Odor descriptive ratings can predict some odor-color associations in different color features of hue or lightness

Participants

We recruited 23 university students for this study (women, n = 11; men, n = 12; and mean age ± SD = 20 ± 1.6 years). None of the participants displayed color vision deficiencies following the Ishihara’s test. Based on self-reports, none of the participants had olfactory or neurological deficits. As the odor-color association depends on cultural and language backgrounds (Levitan et al., 2014; Majid & Burenhult, 2014; Majid et al., 2018), we ensured that all participants were native Japanese speakers and from Japanese cultural backgrounds. The participants were instructed to stop eating and drinking 1 h before the experiment; however, they were permitted to drink water.

Environment and display settings

All visual stimuli were presented on a laptop computer screen (MacBook Pro 13-inch, Retina display, resolution 2,560 × 1,600) using Psychtoolbox-3 (Brainard, 1997; Kleiner, Brainard & Pelli, 2007) programmed in MATLAB (MathWorks, Inc., Natick, MA, USA). The monitor was calibrated following standard methods (Brainard, Pelli & Robson, 2002) using a Chroma Meter (CS150; Konica Minolta, Inc., Tokyo, Japan). We placed the laptop computer display on a portable photography box measuring 60 × 60 cm to control the lightness of the environment (Fig. 1A). The backdrop was black and there was no light-emitting diode inside the box during the experiments.

Odor stimuli

We assessed 13 odors in this study (Table 1). According to a previous report, they were diluted to control the odor intensity, which was almost equivalent (Bushdid et al., 2014).

Five microliters of the odorant solution prepared according to Table 1 was added dropwise to 0.5 × 0.5 cm of cotton wool. Three cotton wool samples with odorant drops were encapsulated in a 20 mL vial (Fig. 1B), and the solution was volatilized for at least 30 min. Immediately before the participant sniffed the sample, the cotton wool was removed and only the odor gas was presented. We counterbalanced the order of presentation of the odorants among the participants. The same 13 odorants were used in both the experiments; the order of presentation was different within the two experiments. We also changed the order of presenting the odorants among the participants. In addition, the participants were not notified that “the odor substances used in the first and second experiments were identical.” The substance name was not written on the vial, and the odor was presented with care such that the participants could not predict the type of odor presented.

Experiment

The participants were instructed to sniff 13 different odorants and indicate the color and semantics associated with each odor. The odor was enclosed in a bottle; the participants opened the bottle upon instruction and sniffed it. Immediately after completing the associative color/semantics evaluation response, the participants sniffed coffee beans for 10 s. Following a 2-min break, they smelled the subsequent odorant (Fig. 1A). The room was ventilated during the break. All participants completed the task twice on different days.

We requested the participants to respond to an associated color with a presented odor and to rate several descriptions. The procedure and color settings were determined in a previous study (Tamura, Hamakawa & Okamoto, 2018). Each participant was handed a vial containing the gaseous odor and asked to sniff the odor. Consequently, the color associated with the odor was reported. First, the participants were asked concerning the hue angle of the associated color and they rotated a cursor corresponding to the hue angle. The angle between the cursor and the center of the circle determined the hue value of the square. The square was presented at the center of the display, and the color was subsequently changed following the cursor movement (Tamura, Hamakawa & Okamoto, 2018). The colors were determined within a circle in the CIE L*a*b* color space, with a center space at L* = 70, a* = 20, b* = 38, and a radius of 60 (Zhang & Luck, 2008) (Fig. 1D). They clicked upon deciding that the current color hue was most associated with the presented odor. Subsequently, we presented three colors with different lightness values of the selected color (L* = 40, 70, and 100). The participants selected the lightness of the color that was most associated with the odor (Fig. 1C).

After deciding the associated color, they were instructed to complete the responses to five descriptor items as follows: Strength, Pleasantness, Familiarity, Edibility, and Arousal, using the visual analog scale (VAS) ranging from 0 (completely different) to 1 (very applicable). For example in the strength evaluation, 1 indicates very strong, 0 indicates very weak, and 0.5 indicates moderate strength. Strength and Edibility would relate to primitive odor evaluation. Pleasantness and Familiarity would reflect basic subjective evaluation for odors, and Arousal would relate to physiological states. The relationship of color-odor association with descriptor items of Strength and Edibility have been reported previously (Kemp & Gilbert, 1997; Maric & Jacquot, 2013). To investigate the influence by different descriptor items, Pleasantness, Familiarity, and Arousal were added. Pleasantness and Familiarity have been used in related olfactory studies with subjective ratings (e.g., Delplanque et al., 2015; Ferdenzi et al., 2017, 2013; Huisman & Majid, 2018). These terms were also used for color-odor association studies (Nehmé et al., 2016). Arousal ratings can be informative to show the participants’ affective states, which has been reported previously Arousal ratings to odors reportedly correlated with the autonomic system (Bensafi et al., 2002).

Our method attempted to measure the colors associated with odors to prevent visual priming effect while choosing associate colors. Conventional studies assessed the selection based on several color patches after sniffing the odors (de Valk et al., 2017; Gilbert, Martin & Kemp, 1996; Levitan et al., 2014; Majid & Burenhult, 2014; Majid et al., 2018). We were concerned that the color patch presentations may could result in the priming of responses since visual priming can support olfactory identification and odor-naming (Gottfried & Dolan, 2003; Guerdoux, Trouillet & Brouillet, 2014; Morrot, Brochet & Dubourdieu, 2001; Olofsson & Gottfried, 2015; Robinson, Reinhard & Mattingley, 2015; van Beilen et al., 2011).

Bayesian estimation

For the statistical analysis, we performed Bayesian estimation with several models. The models were fitted using the R environment (ver.3.4.0) and RStan (ver.2.2.1) with the Markov chain Monte Carlo (MCMC) method. All estimates were made with 3,000 samplings, running four chains to generate random numbers, and a burn-in period of 1,000. We used the Gelman-Rubin statistics $\hat{R}$ to determine if the MCMC estimation converged for all estimation parameters. $\hat{R}$ is generally considered to converge as it approaches 1.10, and each model fit produces $\hat{R}$ < 1.10.

Bayesian multilevel regression analysis

We used Bayesian multilevel regression models to estimate the effects of the following five descriptor items on color responses: Strength, Pleasantness, Familiarity, Edibility, and Arousal. The multilevel models estimated the L*-, a*-, and b*-axis values using odor-level effects. The values of the L*-, a*-, and b*-axes were divided by 100 for normalization. The Bayesian multilevel regression did not require concern about type-1 error from multiple comparisons because the model did not assume a null hypothesis (Gelman, Hill & Yajima, 2012).

We modeled the response value of the a*-axis for the associated colors by each odor as a normal distribution as follows:

$$a_{\left[j\right]}^{\ast }\sim Normal\left({\alpha }_{0\left[i\right]}+{\alpha }_{S\left[i\right]}Strengt{h}_{\left[i\right]}+{\alpha }_{P\left[i\right]}Pleasantnes{s}_{\left[i\right]}+{\alpha }_{F\left[i\right]}Familiarit{y}_{\left[i\right]}+{\alpha }_{E\left[i\right]}Edibilit{y}_{\left[i\right]}+{\alpha }_{A\left[i\right]}Arousa{l}_{\left[i\right]},{\sigma }_{a\left[i\right]}\right),$$

${\sigma }_{a\left[i\right]}>0$where i indicates the odor ID and j denotes the data index. The intercept ( ${\alpha }_{0\left[i\right]}$) and each coefficient, ${\alpha }_{X\left[i\right]}$, followed a normal distribution with mean coefficients as follows:

$${\alpha }_{0\left[i\right]}\sim Normal\left({\alpha }_{0\mathrm{\_}all},{\sigma }_{\alpha 0}\right),$$

$${\alpha }_{S\left[i\right]}\sim Normal\left({\alpha }_{S\mathrm{\_}all},{\sigma }_{\alpha S}\right),$$

$${\alpha }_{P\left[i\right]}\sim Normal\left({\alpha }_{P\mathrm{\_}all},{\sigma }_{\alpha P}\right),$$

$${\alpha }_{F\left[i\right]}\sim Normal\left({\alpha }_{F\mathrm{\_}all},{\sigma }_{\alpha F}\right),$$

$${\alpha }_{E\left[i\right]}\sim Normal\left({\alpha }_{E\mathrm{\_}all},{\sigma }_{\alpha E}\right),$$

$${\alpha }_{A\left[i\right]}\sim Normal\left({\alpha }_{A\mathrm{\_}all},{\sigma }_{\alpha A}\right),$$where ${\alpha }_{X\mathrm{\_}all}$indicates the average coefficient across all odorants. The prior distributions for the parameters of the standard deviations were as follows:

$${\sigma }_{\alpha 0}\sim Normal\left(0,5\right){\sigma }_{\alpha 0}>0,$$

$${\sigma }_{\alpha S}\sim Normal\left(0,5\right){\sigma }_{\alpha S}>0,$$

$${\sigma }_{\alpha P}\sim Normal\left(0,5\right){\sigma }_{\alpha P}>0,$$

$${\sigma }_{\alpha F}\sim Normal\left(0,5\right){\sigma }_{\alpha F}>0,$$

${\sigma }_{\alpha E}\sim Normal\left(0,5\right){\sigma }_{\alpha E}>0,$

${\sigma }_{\alpha A}\sim Normal\left(0,5\right){\sigma }_{\alpha A}>0.$

Regarding the model for a* value estimation, we modeled the b*-axis values as follows:

$$b_{\left[j\right]}^{\ast }\sim Normal\left({\beta }_{0\left[i\right]}+{\beta }_{S\left[i\right]}Strengt{h}_{\left[i\right]}+{\beta }_{P\left[i\right]}Pleasantnes{s}_{\left[i\right]}+{\beta }_{F\left[i\right]}Familiarit{y}_{\left[i\right]}+{\beta }_{E\left[i\right]}Edibilit{y}_{\left[i\right]}+{\beta }_{A\left[i\right]}Arousa{l}_{\left[i\right]},{\sigma }_{b\left[i\right]}\right),$$where each coefficient followed normal distribution with mean coefficients as follows:

$${\beta }_{0\left[i\right]}\sim Normal\left({\beta }_{0\mathrm{\_}all},{\sigma }_{\beta 0}\right),$$

$${\beta }_{S\left[i\right]}\sim Normal\left({\beta }_{S\mathrm{\_}all},{\sigma }_{\beta S}\right),$$

$${\beta }_{P\left[i\right]}\sim Normal\left({\beta }_{P\mathrm{\_}all},{\sigma }_{\beta P}\right),$$

$${\beta }_{F\left[i\right]}\sim Normal\left({\beta }_{F\mathrm{\_}all},{\sigma }_{\beta F}\right),$$

$${\beta }_{E\left[i\right]}\sim Normal\left({\beta }_{E\mathrm{\_}all},{\sigma }_{\beta E}\right),$$

$${\beta }_{A\left[i\right]}\sim Normal\left({\beta }_{A\mathrm{\_}all},{\sigma }_{\beta A}\right),$$where ${\beta }_{X\mathrm{\_}all},$ indicates the average coefficient across all odorants. The prior distributions for the parameters of standard deviations in our model were as follows:

$${\sigma }_{\beta bn}\sim Normal\left(0,5\right),$$where ${\sigma }_{\beta X},$ > 0.

Similar to the steps with a* and b* values, we model the L-axis values as follows:

$$L_{\left[j\right]}^{\ast }\sim Normal\left({\lambda }_{0\left[i\right]}+{\lambda }_{S\left[i\right]}Strengt{h}_{\left[i\right]}+{\lambda }_{P\left[i\right]}Pleasantnes{s}_{\left[i\right]}+{\lambda }_{F\left[i\right]}Familiarit{y}_{\left[i\right]}+{\lambda }_{E\left[i\right]}Edibilit{y}_{\left[i\right]}+{\lambda }_{A\left[i\right]}Arousa{l}_{\left[i\right]},{\sigma }_{L\left[i\right]}\right),$$and the prior distributions for parameters were as follows:

$${\lambda }_{0\left[i\right]}\sim Normal\left({\lambda }_{0\mathrm{\_}all},{\sigma }_{\lambda 0}\right),$$

$${\lambda }_{S\left[i\right]}\sim Normal\left({\lambda }_{S\mathrm{\_}all},{\sigma }_{\lambda S}\right),$$

$${\lambda }_{P\left[i\right]}\sim Normal\left({\lambda }_{P\mathrm{\_}all},{\sigma }_{\lambda P}\right),$$

$${\lambda }_{F\left[i\right]}\sim Normal\left({\beta }_{F\mathrm{\_}all},{\sigma }_{\lambda F}\right),$$

$${\lambda }_{E\left[i\right]}\sim Normal\left({\beta }_{E\mathrm{\_}all},{\sigma }_{\lambda E}\right),$$

$${\lambda }_{A\left[i\right]}\sim Normal\left({\alpha }_{A\mathrm{\_}all},{\sigma }_{\lambda A}\right),$$

$${\sigma }_{\lambda n}\sim Normal\left(0,5\right),$$with ${\lambda }_{X\left[i\right]}$indicating the average coefficient across all odorants, and ${\sigma }_{{\lambda }_X}$ > 0.

Bayesian within-subject analysis for color response reproducibility

The participants repeated the associated color response twice on different days. We performed Bayesian analysis to estimate the mean difference in color responses between days to demonstrate the reproducibility of the color responses among the participants.

We modeled the difference in a*-axis values measured from the associated color responses as a normal distribution as follows:

$$\mathrm{\Delta }{a}_{\left[i,j\right]}^{\ast }\sim Normal\left({\mu }_{odor\mathrm{\_}a\left[i\right]},{\sigma }_{odor\mathrm{\_}a\left[i\right]}\right),$$

$${\mu }_{odor\mathrm{\_}a\left[i\right]}\sim Normal\left({\mu }_{all\mathrm{\_}a},{\sigma }_{all\mathrm{\_}a}\right),$$

$${\sigma }_{odor\mathrm{\_}a\left[i\right]}>0,$$

$${\sigma }_{all\mathrm{\_}a}>0,$$where i indicates the odor ID, j denotes the data index, and $\mathrm{\Delta }{a}_{\left[i,j\right]}^{\ast }$ indicates the difference between the a*-value on day 2 and day 1 for each participant and each odorant. ${\mu }_{odor\mathrm{\_}a\left[i\right]}$ indicates the mean difference of $\mathrm{\Delta }{a}_{\left[i,j\right]}^{\ast }$ within an odor and ${\sigma }_{odor\mathrm{\_}a\left[i\right]}$ indicates its standard deviation. ${\mu }_{odor\mathrm{\_}a\left[i\right]}$ followed a normal distribution with a mean difference across the odors, ${\mu }_{all\mathrm{\_}a}$, and a standard deviation, ${\sigma }_{all\mathrm{\_}a}$. Moreover, we modeled the difference in the b*- and L*-axis values between days as $\mathrm{\Delta }{a}_{\left[i,j\right]}^{\ast }$.

Days-differences of associated colors within participants

Perception from olfaction could vary among participants. We analyzed whether the responses derived from the odorants were consisted among participants. The conventional common approach cannot support the hypothesis that “the mean of differences was equally 0.” To confirm within-participant consistency with the responses derived from the odorants, we estimated the posterior distribution and its 95% Bayesian confidence interval (CI) of the mean day differences within the participants. For the a*-, b*-, and L*-axis values, there were no parameters of day difference whose 95% CI did not include 0 (Fig. 2). The associated color responses did not significantly fluctuate with the days in response to the odorant. The results indicated that the associated color responses did not significantly fluctuate with the days in response to any odorant.

Confirmation of the multicollinearity for multilevel regression

Before implementing the multilevel regression, we confirmed the multicollinearity of five descriptive ratings. Subsequently, we performed Pearson correlation analysis to demonstrate the correlation coefficients and any absolute values of the coefficients ≤0.70 (Table 2), which is the lower limit of a strong correlation in psychology (Akoglu, 2018). We included all descriptive rating data in the multilevel regression model according to the results.

Bayesian multilevel regression

First, we confirmed the model for a*-value estimation and the distribution of the coefficient parameters with odor descriptors. A significantly positive estimated parameter with ratings of a semantic descriptor indicated that a higher descriptor rating would allow the associated colors to be reddish. By contrast, a significantly negative estimated parameter suggested that a higher descriptor would allow the associated colors to be greenish.

The multilevel model for a*-values estimated the parameters with odorant-level effects. We used a multilevel Bayesian regression model that included random intercepts and slopes for each odor to estimate the effect of each descriptive rating on the associated colors. We estimated the coefficients of the five descriptive ratings, and their 95% CIs are demonstrated for each odorant (Fig. 3). For the 95% CIs of Edibility, the three odors, including 2-ethyl pyrazine, limonene, and strawberry aldehyde, did not significantly overlap with zero (Fig. 3). The results indicated colors associated with the three odors related to Edibility ratings. An increase in the Edibility ratings of these odorants would make the associated colors more reddish. The remaining odors did not display a practical difference in the coefficients of Edibility from zero in the a*-value predictive model. The remaining descriptive ratings did not demonstrate any practical differences from zero for any odor.

Figure 4 depicts the colors associated with the three odors that showed higher coefficients with Edibility ratings. The color responses were reddish, according to the increase in Edibility ratings for the three odorants (Fig. 4). The original colors indicated the native responses of the participants. To demonstrate the relationship between the a*-axis values and Edibility ratings, we fixed the b*- and L*-parameters with the initial settings. Subsequently, we changed the a*-values only according to the responses of the associated colors (Fig. 4, middle row). The right row denotes changes in the a*-value (Fig. 4). The associated colors were greenish and reddish for low and high Edibility ratings in the three odors, respectively. These a*-value changes corresponded to the Edibility ratings.

Consequently, we confirmed the model that estimated the b* values and the distribution of estimates of the coefficient parameters with their odor descriptors. A significantly positive estimated parameter with ratings of a semantic descriptor indicated that a higher descriptor rating would allow the associated colors to be yellowish, whereas a lower rating would allow the colors to be bluish. An estimated parameter that was significantly negative from 0 suggested that a higher descriptor would allow the associated colors to be bluish along the yellow-blue axis.

For the Edibility ratings, five odorants, including hydroxy citronellal, butyl acetate, (1S)-(-)-alpha-pinene, trimethyl amine (30%), and 2,3-Dimethylpyrazine, displayed significant coefficients. The 95% CI of the five odors did not significantly overlap with zero (Fig. 5). In the results of the a*-prediction model, the five odors did not reveal significant coefficients with Edibility (Fig. 3). Figure 6 represents the color responses from the participants with Edibility ratings. To demonstrate the relationship between the b*-axis values and Edibility ratings, we fixed the a*- and L*-parameters with the initial settings. Moreover, we changed the b* values only according to the responses of the associated colors (Fig. 6, middle row). The associated colors were bluish for low Edibility ratings.

For Arousal ratings, the two odorants, namely hydroxy citronellal and 4-methyl-3-penten-2-one, displayed higher coefficients (Fig. 7). The associated colors would be more bluish for these odorants following low Arousal ratings. The remaining descriptive ratings did not reveal any practical differences from zero for any odor.

The model for L*-value prediction demonstrated significant coefficients for Strength and intercepts for all odorants. The coefficients of Strength ratings indicated that the associated colors would be darker for all odorants following an increase in ratings (Fig. 8). We displayed some examples to exhibit the relationship between the Strength ratings and the lightness of colors (Fig. 9), which revealed that the colors would be darker for higher ratings.