Introduction
Nonparametric item response theory
Mokken scale analysis
Definition of Mokken’s monotone homogeneity model
Confirmatory Mokken scale analysis
Exploratory Mokken scale analysis
Comparing MSA with PAF and PCA
Empirical application
Results
University restaurant results
Criterion | Tangibles | Reliability | Responsiveness | Assurance | Empathy | |
---|---|---|---|---|---|---|
MSP: c = 0.0 | Scale 1 | t1, t4 | rl1, rl2, rl4 | rs1–rs4 | a1–a3 | e1–e5 |
Scale 2 | t2, t3 | rl3, rl5 | a4 | |||
MSP: c = 0.1 | Scale 1 | t1, t4 | rl1, rl2, rl4 | rs1–rs4 | a1–a3 | e1–e5 |
Scale 2 | t2, t3 | rl3, rl5 | a4 | |||
MSP: c = 0.2 | Scale 1 | rl1, rl2 | rs2–rs4 | a1–a3 | e1–e4 | |
Scale 2 | t1, t2, t4 | rl5 | a4 | |||
Scale 3 | rl3, rl4 | |||||
Scale 4 | rs1 | e5 | ||||
MSP: c = 0.3 | Scale 1 | e1–e4 | ||||
Scale 2 | rl2 | rs2–rs4 | a3 | |||
Scale 3 | t1, t2, t4 | |||||
Scale 4 | a1, a2 | |||||
Scale 5 | rl1, rl3-rl5 | |||||
MSP: c = 0.4 | Scale 1 | e1–e3 | ||||
Scale 2 | rs2–rs4 | |||||
Scale 3 | a1–a3 | |||||
Scale 4 | t1, t2, t4 | |||||
Scale 5 | rl3, rl4 | |||||
Scale 6 | rl1, rl2 | |||||
MSP: c = 0.5 | Scale 1 | e1, e2 | ||||
Scale 2 | rs2, rs3 | |||||
Scale 3 | a2, a3 | |||||
MSP: c = 0.6 | Scale 1 | e1, e2 | ||||
PAFa
| Fact. 1 |
t3, t4
|
rl1, rl2
|
rs3, rs4
|
a1–a3
| |
Fact. 2 |
rl2
|
rs4
|
e1–e3, e4
| |||
Fact. 3 |
rs2–rs4
|
a3
| ||||
Fact. 4 |
rl1,rl3,
rl4
,rl5 |
a3
| ||||
Fact. 5 |
t1,t2,t3,t4
|
rl2
|
a4
| |||
Fact. 6 |
rl2,rl3
| |||||
Fact. 7 |
rl1,rl2
| rs1 | e5 | |||
PCAa
| Fact. 1 |
e1–e3, e4
| ||||
Fact. 2 | t3 |
rl1
|
a1–a3,a4
| |||
Fact. 3 |
rs2–rs4
| |||||
Fact. 4 |
t1,t2,t3,t4
| |||||
Fact. 5 | rl3, rl4, rl5 | rs1 | a4 | |||
Fact. 6 |
rl2,rl3
| |||||
Fact. 7 | rl1 | rs1 | −a4 |
e5
|
Student helpdesk results
Criterion | Tangibles | Reliability | Responsiveness | Assurance | Empathy | |
---|---|---|---|---|---|---|
MSP: c = 0.0 | Scale 1 | t1–t4 | rl1–rl5 | rs2–rs4 | a1–a4 | e1–e4 |
Scale 2 | rs1 | e5 | ||||
MSP: c = 0.1 | Scale 1 | t1–t4 | rl1–rl5 | rs2–rs4 | a1–a4 | e1–e4 |
Scale 2 | rs1 | e5 | ||||
MSP: c = 0.2 | Scale 1 | t1–t4 | rl1–rl5 | rs2–rs4 | a1–a4 | e1–e4 |
Scale 2 | rs1 | e5 | ||||
MSP: c = 0.3 | Scale 1 | t1–t4 | rl1–rl5 | rs2–rs3 | a1–a4 | e1–e4 |
MSP: c = 0.4 | Scale 1 | t1, t2, t4 | rl1–rl5 | a1–a4 | ||
Scale 2 | rs2, rs3 | e1–e4 | ||||
MSP: c = 0.5 | Scale 1 | a1–a4 | ||||
Scale 2 | e1–e4 | |||||
Scale 3 | rl1–rl5 | |||||
Scale 4 | t1–t4 | |||||
Scale 5 | rs2–rs4 | |||||
MSP: c = 0.6 | Scale 1 | a1–a3 | ||||
Scale 2 | e1, e2, e4 | |||||
Scale 3 | rl1–rl4 | |||||
Scale 4 | t1, t2, t4 | |||||
PAFa
| Fact. 1 |
t1,t2,t4
|
rl1–rl5
|
rs4
| a1–a4 |
e1, e2
|
Fact. 2 |
rl1, rl2, rl5
|
rs2, rs3 |
a1, a3 |
e1–e4, e5
| ||
Fact. 3 |
rl2, rl5
|
rs3
|
a1–a4
|
e2
| ||
Fact. 4 |
t1–t4
| rl1, rl2, rl3–rl5 |
a1–a4
| |||
Fact. 5 |
rl1, rl2, rl4
| rs1, rs2–rs4
| a3 | e1, e2, e4, e5
| ||
PCAa
| Fact. 1 |
t1, t4
|
rl1–rl5
| |||
Fact. 2 |
rs2
|
e1–e4
,e5 | ||||
Fact. 3 |
rl5
|
rs3
|
a1–a4
| −e5 | ||
Fact. 4 |
t1-t4
|
rl2
|
−rs1
| |||
Fact. 5 |
rs1–rs4
|