediate satisfaction with the dwelling (σ) can be calculated as the average of the immediate satisfaction with each space of the dwelling (s_r) weighted by the relevance of such a space at a certain time (p_r). This is represented in equation (1):

Variable p_r is not necessarily the same as the probability of visiting a certain space. This happens because of two reasons. First, because people care about themselves and also about other people (e.g. other members of their families), in which case, people’s comfort will be determined by the conditions of more than one space at a certain time. Second, if a person is likely to use two spaces at a certain time (e.g. situations in which a person is constantly moving from one space to another, and back), both spaces will be equally as important at the same time. A potentially good starting point for defining this importance is the fraction of the total occupancy defined in a room’s occupancy schedule (a value that often must be defined in building simulation). For instance, if there is no one in the house, then all spaces have an importance of 0; if everyone is in the same room, then that space gets an importance of 1 while all others get 0; and if half the household is in one room and the other half in another, then both spaces get 0.5 while the rest of the spaces get 0.

Equation (1) accounts for the comfort of the person considering the whole dwelling, but it is incapable of accounting for what inhabitants think the state of the dwelling will be later. This model, however, posits that people are rather good at predicting the future in their own dwellings and thus that it is possible to approximate what they think will happen by what building simulation estimates will happen. In other words—through building simulation—it is possible to account for people’s expected outcomes. This assumption is supported by two main sources. First, the fact that respondents very accurately described how different rooms of their homes performed at different times of the day. And second, on a strong theoretical and empirical foundation. Examples of people’s responses are:

Further, the theoretical foundation for this assumption is supported within the psychology literature. Research by Kahneman (2003) and others has proposed the coexistence of two human reasoning systems. The first system—‘System 1’—is mostly automatic, largely unconscious, and requires low cognitive effort; while the second system—‘System 2’—relates to the analytic intelligence that has most traditionally been studied (Kahneman 2003; Stanovich & West 2000). Systems 1 and 2 are also called intuition and reasoning (Kahneman 2003). This article will use these terms.

Kahneman (2003) points out that intuitive judgements do not always accurately represent measured ‘reality’. These judgments are often emotionally charged and governed by habits and are thus difficult to control and modify. Even worse, people do not know which cues they are using to build these judgments, and subjective confidence is not a reliable indicator of their validity (Kahneman & Klein 2009). Nevertheless, intuition is not necessarily always wrong (Bago & De Neys 2018). On the contrary, people’s intuition can be trusted when trained through prolonged practice and feedback in so-called ‘high-validity environments’ (Kahneman & Klein 2009). These are environments in which there is a stable relationship between objectively identifiable cues and subsequent events. When exposed to these systems, individuals can learn their governing rules.

Based on Kahneman & Klein’s (2009) description, the built environment is a high validity one because its behaviour and causal relationships respond to the highly stable laws of physics. As inhabitants spend a long time within buildings, they are likely to have a highly trained intuition about how the conditions of their homes change. This intuition about the dynamic future-looking behaviour of their home is not accounted for in traditional building science models. Nevertheless, Schweiker et al. (2020b) revealed that people’s thermal expectations are fulfilled most of the time, suggesting that people read environmental cues and make relatively accurate inferences about them. (This does not imply that people know how or why something happens, even if they are sure that they do (Crandall & Hoffman 2013).

After understanding how to estimate what are people’s expected outcomes—i.e. what they think will happen—it is possible to use equation (2) to represent the feeling of comfort κ at time t. Such an equation suggests that the satisfaction σ that people think they will experience in τ units of time in the future has an impact φ on their present feeling of comfort.

But people are not likely to look too far into the future and not all future situations will be regarded as equally important. For instance, people are not expected to worry about how comfortable their home will be in seven days’ time. They certainly care, however, about their comfort right now and, very likely, about how comfortable they will be in 30 minutes’ time. Based on this logic, it is expected that people consider the present to be more important than the near future, and the near future to be more important than the distant future. The impact of people’s future satisfaction with their dwellings is expected to be the highest at the present and lower over time. In other words, φ is expected to be a monotonically decreasing function. In practice, any function can be used for representing the impact of future perceptions on the current feeling of comfort. There is scope for further research to accurately determine the function which better represents people’s intuitive judgements.

3.3.1 Agency and bounded rationality

Equation (2) considers only one future and thus assumes that people cannot imagine multiple futures, corresponding to different potential behavioural choices. However, in practice, people can use their inferences about what will happen to choose between different alternative futures (e.g. windows open, lights on, both or none). Which of these alternative futures will be the one affecting people’s current feeling of comfort? Most likely, the relevant scenario will be the most comfortable one that people consider is within their control, whilst simultaneously considering trade-offs (Κ_best (t)). The reason to choose this one is that all other scenarios are easily avoidable (e.g. people who have a functional heater in their homes do not worry about the possibility of them not turning the heater on). Note that Κ_best is not necessarily an optimal scenario (as explained below), and that people will not always engage in behaviour to achieve this scenario (see Section 3.5).

Finding the optimum Κ(t) (i.e. the unique scenario that maximises people’s comfort) is very challenging because the number of possible futures to choose from increases non-linearly with the number of spaces in the dwelling, with the number of systems in each of them that can be operated, and with the opportunities for adaptations. The number of potential futures becomes unmanageably large for common situations, thus finding the optimum Κ(t) would imply solving a highly complex mathematical problem. However, people are not expected to solve this optimisation problem during their everyday lives. On the contrary, people have bounded rationality (March 1978; Simon 1955; Thaler & Sunstein 2009), meaning that they are more likely to aim for a satisfying result (using heuristics) than to pursue the best possible scenario (e.g. Leaman & Bordass 2000). Incorporating these heuristics not only alleviates the computational intensity of the problem but is also a more realistic representation of people’s behaviour. While further research is required to document how people select Κ_best, this study introduces one possible way of representing this selection process in order to explore how this aspect of the model can be incorporated into performance simulation processes.

If the function $s(\overrightarrow{m})$ was linear in the parameters (an easy to satisfy constrain), then it could be written as shown in equation (3):

3

$s(t)={\displaystyle \sum }_i{x}_i{m}_{ri}(t)$

From the combination of equations (1) to (3), equation (4) can then be derived:

4

$\kappa (t)=\frac{{{\displaystyle \sum }}_{rooms}{{\displaystyle \sum }}_i{{\displaystyle \int }}_0^{\infty }\hspace{0.17em}\phi \frac{p_r x_i m_{ri}}{{{\displaystyle \sum }}_{rooms}\hspace{0.17em}{p}_r}d\tau }{{{\displaystyle \int }}_0^{\infty }\hspace{0.17em}\phi \hspace{0.17em}d\tau }$

The significance of equation (4) is that its double sum can be represented as a table whose elements, when added, correspond to people’s current feeling of comfort. Moreover, the columns of this table represent a space within the dwelling and the rows represent the different elements in vector $\overrightarrow{m}$. This table allows for the identification of the element that is causing discomfort and its location. This allows identifying elements and locations that are, most likely, good candidates to improve people’s comfort. Thus, the number of potential futures that need to be simulated to (heuristically) find Κ_best(t) are reduced from hundreds to a handful. This is represented in Figure 2.

Figure 2

3.4 Modelling attention

As explained above, the feeling of comfort only develops when a certain situation captures a person’s attention. This is an important element in the feeling of comfort model because if there is no attention, the situation will go unnoticed.

While Molina et al. (2023) provided a more sophisticated account of attention, for simplicity, the model of attention introduced here assumes that the probability of a situation capturing a person’s attention (α) is a function of how busy the person is (β) and how satisfied that individual is with the space (s). A more sophisticated model of attention—informed by further research focusing on how and why people attend to situations—can potentially be accommodated in a future version of the model. The reason to keep busyness β as a factor is that it seems to have a relatively clear and simple relationship with attention: the busier a person is, the less likely they are to attend to a situation.

The rationale for using s as opposed to the feeling of comfort (κ or Κ) is that if the situation does not capture the individual’s attention, no cognitive processes will be triggered and thus no inferences about the future will be built. With these insights, equation (5) is proposed as a candidate for representing the probability of a person attending to a situation.

Equation (5) is designed by algebraically rearranging a logit model, one of the most widely used models for representing probabilities of binary phenomena (Train 2012: 34). The modification has the purpose of giving a specific meaning to the parameter β: the subjective dissatisfaction at which it is nearly certain that the person will attend to the situation. In other words, evaluating equation (5) with β = –s leads to a probability of attention of nearly 1.0. The word ‘nearly’ is emphasised because logit models never reach a probability of 1.0, and thus it is necessary to introduce the parameter ɛ. This parameter represents a value that the modeller considers small enough so that 1–ɛ can be considered certainty; that is, nearly 1.0.

3.5 Modelling behaviour

Although this paper does not directly address behaviour (because its focus is cognition and its effect on people’s comfort, not behaviour), people’s comfort is very much related to their actions. Thus, a simple function (equation 6) is introduced to represent the probability of people engaging in adaptive behaviour. This particular equation was designed to enable the simulations to be presented in section 4 below. It was not informed by state-of-the-art models of behaviour due to the scope of this research. Producing a more realistic representation of why and when people engage in adaptive behaviour is considered future research.

This function depends on the estimated increase in comfort that taking action would result in (ΔΚ) and on people’s Indifference (π). Indifference is an instrumental parameter representing how little a person is interested in fixing their discomfort. (For instance, Haigh (1981) noticed that people are not always very responsive at adjusting their clothing.) A value of π = 0 implies that the individual will always behave if there is any benefit. A value of π = 0 is the de facto assumption of conventional building science models, as they presume that if the light level falls below a set point, the lights will always be turned on, or if a temperature rises above a target level, then cooling actions will be taken. As with equation (5), equation (6) is designed as a logit model rearranged so that Indifference parameter π has a specific meaning: the potential increase in comfort that virtually ensures that the person will engage in adaptive behaviour. In other words, evaluating equation (6) with a value of ΔΚ = π leads to a probability of engaging in adaptive behaviour of nearly 1.0. Again, the word nearly is emphasised because logit models never reach a probability of 1.0, hence the requirement for the parameter ɛ. This parameter has the same meaning in equation (6) as that given in equation (5).

4.1 Inputs to the simulation

The main inputs to the simulation are the dwelling’s architecture (i.e. geometry/configuration, materials, etc.), inhabitants (e.g. their satisfaction function, proactivity, busyness, etc., as explained in Section 3) and environmental influences, e.g. the solar, wind temperature and humidity patterns (the ‘weather data’ of conventional thermal simulation models).

The environmental influences used for the simulations was based on the typical meteorological year weather data corresponding to Santiago (Chile), acquired from the EnergyPlus website (US Department of Energy 2021). Since information about external noise is absent from typical meteorological years—but required by the acoustic model—a daily schedule was provided. This schedule represented a commuter road noise scenario during a weekday (Figure 3). While the translation of external noise into internal loudness was performed through a mock-up simulation module, this can potentially be improved by using measured traffic noise data and a tool for predicting sound insulation through buildings’ facades (INSUL 2021).

Figure 3

The dwelling has two bedrooms with a separate kitchen and bathroom, and a hallway that serves as a connection between them (Figure 4). From these six spaces, the most important ones for the people who live there are the bedrooms and the living room. It is worth noting that while the importance can potentially vary over time, this particular simulation assumes it to be constant. Table 1 shows the relative importance of the different spaces (they are used for estimating the satisfaction with the dwelling, as per equation 1). Since the focus of this simulation is on people’s feeling of comfort, the physical components of the simulation are only mock-ups; the details of the physical properties of the dwelling are not considered relevant.

Figure 4

The model of the inhabitant living in the dwelling is concerned with five perceptions: thermal sensation (TS), clothing annoyance (e.g. having too much or too little clothing; Clo), loudness (L), brightness of the space (Br) and the desire to reduce utility bills (UB). Note that, for simplicity, the perceptions associated with daylight have been summarised in a single ‘brightness’ perception.

Equation (7) shows the satisfaction function for this individual. While this function was arbitrarily designed, it respects the interview respondents’ positive or negative perceptions and is consistent with the literature. For instance, positive brightness always increases satisfaction, and a positive utility bill always decreases it. Similarly, thermal sensation (TS), clothing annoyance (Clo) and loudness (L) are all squared because their best possible value is 0.0, and they all reduce people’s satisfaction when positive or negative. This is not meant to suggest that thermal sensation, clothing or loudness dominate people’s feeling of comfort. The purpose here is merely to demonstrate that such a representation can be incorporated into a computer simulation. Future research is needed to develop this concept further. This would involve developing a more detailed representation of perceptions in the proof-of-concept model.

People’s awareness of the future (used for modelling the effect of expected outcomes over people’s comfort, as shown in equation 4) was modelled according to equation (8). The parameter h in this equation was set to three hours; anything that happens further than three hours into the future has no effect on this person’s feeling of comfort. The parameter ɛ has the same interpretation as in equations (5) and (6).

What remains of this section shows and discusses the results from the simulation.

4.2 Comfort depends on multiple domains

The feeling of comfort model posits that perceptions, expected outcomes and trade-offs are the determinants of the feeling of comfort. The custom simulation tool used and described in this section was designed to incorporate these three elements. Figure 5 shows that this model has the potential to simulate this more sophisticated feeling of comfort.

Figure 5

Figure 5 not only shows that this model allows for the consideration of multiple physical (i.e. lighting, thermal and acoustic) and non-physical (e.g. utility bills and clothing annoyance) factors simultaneously, but that the simulated individual behaves and responds to these factors at runtime. For instance, it reveals that when the person puts on clothes, their thermal sensation and clothing annoyance change without affecting the concern for high utility bills. Similarly, turning a heater on affects the thermal sensation and the utility bills, all this while not affecting anything else.

Another element to notice in the results is that the person’s loudness perception starts to decay about three hours before the noisy rush hour (Figure 3 shows details of the external noise). This happens because the person being simulated has an awareness of three hours (modelled according to equation 8). This does not mean that the person is indeed hearing any noise, but only he/she is already concerned about it. These are the individual components of the feeling of comfort model.

4.3 Agency and personal control

It is well-known that people’s control over their environment affects their feeling of comfort (Lolli et al. 2020; Luo et al. 2014; Veitch & Newsham 2000; Zhou et al. 2014). The feeling of comfort model describes this phenomenon through the concept of expected outcomes. Specifically, it states that if people know they can fix potentially uncomfortable situations (e.g. heating to prevent cold), then their mind is less troubled and therefore they feel more comfortable. Figure 6 presents the feeling of comfort, combining the components presented in Figure 4.

Figure 6

The feeling of comfort ‘scores’ plotted are the results of two distinct simulations. In one of them, the person is free to change their clothes and every room has a heater and luminaires. In the other simulation, the simulated individual cannot change their clothing, there are no luminaires or heaters in the dwelling, and no windows are openable. Additionally, the simulation was set up so neither of these two individuals ever engaged in any behaviour by setting indifference (π in equation 6) to a very high number. This means that the only difference between both simulations is what the individuals know they can do, not the actual physical conditions of the dwelling. The model is shown to be capable of representing the overall feeling of comfort.

4.4 Inhabitants’ attention

Not all sensations have an intensity capable of eliciting perceptions (Feher 2012) which means people are not constantly assessing their level of comfort. This is reflected in the feeling of comfort model that states that not every situation is capable of capturing people’s attention.

Equation (5) models the probability of a person attending a situation (α) as a function of the satisfaction with the environment (s) and a busyness parameter (β). That equation states that the probability of attending a situation is greater when said situation becomes more unpleasant, and lower when the person is busy.

The implication of attention level being a prerequisite for feeling comfort is that even if they are exposed to situations whose environmental conditions would allow estimating comfort indices, people very often feel neither comfortable nor uncomfortable. Sometimes the feeling of comfort does not develop.