One or two factor? - or something else?
RECSM Seminar 1 2010/2011
Ákos Münnich
University of Debrecen
Hungary
Barcelona 2010 October 29
Experiment 2: subjective goodness of behavior
People behave differently in a day, both good and bad.
Please indicate on the line (of circles) how much they
are good or bad for you.
very bad
very good
1. collect aid for the unemployed
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
2. shouting to his parents
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
3. help old people cross the road
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
4. smokes a joint
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
5. help in learning
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
6. donate blood for a surgery
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
7. help with the housework
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
8. steal a good quality pen from a shop
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
9. maintain the weaker
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
10. drink wine 5 dl
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
11. organize the class party
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
12. smokes a pack of cigarettes
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
13. ridicule the teacher
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
Subjective value of goodness of behaviors
response range: 1 - 53
middle: 26
larger number means more positive valuation
1 collect aid for the unemployed
2 shouting to his parents
3 help old people cross the road
4 smokes a joint
5 help in learning
6 donate blood for a surgery
7 help with the housework
8 steal a good quality pen from a shop
9 maintain the weaker
10 drink wine 5 dl
11 organize the class party
12 smokes a pack of cigarettes
13 ridicule the teacher
also principal factor analysis with promax rotation
were used
1 factor: explained variance is about 26%
2 factors: explained variance is about 40%
their correlation = -0.175
Factor weights
2-factor (promax rotation)
behavior (good-bad)
donate blood for a surgery
help in learning
help old people cross the road
maintain the weaker
help with the housework
organize the class party
collect aid for the unemployed
drink wine 5 dl
ridicule the teacher
smokes a pack of cigarettes
smokes a joint
shouting to his parents
steal a good quality pen from a shop
1-factor
1. faktor
2. faktor
0.796
0.742
0.683
0.785
0.801
0.628
-0.041
0.125
-0.178
0.681
0.653
0.531
0.436
0.051
-0.051
0.706
0.636
0.603
0.450
0.259
0.058
0.054
-0.061
0.176
0.031
0.624
0.344
-0.116
-0.183
-0.368
-0.418
0.067
0.004
-0.260
-0.267
0.604
0.643
0.379
0.586
"attitudes are commonly viewed as summary evaluations of objects
(e.g., oneself, other people, issues, etc.) along a dimension ranging
from positive to negative"
"Attitudes are therefore first and foremost evaluations."
"Attitudes are expressed in the language of 'like/dislike',
'approach/avoid', and 'good/bad'."
- attitudes are not directly observable
- attitudes can only be inferred from people's responses
(so, we need proper measurement models and techniques)
Mussweiler (2003):
"Human judgment is comparative in nature.
When people evaluate a given target, they don't do so in a vacuum.
Rather, such evaluations are made within and in relation to specific
context.
In fact, any evaluation is relative in that it refers to a comparison of
the evaluated target with a pertinent norm or stanfard."
An axiomatic characterization of
value judgments
relative to a reference point
Value judgment test situation
• A subject is faced with a set of stimuli, and
• asked to express his level of preference toward
the stimuli in task-specific ways,
• for example, by indicating on a line how much
he likes or dislikes the amount of money
offered for a particular job, or the length of a
car.
like
dislike
Value judgment test situation
(assumptions)
We suppose that the set of all possible stimuli are unidimensional
parametric in the sense, that a (not necessarily directly observable)
real number (e.g., in this example, the length of a car) is attached to
them.
The real number attached to the stimuli may reflect to a scale of a
property of the stimuli (e.g., possible amounts of money offered for
a specific job),
and will be denoted by x, y, ... , and called stimulus parameter.
This underlying property will be called the domain of the stimuli,
and x<y means that y is more then x in the domain in question.
Value judgment test situation
(more assumptions)
• The subject identifies a reference stimulus and then
compares this reference stimulus (with parameter z) with
the the test stimuli (with parameter x), and the result of
the comparison is a real number, denoted by K(x,z).
• In what follows, K is called a reference comparison
function.
• The parameter value z of the reference stimulus plays the
role of a kind of reference point (or subjective standard,
or status quo) in which the subject is more or less sure.
• The result of the comparison K(x,z) is understood as the
subjective value of the reference stimulus over the test
stimulus.
the key idea
a
reference point
0
z
y – x = (z – x) – (z – y) →
x
y
G(x,y) = H ( K(x,z), K(y,z) )
? how does function K look like ?
Unfortunately,
the solution is too general, we need more
specifications to obtain a closed formula for the
reference comparison function K.
Additive invariant comparison function
• K is additive invariant if
K(x+t,y+t)=K(x,y)
• example: in calculating the profit, the total
expenditures y can be regarded as the reference point,
and the total incoming x is compared to the total
expenditures.
• The profit is calculated relative to the total
expenditures, e.g. x-y.
• Increasing the total incomings and the the total
expenditures with the same amount will not change
the profit: (x+t)-(y+t)=x-y.
Multiplicative invariant comparison
function
• K is multiplicative invariant if
K(x t,y t)=K(x,y)
• example: the profit is not multiplicative
invariant. Multiplying x and y with the same
positive constant may substantially change the
profit. (x t - y t < > x – y)
• But a well known example is that the change
rate between two currencies is multiplicative
invariant.
Additive and multiplicative
comparison functions (assumptions)
H
additive invariant
K
multiplicative
invariant
additive invariant
multiplicative
invariant
K(x+t,y+t)=K(x,y)
H(u+r,v+r)=H(u,v)
K(x+t,y+t)=K(x,y)
H(ur,vr)=H(u,v)
K(xt,yt)=K(x,y)
K(xt,yt)=K(x,y)
H(u+r,v+r)=H(u,v) H(ur,vr)=H(u,v)
Solutions for the comparison functions
(z is the reference point)
Linear preference function and the
reference point
judgment
70
judgment
70
60
60
50
50
40
40
mean
30
A
mean
30
reference point
20
20
10
10
B
salary
25000
30000
35000
salary
40000
25000
30000
35000
40000
judgment
70
judgment
70
60
60
A
A
50
50
B
B
40
40
mean
30
20
20
10
10
salary
25000
30000
35000
mean
30
40000
salary
25000
30000
35000
40000
Log and Exp preference functions
Log function
Exp function
reference point = 1
reference point = 1
orientation = -4.5
orientation = -0.25
12
12
10
10
8
8
6
6
4
4
2
2
2
4
6
8
10
2
4
6
8
10
Testing the models by
experiments
Experiment 1: subjective value of salary
Experiment 2: subjective goodness of behavior
Experiment 3: attitude towards pollution
and two more example:
employee loyality
political behavior
Experiment 2: subjective goodness of behavior
People behave differently in a day, both good and bad.
Please indicate on the line (of circles) how much they
are good or bad for you.
very bad
very good
1. collect aid for the unemployed
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
2. shouting to his parents
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
3. help old people cross the road
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
4. smokes a joint
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
5. help in learning
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
6. donate blood for a surgery
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
7. help with the housework
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
8. steal a good quality pen from a shop
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
9. maintain the weaker
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
10. drink wine 5 dl
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
11. organize the class party
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
12. smokes a pack of cigarettes
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
13. ridicule the teacher
ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
Subjective value of goodness of behaviors
response range: 1 - 53
middle: 26
larger number means more positive valuation
1 collect aid for the unemployed
2 shouting to his parents
3 help old people cross the road
4 smokes a joint
5 help in learning
6 donate blood for a surgery
7 help with the housework
8 steal a good quality pen from a shop
9 maintain the weaker
10 drink wine 5 dl
11 organize the class party
12 smokes a pack of cigarettes
13 ridicule the teacher
the order of the behaviors are not obvious !!
the starting value of the behaviors were intuitive
starting value of the orientation parameter = -1
(because in the model it has a negative coefficient, and so, it will be increasing)
K(x,z) = γ(z – x) + ω = (γz + ω) – γx
Group means, standard error of mean
Parameters of behaviors
behaviors (good-bad)
donate blood for a surgery
help old people cross the road
help in learning
maintain the weaker
help with the housework
organize the class party
collect aid for the unemployed
ridicule the teacher
drink wine 5 dl
smokes a pack of cigarettes
smokes a joint
shouting to his parents
steal a good quality pen from a shop
parameter value
initial value
original order of
the questions
4.98
3.63
3.60
3.37
3.12
2.06
1.89
-1.16
-1.53
-3.04
-4.77
-6.04
-6.12
6
5
4
3
2
1
0
-1
-2
-3
-4
-6
-5
6
3
5
9
7
11
1
13
10
12
4
2
8
Overall fit (R2=0.86)
Observed and estimated fit by groups
group
3
7
12
19
22
24
26
28
29
30
correlation
0.82
0.89
0.91
0.91
0.80
0.90
0.88
0.97
0.95
0.94
R2
0.67
0.79
0.82
0.83
0.64
0.81
0.77
0.94
0.91
0.88
reference
point
orientation
-2.55
16.0
-2.09
-0.27
-0.57
-1.87
-1.07
-0.40
1.25
0.71
-2.93
-0.90
-2.91
-3.95
-0.79
-3.85
-3.74
-5.19
-3.10
-3.39
Group 19
all the groups (linear and group 19 nonlinear)
also principal factor analysis with promax rotation
were used
1 factor: explained variance is about 26%
2 factors: explained variance is about 40%
their correlation = -0.175
Factor weights
2-factor (promax rotation)
behavior (good-bad)
donate blood for a surgery
help in learning
help old people cross the road
maintain the weaker
help with the housework
organize the class party
collect aid for the unemployed
drink wine 5 dl
ridicule the teacher
smokes a pack of cigarettes
smokes a joint
shouting to his parents
steal a good quality pen from a shop
1-factor
1. faktor
2. faktor
0.796
0.742
0.683
0.785
0.801
0.628
-0.041
0.125
-0.178
0.681
0.653
0.531
0.436
0.051
-0.051
0.706
0.636
0.603
0.450
0.259
0.058
0.054
-0.061
0.176
0.031
0.624
0.344
-0.116
-0.183
-0.368
-0.418
0.067
0.004
-0.260
-0.267
0.604
0.643
0.379
0.586