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Modeling Semantically Multilayered
Affective and Psychophysical Responses
Toward Tactile Textures
Hikaru Nagano, Shogo Okamoto, and Yoji Yamada,
Abstract—Subjective responses related to touch are described via perceptual and affective adjectives. Understanding relationships
among such responses is useful for industrial surface design. We developed a method for investigating relationships among touchrelated responses by constructing multilayered adjective models without assumptions regarding model structure such as adjective
hierarchy or a definition of layers. The method consists of two processes through which a model structure and parameters are estimated.
To acquire the model structure, subjectively evaluated causal relationships among adjective pairs are used. Free parameters, such as
effects among adjectives, are then statistically estimated through sensory evaluation and structural equation modeling. To validate themethod, two models with different levels of details were developed using 29 adjective pairs and 46 texture samples. For example, themodel with three layers, which we categorized into psychophysical, affective, and hedonic layers, was constructed. Moreover, a detailed
model with four layers was provided, which was more complex than previously reported models. The present method helps advanceour understanding and design of connections among subjective surface ratings.
Index Terms—Texture, multilayer, effect matrix, structural equation modelingT

OUCHING object surfaces elicits a variety of tactile sensa-

tions. To understand subjective response using adjectives,
such as “rough-smooth” as mediators of subjective ratings,
some studies have investigated relationships among touchrelated adjectives through specifying the multidimensional
space of tactile perception [1], [2], [3], [4], [5], [6], [7].
These studies focused on psychophysical aspects of touch
perception, whereby dimensions typically consist of “roughsmooth,” “uneven-flat,” “hard-soft,” “warm-cold,” and “stickyslippery” descriptions [8], [9], [10], [11].
Touching an object causes not only psychophysical responses but also affective ones. Some studies have proposeda multilayered space consisting of a few word types thatinterpret, for example, psychophysical, affective, and hedonic
aspects of tactile textures [12], [13], [14], [15], [16], as shownin Fig. 1. Additionally, the relationships between perception
and the physical properties of textural stimuli have been
identified in many studies [17], [18], [19], [20]. Therefore,by combining relationships with a layered model, a layered
adjective relationship becomes instrumental in understanding
the physical properties that influence affective and hedonic
ratings for product surfaces.
Thus far, a method for constructing a layered adjectivemodel pertaining to touch has not been established. The
greatest difficulty lies in determining a model structure. Here,studies on multilayered perceptual and affective models fortactile textures are reviewed to illustrate remaining problems.
• HN is with the Graduate School of Informatics, Tohoku University, Sendai,
Japan. SO and YY are with the Department of Mechanical Systems
Engineering, Nagoya University, Nagoya, Japan.
Manuscript received September xx, 2017; revised January xx, 201x.

Rich/
Poor

Like/
Dislike…

Happy/
Sad
0.43

Affective

I NTRODUCTION

Psychophysical1

HedonicF

0.30
Exciting/
Boring0.37

0.84

Beautiful/
Ugly

…

0.45
Comfortable/
Uncomfortable

-0.67
-0.73
Rough/
Smooth

0.51
Uneven/
Flat

0.37
…

Wet/
Dry

Fig. 1. Concept of a semantically layered model for tactile
textures. Values represent the magnitude of influencesamong adjectives. Modified from [21].

Guest et al. [13] systematically classified a variety of adjectives
into two layers, referred to as psychophysical and affective
layers, and then investigated the multidimensional space ineach layer. Some studies have linked these two layers throughmultivariate analyses [6], [15], [22], [23]. However, no priorwork has proposed how such approaches could be extended
to complex structures with more than three layers. In fact,some researchers suggested that three or four layers are
possible [12], [24], [16]. Kidoma et al. [21] constructed amultilayered model wherein they located adjectives representing physical aspects of objects at the base of the hierarchy.
They displaced adjectives representing affective aspects at
higher layers that depended on how much the layers could

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be directly explained by physical adjectives. Nevertheless,semantically causal relationships among the words were notconsidered. Chen et al. [12] introduced a multilayered model
among adjectives representing tactile textures. However, they
did not elaborate on how the model was structured, as themodel was not the main scope of their study. Outside of
the texture domain, Ueda et al. [25] proposed a multilayered
model of timbre where the hierarchy was determined basedon the semantic abstractness of the adjective words.

The present study developed a novel method for constructing multilayered models for perceptual and affective
responses caused by touching textures. Unlike earlier research,
we directly evaluated subjective influences among adjectives,
which enabled us to acquire the model structure without any
assumptions regarding causal relationships among perceptualand affective responses. For this purpose, we questioned
experimental participants about, for example, how much theratings for “rough-smooth” influenced those for “rich-poor.”
This method is grounded in our previous reports [14], [24].
Although this approach resolves a difficulty with defining thelayered adjective structure, it does not explain results regarding
sensory evaluations that typically use adjectives as criteria.
To complete the model, we then applied structural equation
modeling to the data acquired through sensory evaluation
tasks. Consequently, a systematic method for constructing a
multilayered model of subjective responses was developed forthe first time. This model enables an understanding as torelationships among adjectives representing several types oftouch-related responses.
In Sec. 2, we describe general methods and theories followed by Sec. 3, wherein the specific experiments are explained. In Sec. 4, the models established from the experimental data are shown, and then we discuss the validity ofthe method. We used data collected for a Ph.D. thesis [26]where sensory evaluation tasks were conducted toward various
types of materials to produce a data bank. Given its inherent
generality, the data were also used in our earlier studies [14],[21], [24]. Finally, in Sec. 5, we summarize a guidance forestablishing multilayered models.

d

…

n

c

…

m

j

i

Questionnaire:
Causal relationships
between adjectives

a

b

…

Σ
Covariancestructure

l

… n
Įm4

4

Rough

SmoothĮ24...

To sum up, it is difficult to define causal relationships among
adjectives, or which adjectives are causes and located at lower
layers versus which adjectives are results at higher layers.
Adjectives at lower layers semantically explain adjectives athigher layers. These difficulties are especially apparent when
judging how many layers should be considered and which
adjectives belong to each layer. These difficulties have beenreported in the literature; however, a standard method forconstructing multilayered models of touch-related adjective
ratings has yet to be developed. Some of the aforementioned studies assumed the number of layers or determined
the adjective hierarchy by using information that indirectlysuggests causality. From a multivariate analytical viewpoint,
techniques based on the covariance or correlations among
simultaneously observed variables do not necessarily provide
causal relationships. In general, additional information uniqueto the problem is necessary for judging causal relationships
among adjectives.

First process: Determine a model structure basedon causal relationships between adjectivesSensory evaluation

Samplecovariancematrix

Įmn

Į34
2

3

…

Į12

Į13

Į13 Įlm
Į1m
… l

1

m

Second process: Sensory evaluation and structural equation modelingFig. 2. Construction process of the layered model

2 M ETHOD FOR C ONSTRUCTING A M ULTILAY ERED M ODELWe propose a method for constructing a semantically multilayered model expressing subjective responses represented by
adjectives. The method consists of two processes as shown in
Fig. 2. In the first process, semantically causal relationships
among adjectives are evaluated based on a questionnaire.
Reported causal relationships determine the structure of amultilayered model [14], [24]. In the second process, which isa new attempt for the present study, undefined parameters inthe structure for the first process are statistically estimatedusing sensory evaluation and structural equation modeling.
Detailed procedures of these two processes are described in
the following sections.
To express human perceptual, affective, and hedonic responses, we used bipolar adjective pairs. Each pair is composed of adjectives with opposite meanings, such as “warmcold” and “rich-poor.” This follows standards of sensory
evaluation using adjectives as criteria.
2.1 First process: Determining model structure
based on subjective causal relationships among adjectives
The first process determines a layered structure based on
subjective causal ratings among adjective pairs. Details forthis process can be also found in [14], [24].
2.1.1 Subjective ratings on causal relationships among
adjectives
Participants touch textures that are individually presented ina randomized order. After experiencing all the textures, the(k)participant scores the semantic causality xi j between adjective
pairs i and j to the extent that the subjective evaluation
using adjective pair i influences another evaluation using
adjective pair j on a multiple-point scale (e.g., 5 = very
influential; 0 = no influence). k is an index of the participant

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3(k = 1, 2, . . . , n); i and j are indices of the adjective pairs:(i, j = 1, 2, . . . , m). Two influences between two pairs of adjectives are asymmetric; for example, although subjective ratingsfor “comfortable-uncomfortable” are expected to be affectedby those for “hard-soft,” an opposite direction is not expected.
(k)(k)
Hence, xi j is not usually identical to x ji .

a) Removal of small subjective causal relationships

2.1.2 Calculation of the effect matrix
Given that participant k rated the causal relationships among m(k)pairs of adjectives, an individual effect matrix X (k) = (xi j ) ∈Nm×m is normalized to Z (k) as follows:1
Z (k) = (k) X (k) ,(1)sb) Simplification

where s(k) based on [27] is the maximal summation of rows
or columns and is determined by)(s(k) = max

m

m

i=1

j=1

∑ xi j (k) , ∑ xi j (k)(i, j = 1, 2, . . . , m).

(2)

Next, referring to general opinions, an average effect matrix
A is computed across all participants as follows:
ai j =

1 n∑ zi j (k) ,
n k=1

(3)

where ai j and zi j (k) are elements of A and Z (k) , respectively.
This matrix indicates how much the evaluation of one adjective
pair influences the evaluation of another adjective pair.
We use the average data from all participants with theintention of exemplifying our computational method. However,their responses are individually different. It is also recommended to apply our method to a small group of participants
with similar effect matrices [24].
2.1.3 Construction of a multilayered structure based on
the effect matrix
Using the average effect matrix A, a multilayered structure of
adjectives is determined. The structure is expressed as a graphand consists of nodes and directional arcs, which represent
adjectives and the effects among adjectives, respectively. As
shown in Fig. 3a, when an element ai j of A is greater thana given threshold, a directional arc is set from adjective pairs
i to j. If ai j is small, considering the natural fluctuation ofquestionnaire answers, then we can reasonably judge that a
direct effect from i to j does not exist.
A model structure varies according to a selected thresholdvalue. There is no standard threshold value, and it should
be determined based on objectives of the analysis. When athreshold value is smaller, the number of nodes and arcs
will typically become greater, thereby resulting in a more
complex structure containing weak connections. Nonetheless,statistically non-significant arcs are removed during subsequent structural equation modeling analysis. A developer oflayered models can select a threshold value according tohis/her purpose for modeling. For example, if a developer
would like to show a simple structure with a small numberof strong connections for briefly interpreting a relationshipamong adjectives, s/he should choose a greater threshold value.

f

0.05

f

0.8

0.3
0.01

e
0.5

e

0.02

Remove arcs
with small aij

d

d

l

l

j

k

g

h

j

i

g

k

h

i

Correlated

Fig. 3. Construction of the model structure. a) Removalof arcs with subjective effects smaller than a threshold. b)
Rule for omitting the arc while maintaining reachability.

In the latter part of this article, we introduce simple anddetailed model examples with two different threshold values.
For model simplification, we minimize the number of arcs
while maintaining reachability among nodes, because sucharcs are unnecessary to inform causal relationships amongnodes. For example, as shown in Fig. 3b, the arc between
nodes h and l is omitted when three arcs occur across thethree nodes h, k, and l. Even after this removal, node l isstill reachable from node h by way of node k. Similarly,
the direct arc from nodes i to l is removed. In exchange forclarity, the simplified structure models the observed data lessaccurately. Hence, simplification is an optional procedure. In
the present study, we employed the minimum arc set that does
not influence reachability among nodes.
Two nodes, such as nodes g and h, mutually influence. Thistypically happens when the two nodes are conceptually similar.
In the sensory evaluation task described later, the scoresfor these nodes are highly correlated. When their correlation
coefficient is very high, it is reasonable to combine them forfurther simplification, which we did not do in the present study.
Through these processes, the model structure is determined.
Root nodes that are not influenced by other nodes are locatedat the bottom of the hierarchy. Leaf nodes that do not influence
the others are located at the top of the layers. As a result, thestructure in Fig. 3b is built. This structure is expressed as aform of the effect matrix for which ai j is set to zero whenthe effect from i to j is nullified. There exists a unique effectmatrix for every directional graph. An example with numericalvalues in [24] may facilitate understanding of this process.
2.2 Second process: Optimization of the structure
based on sensory evaluation tasks and structural
equation modeling
As described in Sec. 2.1, structures are constructed basedon subjective causal relationships among adjectives. However,

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TABLE 1
Forty-six textures used in the experimentparameters in a structure, such as the influence values among
adjectives, the covariance among adjectives, and the variableerrors, remain undefined. We conduct a sensory evaluationand then statistically estimate these parameters using structural
equation modeling.

Aluminum foil cloth
Artificial grass
Coarse woven straw
Cork board
Corrugated paper
CottonCotton cloth
Crumpled paper
Denim
Fake alligator hide
Fake boa
Fake cowhide
Fake suede
Fake woven leather
Felt
Fine Japanese paper

2.2.1 Sensory evaluation for textures
Assessors, who also participate in the experiment during thefirst process, rate each textural stimulus by touching it andusing multiple-point adjective scales. The evaluated values for
all textures are normalized such that the mean and varianceare 0 and 1, respectively, for each adjective pair within aparticipant. The values are then averaged across all participants
before computing the covariance matrix among adjectives.
2.2.2 Parameter estimation using structural equation
modeling
Structural equation modeling [28], [29] is a multivariate analysis based on a covariance structure, and is used for investigating the linear relationships among observed variables.
It compares a covariance structure represented by undefinedparameters with a sample covariance matrix of variables
observed through experiments, which then estimates the undefined parameters in a structure. In the present study, the covariance structure was determined during the first process, andthe covariance matrix is sampled during the aforementioned
sensory evaluation tasks.
During a structural equation modeling analysis, a model
variable yi , that is the normalized rating for adjective pair i,
is expressed by a linear synthesis of the other variables anderror ei that follows a Gaussian distribution N(0, σi2 ):nyi = ∑ b ji y j + ei

(i ̸= j)(4)

j=1

where b ji ∈ R is the influence of y j on yi and corresponds tothe partial correlation coefficient between y j and yi . For allmodel variables, using a vector y = (yi ) ∈ Rm×1 , this equation
is written as
y = By + e(5)where B = (b ji ) ∈ Rm×m and e = (ei ) ∈ Rm×1 .
The parameters that are estimated in structural equation
model are B and e. Here, the influence of yi on y j isconstrained to be zero if the subjective effect from adjective
pairs i to j is smaller than a threshold:bi j = 0 for (i, j) ∈ O(6)where O is the set of directional arcs (i, j) for which ai j <threshold or those that were removed for simplification of themodel. In the present study, a maximum likelihood estimation
was used for an estimation of parameters such that the covariance structure, which is computed as the expected valueof yy T , approximates the sample covariance matrix among
the observed variables. The estimated covariance structure isexpressed byΣ̂ = E[yy T ].
(7)

3

Fine woven straw
Glass beads (1.5mm)
Glass beads (3.5mm)
Glass beads (5mm)
Glass beads (7mm)
Glossless vinyl sheet
Glossy vinyl sheet
Goose feathers
Iridescent sheet
Long hair fake fur
Magnolia wood
Mirror plate
Mosaic tile
Oak wood
Perforated aluminum
Pyramid rubber

Sapelli wood
Satin
Short hair fake fur
Soft fake fur
SpongeStainless scrubber
Steel wool
Tile
Towel
Urethane resin
Wall paper
Woven linen
Woven rush grass
Woven wire mesh

E XPERIMENTAL VALIDATION

To validate the proposed method, we used data from experiments conducted in [26] where touch-related subjective
responses were collected. Here, we reviewed the experimental procedures. Unlike typical studies on sensory evaluation,
we did not give participants any information regarding the
products or scenarios for which the textures would be used.
All experimental procedures, including participant recruitment,
were approved by the internal review board of the School ofEngineering at Nagoya University (#12-6).
3.1 ParticipantsParticipants were 11 student volunteers including seven men
and four women, aged 19 to 23 years, with no history of
deficits in tactile perception. Participants were unaware of thestudy objectives.
3.2 Texture stimuli
We used 46 textures listed in Table 1. Textures included awide variety of materials comprising wood, paper, fur, plastic,
and fabric. We previously checked that these textures caused
a variety of perceptual, affective, and hedonic responses. The
size of each stimulus was 90 mm × 90 mm square, which
was sufficiently large for participants to push and stroke.
Participants were not allowed to bend or grab the textures.
The textures were remained on a desk during the experiments.
Pliable and loose materials were attached to a flat plate withdouble-sided tape.
3.3 Adjective pairs representing touch-related responses
We selected adjectives based on earlier studies assessing perceptual and affective responses for tactile textures (e.g., [13]).
Those with semantic similarities and inappropriate adjectives
for which scores varied little during the tasks were excluded
a priori. As a result, 29 adjective pairs listed in Table 2
were used to represent touch-related responses. Nonetheless,example models introduced in Sec. 4 do not include all of the

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TABLE 2
Twenty-nine adjective pairs used in the experiment
Beautiful-ugly
Clean-dirty
Clear-vague
Comfortable-uncomfortable
Concrete-abstract
Dangerous-safe
Delicate-bold
Exciting-boring
Friendly-unfriendly
General-specificGood-bad
Happy-sadHard-soft
Interesting-uninteresting
Itchy-not itchy

Like-dislike
Modern-classic
Natural-artificial
Regular-irregularRich-poor
Rough-smooth
Sharp-dullSignificant-insignificant
Simple-complex
Sticky-slippery
Strange-usual
Uneven-flat
Warm-cold
Wet-dry

adjective pairs. Adjectives that are not connected with others
do not appear in the final models. The final models comprise adjectives representing the psychophysical and affective
aspects of tactile textures and terms, such as “comfortableuncomfortable” and “rich-poor,” which represent aesthetics felt
via touching textures and are helpful in manufacturing commercial products [30], [31]. We selected words such that eachpair was composed of semantically opposite adjectives. All
adjectives were presented in the participants’ native language(i.e., Japanese).
3.4 Tasks for evaluating causal relationships among
adjectives (first process)Participants rated the causal relationships among adjective
pairs during the first process, as described in Sec. 2.1.1.
Participants judged the strengths of influence between the twoamong the m adjective dyads on the basis of texture stimuli.
Each texture was placed in a box with a curtain such that
their appearance did not influence the causality rating. After
experiencing all the textures, which were presented in random
order, each participant rated the causal relationships for all
permutations of the adjective pairs: m P2 = 812, where m was
the number of adjective pairs (m = 29). The causality fromone adjective pair to another was rated using a 6-point scale
on printed forms. The order of adjectives was random forindividual stimuli. A break was taken every half-hour during
the experiment. The total evaluation time was about five hours.
3.5 Tasks for sensory evaluation (second process)
After the first experiment, participants conducted the sensory
evaluation task. Participants evaluated each of the 46 texturesby touching and using a 7-point scale in terms of the 29 bipolar
adjective pairs. Rating sheets for each adjective in a pair at anextreme end of the 7-point scale were provided. The adjective
order was randomized for each texture stimulus. Forty-six
textures were tested in random order, and each texture was
not seen in a box with a curtain. The sensory evaluation task
lasted approximately two hours, including a 15-minute break.

4

R ESULTS : M ULTILAYEREDTHEIR VALIDATIONMODELSAND

We created several adjective models by using the same experimental results. Here, two are introduced and discussed. For
the computation of structural equation modeling, we used theSEM (version 3.1) package for R.

4.1 Model structures based on subjective causal
relationships
In terms of the causal relationships among adjectives, the reported values fairly fluctuated across participants. The standard(k)deviations of the 6-grade responses xi j ranged 0.45–1.05. As
described in Sec. 2.1.2, we calculated effect matrix A expressing the average causal relationships among adjective pairs.
Using this matrix and 6-levels of threshold values, several
structures were determined. The two types of structures, as
shown in Figs. 4 and 5, were based on two threshold levels:.047 and .039. In these figures, the line type represents themagnitude of influence values estimated in Sec. 4.2.

4.2 Estimation of model parameters
We applied structural equation modeling to the acquired structures using mean subjective ratings obtained in Sec. 3.5. The
standard deviations of 7-point ratings for the same adjective
pair among participants ranged 0.77–1.62. The estimated parameters included influence values between adjectives, error
variances in adjective ratings, and covariances among adjectives enclosed with black dashed lines in Figs. 4 and 5.
Two of the multilayered models are shown in Figs. 4 and 5.
The models include the statistically significant influence values(z-test, p < .05) and listed in Tables 3 and 4. The arcs in
Figs. 4 and 5 correspond to values listed in Tables 3 and 4,
respectively. The simple model in Fig. 4 includes 21 nodes and
38 arcs, while 23 nodes and 47 arcs in the complex model are
shown in Fig. 5.
In both models, the lowest layer contained adjective pairs:“rough-smooth,” “uneven-flat,” “hard-soft,” “cold-warm,” and“sticky-slippery,” which were not affected by other nodes andwere related to the perception of material physical properties.
On the other hand, middle to high layers included the affective and hedonic adjectives. In the top layer, four types ofadjectives—“rich-poor,” “good-bad,” “happy-sad,” and “likedislike”—were observed, which were linked to individual
preferences and were more subjective than those in the lower
layers. In the complex model shown in Fig. 5, the locus of“dangerous-safe” was not determined because the lowest layer
did not influence it.
Regarding the magnitudes of influence values, as shownin Tables 3 and 4, the values from the middle to top layers
tended to be smaller than those from the bottom to middle
layers. While adjectives at the middle layers were relatively
well explained by those in the bottom layer, adjectives in the
top layers (that were related to individual preferences) were
not strongly mediated by the other adjectives.

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Good/
Bad

Delicate/
Bold

Simple/ComplexRough/
SmoothClear/
Vague

Strange/
Usual

Like/
Dislike

General/SpecialUneven/Flat

Happy/
Sad

Concrete/
Abstract

Exciting/
Boring

Hard/
Soft

Rich/
Poor

Beautiful/
Ugly

Interesting/
Uninteresting

Warm/
Cold

Friendly/Unfriendly

Comfortable/
Uncomfortable

Wet/
Dry

Sticky/SlipperyFig. 4. Simple three-layered model (threshold is .047) with 21 adjective nodes. Black solid, gray solid, and gray dashedlines represent the causal relationships with magnitudes of estimated influence values of .5 and over, from .3 to .5,
and under .3, respectively. Covariances among the adjectives in the same dashed box are not shown.
Good/
Bad

Like/
DislikeExciting/
BoringBeautiful/
Ugly

Happy/
Sad

Interesting/
Uninteresting

Rich/
Poor

Friendly/Unfriendly

Comfortable/
Uncomfortable
Dangerous/
Safe

General/SpecialConcrete/
Abstract

Delicate/
Bold

Clear/
Vague
Simple/ComplexRough/
SmoothRegular/
Irregular

Sharp/
Dull

Uneven/Flat

Strange/
Usual

Hard/
Soft

Warm/
Cold

Sticky/SlipperyFig. 5. Complex 4-layered model (threshold is .039) with 23 adjective nodes.

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Rich/
Poor

Happy/Sad

Like/
DislikeGood/
Bad

Comfort./Uncomfort.

Friendly/Unfriendly

Interesting/
Unint.

Beautiful/
Ugly

Exciting/
BoringConcrete/
Abstract

General/SpecialStrange/
Usual

Clear/
Vague

Simple/Complex

Delicate/
Bold

TABLE 3
Estimated influence values among adjectives in the simple model shown in Fig. 4.

Rough/Smooth-0.48-0.81 0.75
-0.35
-0.77
-0.73
-0.36
-0.67
Uneven/Flat-0.33 -0.48
0.21
0.17
0.55
0.51
0.50
Hard/Soft
-0.33
0.52
-0.30 0.59
-0.38
Warm/Cold
0.32
Wet/Dry
0.23
-0.37
0.37
0.46
Sticky/Slip.
-0.13
0.23
Strange/Usual-0.27
Concrete/Abst.
-0.17
Exciting/Boring
0.30
0.30
-0.21
Beautiful/Ugly
0.33
Friend./Un.
0.56
Comfort./Un.
0.51
0.85
0.45
0.84
Within an adjective pair, the first word was on the positive side, and the second word was on the negative side. For example, the influence value between“rough-smooth” and “comfortable-uncomfortable” was negative, which indicates that rougher textures feel less comfortable.

Strange/Usual
General/Spec.
Concrete/Abst.
Delicate/Bold
Clear/Vague
Exciting/Boring
Beautiful/Ugly
Friendly/Un.
Comfortable/Un.
Dangerous/Safe

-0.27

0.42

Comfort./Uncomfort.

-0.53

Friendly/Unfriendly-0.85Interesting/
Unint.

-0.38

Beautiful/
Ugly

-0.66
0.59

Exciting/
BoringClear/
Vague

-0.79
0.67
1.04

Delicate/
Bold

General/Special

0.60

-0.46

Concrete/
Abstract

Strange/
Usual

-0.48

Sharp/
Dull

Regular/
Irregular

-0.47
-0.57

-0.33

-0.33

0.43

0.11

-0.27
0.65
-0.32

0.33
-0.34
-0.43

-0.18

0.64

Rich/
Poor

Happy/Sad

Like/
Dislike

0.75
Good/
Bad

Rough/Smooth
Uneven/Flat
Hard/Soft
Warm/Cold
Sticky/Slip.
Simple/Comp.
Regular/Irreg.
Sharp/Dull
Strange/Usual

Simple/Complex

TABLE 4
Estimated influence values among adjectives in the complex model shown in Fig. 5

0.25
-0.13
-0.21
0.20
0.20
0.37
0.21
0.18
0.44

0.25
0.68

0.33
-0.18
0.56
0.43
0.16

0.54
0.49

4.3 Model validity
There are no standards for validating the multilayered and multidimensional structure of human tactile responses. Thus, weemployed multiple criteria and validated the models via quantitative and semantic approaches. For the former approach, we
assessed similarities among covariance matrices between theobservation and estimation. For the latter approach, the models
estimated in the present study were semantically comparedwith those in earlier studies. Both validation types are equallyvalued.

4.3.1 Quantitative assessment
To quantitatively assess the estimated models, we computed fit
indices demonstrating the extent to which a model represents
results of the sensory evaluation. Among several types ofindices [32], [33], we used the following two most popular
indices.
The goodness-of-fit index (GFI) assesses the entire modeland is computed by
GFI = 1 −tr((Σ̂−1 S − E)2 )tr((Σ̂−1 S)2 ),(8)

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8

GFI and CFI

Simple modelin Fig. 4

Complex modelin Fig. 5

1
0.8
0.6
0.4

GFI
CFI

0.2
0
0.03

0.035

0.04

0.045

0.05

0.055

0.06

Threshold value

Fig. 6. Threshold values for model structure vs. GFI and
CFI
where S, Σ̂, and E are the sample covariance matrix of theadjective ratings, the covariance matrix of the model estimatedfrom (7), and unit matrix, respectively. S was computedby using the adjective ratings averaged over all participants.
Here, tr(C 2 ) is tr(CC T ). If a constructed model explains themeasured data well, S and Σ̂ are similar, and GFI is close to
its maximum value of 1.
We also used the comparative fit index (CFI) [34] forwhich the sample size and degrees of freedom of the model
are considered and is used to compare models with different
degrees of freedom. The CFI ranges from 0–1, and a greater
value indicates better fit. The .90–.95 criterion is used to judge
model acceptability [33].
The GFI and CFI values are shown in Fig. 6 for the six
types of threshold values (.035, .039, .043, .047, .051, and.055). The simple model (threshold = .047) in Fig. 4 exhibitedthe largest GFI (0.73) and CFI (0.93) among the six models.
When a threshold greater than .047 was used, the model’s
structure was overly simplified (e.g., the model based on thethreshold value of .055 had merely two featureless layers),
which resulted in a decrease in fitness. On the other hand,when the threshold was smaller than .047, fitness decreased
because of an increase in the number of adjectives that scarcelyaligned with the observed data.
In order to investigate robustness of the model against
individuality, we conducted a leave-one-out test where a CFI
value was computed by involving a model based on 10
out of 11 participants to estimate the response of the 11th
participant. This test was performed for every participant. Withthe threshold value at .047, the CFI average and standard
deviation were .91 ± .04, which suggests the model fairly
estimates excluded participant responses.
Nonetheless, these indices do not exclusively corroborate
the model with the highest values especially because GFIand CFI grossly assess similarities between the observed andestimated covariance matrices.
4.3.2 Semantic validity: Layered structure
Models with more than three layers are uncommon in previous
studies. Therefore, a method for discussing semantic validityof a multilayered model has not yet been established. It isreasonable to compare the present models and those fromearlier studies wherein multilayered and multidimensional
responses were structured.
Table 5 summarizes the adjectives included in the structured
layers from previous studies where perceptual and affective
responses for tactile textures were examined. Although previous studies used different adjectives and texture stimuli, acomparison of adjectives at each layer is fairly meaningful.
Except for studies [12] and [21], most reported two-layered
structures that were composed of perceptual and affective
layers. Chen et al. [12] employed a three-layered structure,
and Kidoma et al. [21] did not classify adjectives in discrete
layers. These studies share common traits in terms of adjective
loci, as discussed below.
4.3.2.1 Psychophysical layer: All models in Table 5
allocated adjectives that are directly linked to the perceptionof physical properties at the bottom of the layered model.
These pairs are typically “rough-smooth,” “hard-soft,” “coldwarm,” and “sticky-slippery.” Some studies used “bumpy,”
which corresponds to “uneven” in the present study. We did
not use adjectives that are accompanied with fibers, suchas “fluffy” and “hairy,” whereas a few previous studies employed these terms. Researchers agree that these adjectives areplaced at the bottom layer. Our computational method is also
consistent with previous studies regarding the bottom layer.
Nonetheless, rationales employed in earlier studies require
further confirmation.
4.3.2.2 Affective and hedonic layers: None of the adjectives in the middle to high layers listed in Table 5 directly
express physical stimulus properties. We may be able toclassify these adjectives into further groups, as adjectives
expressing physical attributes and affective and hedonic aspects, even if their boarders are unclear. Adjectives related
to physical stimulus attributes would comprise words suchas “regular,” “simple,” “natural,” “dangerous,” and “sharp.”
Hedonic words comprise “rich,” “premium,” “like,” “good,”“enjoyable,” “pleasurable,” “comfortable,” and “significant.”
The other words are comprehended in the group of affective
words. In the two-layered models in reflected in Table 5, thesewords collectively appear in the upper layer. In contrast, forthe three-layered models, these words tend to constitute further
layers.
The model reported in Chen et al. [12] is comprisedof one psychophysical and two affective layers in which
psychophysical words influence the middle and top affective
layers. “Natural” and “simple,” which express the textures’
physical attributes, are included in the middle layer whereas“pleasurable” and “premium,” which express hedonic aspects,
are in the top layer. Other affective words appear in the middle
and top layers.
Kidoma et al. [21] used the same set of adjectives as thepresent study and created a hierarchical model. Although they
did not use a clearly layered structure, adjectives regarded as
attribute words, such as “natural,” “clear,” “dangerous,” and“sharp,” were placed in the lower portion of the hierarchy. Hedonic adjectives comprising “significant,” “rich,” and “good”
were placed in the higher portion.
In the present model, the hedonic and attribute adjectives were also located in the higher and lower portions,This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TOH.2018.2840703, IEEE
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TABLE 5
Adjectives included in multilayered models of related studies. Representative adjectives are listed for [6], [13], [15].
The present model is based on the complex one shown in Fig. 5. The bottom row represents the psychophysical layer
and the top rows represent the affective and hedonic layers. This table is in part from the authors’ earlier study [21].
Present modelGood, like,
happy, richExciting,
beautiful,interesting,friendly,
comfortable
General, concrete,delicate, clear

Simple, regular,
sharp, strange

Rough, uneven,
hard, sticky, warm

Kidomaet al. [21]Significant
Exciting, delicate,
general,interesting

Chen et al. [12]Clean, itchy,
modern, regular,
like, happy

Sharp, natural,clear, dangerous,
sharp
Rough, uneven,
hard, sticky, wet,warm

Ackerlay
et al. [6]Matsuoka
et al. [23]Drewing
et al. [15]Enjoyable,
exciting, sexy,relaxing, calming,
comfortable,
sensual, irritating

Enjoyable,pleasurable,
relaxing, calming,
comfortable,
sensual, arousing,irritating

High-quality,
high-class,luxurious,
genuine, elegant,
adult, casual,delicate, simple

Relaxing,
pleasant,
pleasurable,
comfortable,
irritating,exciting,
dominant,
awesome

Bumpy, lumpy,
firm, hard, fuzzy,
fluffy, hairy, wet,greasy, cold,
slipperyWarm, hard,fluffy, thick,elastic,
voluminous,
bumpy, smooth,slippery, dry

Playful,pleasurable,
sophisticated,premium,
precious, exciting

Beautiful, rich,
good

Comfortable,
strange, friendly,
concrete

Guest et al. [13]Natural,indulgent,sensual, relaxing,
delicate, simple

Rough, hard,
warm, sticky, dry

Hot, rough,coarse, sticky,
hard

respectively. The hedonic adjectives including “good,” “like,”“happy,” and “rich” were in the highest layer. Additionally,“beautiful-ugly,” which is considered a hedonic pair, waslocated in the higher portion. Attribute words such as “sharp,”“regular,” “simple,” and “strange” were in the relatively lower
place. A substantial inconsistency between the present modeland the one by Kidoma et al. [21] is the positions of “general”
and “delicate.” These two adjectives were in the higher placein the previous model [21] whereas they are in the lower or
middle layer in the present model. Both models may reasonably explain their own data, and a quantitative comparison of
two models with different mathematical bases is difficult.

Nonetheless, it should be noted that affective and hedonic
words were not clearly separated, as in the experiment conducted by Guest et al. [13] who investigated whether hundredsof adjective words were semantically categorized into threegroups: namely, sensory, emotional, and evaluative words.
Emotional words, which we call affective words, were referred
to as feelings experienced by touch. Evaluative words referredto the overall significance or importance of touch experiences,which corresponds to hedonic words. Emotional and evaluative
words were not clearly separated whereas sensory words weresegregated by emotional and evaluative words. Because of
the nature of affective and hedonic adjectives, this semantic
assessment does not fully validate the model.

Fluid, rough,hard, heavy,
granular, fibrous

4.3.3 Semantic validation: Representative connections
between adjectives
It is important that the connections in the model are semantically valid. Connections with large influence values in themodels of Figs. 4 and 5, are easily interpreted. Here, we
mention the validity of those with influence values greaterthan 0.5.
First, the connections between “comfortable” and the highest layer (“like,” “rich,” and “good”) indicate that comfortablestimuli were positively evaluated, which is fairly acceptable.
Further, the models indicate that rough or uneven textureswith characteristic asperity on their surfaces were felt as
strange (unusual). Uneven textures were also felt as special
than general. Those textures lead to interesting and exciting(non-boring) experiences. At the same time, rough or uneventextures typically cause negative feelings such as “uncomfortable” and “ugly.” Conversely, smooth and flat textures are felt
as simple and beautiful as in Fig. 5. These connections makereasonable sense.
In the complex model shown in Fig. 5, soft textures werefelt as special and delicate. When the majority of the texture
stimuli were rigid, soft textures might have caused special(non-general) feelings. Additionally, soft surfaces would be
regarded as delicate because they exhibit vulnerable impressions.
The abovementioned connections are semantically sound.
In contrast, a few connections are not easily interpreted.
The connections among “rough,” “uneven,” “abstract,” and“vague” are difficult for us to explain. This may be in

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part because “abstract” and “vague” are unfamiliar for theparticipants to express their tactile feelings. These connections
are statistically effective for estimating the results of thesensory evaluation tasks, although their substantial causality
is inconclusive.

5

D ISCUSSION : G UIDANCETOESTABLISH

THE MULTILAYERED MODEL

The validity of the models was mainly discussed in Sec. 4.3.
Here, we describe how the method in the present study should
be used while mentioning some warnings and limitations.
5.1 Model dependence on stimulus and adjective
sets
Similar to other studies involving sensory evaluation, a userof the method developed in this study must remember thatthe established model depends on the stimulus set. This isbecause the method is based on linear analysis techniques,
which best approximate nonlinear phenomena within a region
where the sample was observed. Hence, we should not expectthat the model can estimate human responses for the categoryof stimuli that were not used in the experiment. Additionally,for better estimation, a limited set of stimuli that the user isinterested in should be tested instead of haphazardly using awide variety of stimuli. In other words, our method is notintended to establish a general model of various types oftextures but for a model of a set of relatively similar textures
for which linear approximation applies, whereas we used a
broad type of surfaces in the present study. A model basedon linear methods less accurately explains various types oftextures, but it does so for textures belonging to a limited
category.
Determining a minimum adjective set is an open question,although the complete list of adjectives was proposed by Guest
et al. [13]. One suggestion is that every adjective that is likely
to be located in the lower or middle layers is better included.
If adjectives in the lower layers are missing, those in the upper
layers are not well explained by the model.
5.2 Setting threshold values for flexible modeling
The complexity of the model structure, which is represented by
the numbers of nodes, arcs, and layers, can be changed by thethreshold value. This threshold is a parameter that makes themodel flexible and allows us to acquire several models withdifferent complexity. A model based on a greater threshold
will become a simple one containing fewer nodes and arcs,
which is suitable for easily understanding a model of human
responses. On the other hand, for a detailed analysis or an
application to product design, a complex model with a higher
fitness index is better in terms of accurate prediction of human
responses. Nonetheless, it is not true that the more complex
model exhibits better fitting accuracy as shown in Fig. 6. Thus,in determining the structure of a model, we recommend thatseveral threshold values are tested.

5.3 Validity check of the model
We propose checking the following four items to test thesoundness of the model. The first two items should be satisfied
while meeting the others is preferable.
First, the fit indices for structural equation modeling shouldbe acceptably high. Otherwise, the model does not explain
the observed data. In this study, we assessed the models in
Sec. 4.3.1 from this aspect.
Second, there should not be semantically wrong connections among adjectives in the model. In general, structural
equation modeling may produce impractical models, which
are nonsense in terms of causality, because it is merely amathematical optimization process. At least, connections thatare estimated to be strong should be reasonably interpreted
as in Sec. 4.3.3. Nonetheless, our method hardly allows
irrational connections among adjectives because of the firstprocess where connections are set based on subjective causal
relationships among adjectives.
Third, psychophysical (sensory or perceptual) adjectives are
better located at the bottom of the layered model. As discussed
in Sec. 4.3.2, all earlier studies are consistent with this point.
The adjectives directly linked to the physical properties of texture stimuli are semantically the causes of affective responses.
Finally, it is preferable that hedonic adjectives are locatedin the higher level of the model, and adjectives relating to
the physical attributes of textures are in the middle level ofhierarchy. Nonetheless, because of the reasons discussed inSec. 4.3.2, it is not given that this property is necessary.

6

C ONCLUSION

We presented a computational method of a semantically multilayered model expressing subjective responses to touching
textures. The proposed method comprises two processes consisting of structure construction and estimation of parametersin the structure. This combination allows us to overcome adrawback of earlier modeling methods based on multivariate
analyses, that correlations among the ratings of adjectives
are never transformed into causal relationships among theadjectives. In the first process, the causal relationships among
adjectives are subjectively rated for construction of a layered
model structure. In the second process, structural equation
modeling optimizes the unknown parameters of the model
acquired in the first process such that the model is corroborated
by data from sensory evaluation tasks.
To practice the developed method, using the data collectedin [26], we constructed models to represent the relationships
among touch-related adjectives. The two models that we elaborated on comprise three types of layers that include adjectives
representing psychophysical, affective, and hedonic responses.
The models were validated from multiple viewpoints including
quantitative and semantic assessment. The developed methodof connecting subjective responses to touching textures will
help in the estimation and analysis of various feelings madeby product surfaces.

ACKNOWLEDGMENT
This work was in part supported by MEXT JSPS Kakenhi(15H05923).

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Hikaru NAGANO received M.S. and Ph.D. degrees in engineering in 2012 and 2015, respectively, from Nagoya University. He has been with
the Graduate School of Informatics, Tohoku University as an assistant professor since 2015. His
research interests include human perception,
haptics, and robotics.

Shogo OKAMOTO received a B.S. degree inengineering from Kobe University in 2005, and
M.S. and Ph.D. degrees in information sciencesin 2007 and 2010, respectively, from the Graduate School of Information Sciences, Tohoku University. Since 2010, he has been with the Graduate School of Engineering, Nagoya University.
His research interests include haptic interfaces
and human-assistive technology.

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Yoji YAMADA received a Ph.D. degree from theTokyo Institute of Technology, Japan, in 1990.
He has been an associate professor at the Toyota Technological Institute, Nagoya, Japan since1983. In 2004, he joined AIST as a group leaderof the Safety Intelligence Research Group at theIntelligent Systems Research Institute. In 2008,
he moved to the Graduate School of Engineering, Nagoya University, as a professor.

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