40 H.B.Gunay et aL Building and Environment 70(2013)31-47 Time (hour) presents a comparison of existing modeling methodologies with 810121416182022 their limitations and challenges. 3.1.Adaptive behavior models Seasonal vvariations Systematic observations on the system states (e.g.window 0.8 open/closed).once plotted with respect to the monitored variables (e.g.indoor temperature)resulted in a data scatter,as shown in Fig.6.Early researchers [118-120]and most of the current practi- tioners used deterministic models to predict the adaptive occupant variations behaviors.These models are simple enough to be easily incorpo- rated in the BPS-based design process.For example,in these models,the probability of an occupant being uncomfortable below .4 the defined threshold value is zero and the probability becomes one just after the predictor variable or variables reach the threshold value,as shown in Fig.6.A comparison between the data scatter JAN MAR MAY JUL SEP NOV and the probability curve,which is a step function,showed that a Time(month) deterministic model cannot predict the observed adaptive occu- pant behavior shown in Fig.6.Occupants'adaptive behaviors, Fig.5.Seasonal and diurnal variations in the mean clothing level reported by Haldi despite being influenced by the physical conditions,are governed and Robinson 106]. by a stochastic,rather than a precise,relationship [121].Stochastic models estimate an adaptive behavior by assuming a probabilistic 2.2.4.Non-physical parameters relationship with the predictor variable or variables.Numerous Morgan and De Dear [115]underlined social and cultural con- researchers [31.38,51,55]proposed using linear-response (e.g. straints that should be taken into account in predicting a model for linear or polynomial regression)models to estimate the probability clothing levels.For example,it was reported that women tend to of the adaptive occupant behavior as a function of a predictor wear less in summer and more in winter than men.However,a variable.Linear-response models assume a linear relationship be- recent work by Schiavon and Lee [107]reported that men and tween the response and predictor variables,as follows: women wear clothing at similar insulation levels.The dress codes in an office environment may restrain the ability to undertake Pi Bo +81x1i+82x2i++8mxmi (1) clothing adjustments.Haldi and Robinson [108]suggested that different models (e.g.strict dress code,casual working environ- where pi is the probability of success (e.g.probability of window ment,residential environment)can be established for offices with opening).B is the vector for the regression coefficients and x is the different dress codes.Similarly,drinking traditions(e.g.a cup of hot vector for the predictor variables(e.g.indoor temperature,outdoor coffee or tea in the morning of a summer day)cannot be directly temperature,CO2 concentration). associated with the physical variables.Researchers should Haldi and Robinson [108]reported linear regression as a sub- acknowledge these non-physical variables and try to incorporate optimal method to model the adaptive occupant behavior.It is their effects in the modeling process.For example,Haldi and Rob- evident that the linear regression model poorly predicts the upper inson [108]suggested to modify their stochastic clothing model for and the lower bounds of the observations as shown in Fig.6.This different offices with different dress-codes. can be explained since the linear-response models (e.g.linear or polynomial regression)are not appropriate to model response 2.2.5.HVAC system and operation variables that have a non-normal distribution.Generalized linear Newsham and Tiller [116]carried out a self-reported question- models(e.g.logistic regression or probit)cover such cases by letting naire survey in four fully conditioned offices during fall and winter. In this study,about 15%of the occupants reported that they adjusted their clothing in the previous hour.On the contrary.Haldi ++Observations and Robinson [108]surveyed office occupants in a naturally -----Deterministie Model ventilated office building and revealed that occupants rarely adjust Linear Regression Model Logistic Regression Model their clothing level during the day.This may imply that once the ”十 occupants are given the option to make changes in their environ- ment (e.g.opening a window),they undertake changes in their environment before they try to adapt to the environment (e.g. 0.8 clothing adjustments).This hypothesis opens a further discussion for researchers:whether or not the order at which the occupants 0.6 undertake adaptive behaviors can be stated in a statistically coherent way.In line with this,Andersen [117]reported that the order of the manual control sequence(e.g.thermostat-window 4 blinds-lights)may be responsible for up to 3.3 fold variation in the energy use predictions.This underlines the importance of 0.2 being able to predict the order of manual control actions. 3.Model prediction + Variable (0) Once researchers obtain their observations,they focus on Fig 6.Generic univariate deterministic,linear regression,logistic regression occupant establishing models that predict adaptive behaviors.This section models(data scatter is extracted from Nicol 119]).2.2.4. Non-physical parameters Morgan and De Dear [115] underlined social and cultural con￾straints that should be taken into account in predicting a model for clothing levels. For example, it was reported that women tend to wear less in summer and more in winter than men. However, a recent work by Schiavon and Lee [107] reported that men and women wear clothing at similar insulation levels. The dress codes in an office environment may restrain the ability to undertake clothing adjustments. Haldi and Robinson [108] suggested that different models (e.g. strict dress code, casual working environ￾ment, residential environment) can be established for offices with different dress codes. Similarly, drinking traditions (e.g. a cup of hot coffee or tea in the morning of a summer day) cannot be directly associated with the physical variables. Researchers should acknowledge these non-physical variables and try to incorporate their effects in the modeling process. For example, Haldi and Rob￾inson [108] suggested to modify their stochastic clothing model for different offices with different dress-codes. 2.2.5. HVAC system and operation Newsham and Tiller [116] carried out a self-reported question￾naire survey in four fully conditioned offices during fall and winter. In this study, about 15% of the occupants reported that they adjusted their clothing in the previous hour. On the contrary, Haldi and Robinson [108] surveyed office occupants in a naturally ventilated office building and revealed that occupants rarely adjust their clothing level during the day. This may imply that once the occupants are given the option to make changes in their environ￾ment (e.g. opening a window), they undertake changes in their environment before they try to adapt to the environment (e.g. clothing adjustments). This hypothesis opens a further discussion for researchers: whether or not the order at which the occupants undertake adaptive behaviors can be stated in a statistically coherent way. In line with this, Andersen [117] reported that the order of the manual control sequence (e.g. thermostat / window / blinds / lights) may be responsible for up to 3.3 fold variation in the energy use predictions. This underlines the importance of being able to predict the order of manual control actions. 3. Model prediction Once researchers obtain their observations, they focus on establishing models that predict adaptive behaviors. This section presents a comparison of existing modeling methodologies with their limitations and challenges. 3.1. Adaptive behavior models Systematic observations on the system states (e.g. window open/closed), once plotted with respect to the monitored variables (e.g. indoor temperature) resulted in a data scatter, as shown in Fig. 6. Early researchers [118e120] and most of the current practi￾tioners used deterministic models to predict the adaptive occupant behaviors. These models are simple enough to be easily incorpo￾rated in the BPS-based design process. For example, in these models, the probability of an occupant being uncomfortable below the defined threshold value is zero and the probability becomes one just after the predictor variable or variables reach the threshold value, as shown in Fig. 6. A comparison between the data scatter and the probability curve, which is a step function, showed that a deterministic model cannot predict the observed adaptive occu￾pant behavior shown in Fig. 6. Occupants’ adaptive behaviors, despite being influenced by the physical conditions, are governed by a stochastic, rather than a precise, relationship [121]. Stochastic models estimate an adaptive behavior by assuming a probabilistic relationship with the predictor variable or variables. Numerous researchers [31,38,51,55] proposed using linear-response (e.g. linear or polynomial regression) models to estimate the probability of the adaptive occupant behavior as a function of a predictor variable. Linear-response models assume a linear relationship be￾tween the response and predictor variables, as follows: pi ¼ bo þ b1x1;i þ b2x2;i þ / þ bmxm;i (1) where pi is the probability of success (e.g. probability of window opening), b is the vector for the regression coefficients and x is the vector for the predictor variables (e.g. indoor temperature, outdoor temperature, CO2 concentration). Haldi and Robinson [108] reported linear regression as a sub￾optimal method to model the adaptive occupant behavior. It is evident that the linear regression model poorly predicts the upper and the lower bounds of the observations as shown in Fig. 6. This can be explained since the linear-response models (e.g. linear or polynomial regression) are not appropriate to model response variables that have a non-normal distribution. Generalized linear models (e.g. logistic regression or probit) cover such cases by letting Fig. 6. Generic univariate deterministic, linear regression, logistic regression occupant models (data scatter is extracted from Nicol [119]). Fig. 5. Seasonal and diurnal variations in the mean clothing level reported by Haldi and Robinson [106]. 40 H.B. Gunay et al. / Building and Environment 70 (2013) 31e47