Same but different? Measurement invariance of the PIAAC motivation-to-learn scale across key socio-demographic groups

Gorges, Julia; Koch, Tobias; Maehler, Débora B.; Offerhaus, Judith

doi:10.1186/s40536-017-0047-5

Large-scale Assessments in Education

An IERI – International Educational Research Institute Journal

Table 6 Detailed model fit with migration background (i.e., native language same as test language) as grouping variable

From: Same but different? Measurement invariance of the PIAAC motivation-to-learn scale across key socio-demographic groups

Model	χ²	df	p	CFI	ΔCFI	RMSEA [CI]	ΔRMSEA
Australia
Configural	85.551	4	<.001	.996		.079 [.065–.094]
Weak	65.431	7	<.001	.997	+.001	.051 [.040–.062]	−.028
Strong	146.139	22	<.001	.994	−.003	.042 [.035–.048]	−.019
Austria
Configural	72.68	4	<.001	.995		.091 [.073–.110]
Weak	59.994	7	<.001	.996	+.001	.061 [.047–.075]	−.030
Strong	118.108	22	<.001	.993	−.003	.046 [.038–.054]	−.015
Canada
Configural	164.491	4	<.001	.995		.060 [.053–.068]
Weak	136.178	7	<.001	.996	+.001	.041 [.035–.047]	−.019
Strong	264.565	22	<.001	.992	−.004	.032 [.028–.035]	−.009
Denmark
Configural	37.121	4	<.001	.998		.052 [.037–.067]
Weak	35.175	7	<.001	.998	.000	.036 [.025–.048]	−.016
Strong	259.287	22	<.001	.984	−.014	.059 [.053–.065]	+.023
Partial strong	119.111	19	<.001	.993	−.005	.041 [.034–.048]	+.005
France
Configural	106.976	4	<.001	.994		.094 [.079–.110]
Weak	75.066	7	<.001	.996	+.002	.058 [.047–.070]	−.036
Strong	96.052	22	<.001	.995	−.001	.034 [.027–.041]	−.024
Germany
Configural	82.137	4	<.001	.993		.095 [.078–.114]
Weak	92.633	7	<.001	.993	.000	.075 [.062–.089]	−.020
Strong	121.364	22	<.001	.991	−.002	.046 [.038–.054]	−.029
Ireland
Configural	132.024	4	<.001	.993		.111 [.095–.127]
Weak	91.795	7	<.001	.996	+.003	.068 [.056–.081]	−.043
Strong	246.612	22	<.001	.988	−.008	.063 [.056–.070]	−.005
Italy
Configural	70.996	4	<.001	.996		.091 [.073–.110]
Weak	68.216	7	<.001	.996	.000	.066 [.052–.080]	−.025
Strong	85.641	22	<.001	.996	.000	.038 [.030–.046]	−.028
The Netherlands
Configural	57.754	4	<.001	.997		.080 [.063–.099]
Weak	46.094	7	<.001	.998	+.001	.052 [.038–.066]	−.028
Strong	110.544	22	<.001	.995	−.003	.044 [.036–.052]	−.008
Norway
Configural	37.756	4	<.001	.996		.065 [.047–.085]
Weak	31.434	7	<.001	.997	+.001	.042 [.028–.057]	−.023
Strong	254.662	22	<.001	.972	−.025	.073 [.065–.081]	+.031
Partial strong	159.394	20	<.001	.983	−.014	.059 [.051–.068]	+.017
Slovak Republic
Configural	110.189	4	<.001	.998		.108 [.091–.126]
Weak	86.835	7	<.001	.998	.000	.071 [.058–.084]	−.037
Strong	116.951	22	<.001	.998	.000	.044 [.036–.051]	−.027
Spain
Configural	144.822	4	<.001	.987		.119 [.103–.136]
Weak	142.655	7	<.001	.987	.000	.088 [.076–.101]	−.031
Strong	120.345	22	<.001	.991	+.004	.042 [.035–.050]	−.046
Sweden
Configural	37.098	4	<.001	.996		.068 [.049–.088]
Weak	27.512	7	<.001	.998	+.002	.040 [.025–.057]	−.028
Strong	160.727	22	<.001	.985	−.013	.059 [.051–.068]	+.019
Partial strong	156.084	20	<.001	.985	−.013	.061 [.053–.070]	+.021
United Kingdom
Configural	119.614	4	<.001	.995		.087 [.074–.101]
Weak	100.439	7	<.001	.996	+.001	.059 [.049–.070]	−.028
Strong	212.626	22	<.001	.991	−.004	.048 [.042–.054]	−.011
United States
Configural	100.785	4	<.001	.993		.109 [.091–.128]
Weak	74.171	7	<.001	.995	+.002	.069 [.055–.083]	−.040
Strong	109.647	22	<.001	.994	−.001	.044 [.036–.053]	−.025

df, degrees of freedom; CFI, comparative fit index; RMSEA, root mean square error of approximation; CI, confidence interval; following Cheung and Rensvold (2002) and Chen (2007), model fit of the more restrictive model should be considered to be significantly worse if the CFI drops by more than .01 and the RMSEA increases by more than .015; changes in CFI and RMSEA that exceed these cutoff values are printed in italic; partial MI has only been tested if assumptions of full MI did not hold

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