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 IEA-ETS Research Institute Journal

Table 4 Detailed model fit with age groups 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	70.339	6	<.001	.997		.071 [.056–.086]
Weak	53.053	12	<.001	.998	+.001	.040 [.029–.051]	−.031
Strong	229.439	42	<.001	.991	−.007	.046 [.040–.051]	+.006
Austria
Configural	69.963	6	<.001	.995		.088 [.070–.107]
Weak	63.326	12	<.001	.996	+.001	.056 [.043–.070]	−.032
Strong	333.863	42	<.001	.978	−.018	.071 [.064–.078]	+.015
Partial strong	165.872	38	<.001	.990	−.006	.049 [.042–.057]	−.007
Canada
Configural	138.55	6	<.001	.996		.055 [.047–.063]
Weak	143.366	12	<.001	.996	.000	.039 [.033–.044]	−.016
Strong	463.435	42	<.001	.987	−.009	.037 [.034–.040]	−.002
Czech Republic
Configural	10.956	6	<.001	.999		.023 [.000–.045]
Weak	29.365	12	<.001	.996	−.003	.031 [.017–.045]	+.008
Strong	155.095	42	<.001	.974	−.022	.042 [.035–.049]	+.011
Partial strong	108.095	38	<.001	.984	−.012	.035 [.027–.042]	+.004
Denmark
Configural	35.701	6	<.001	.998		.049 [.034–.065]
Weak	50.137	12	<.001	.998	.000	.039 [.028–.051]	−.010
Strong	250.675	42	<.001	.987	−.011	.049 [.043–.055]	+.010
Partial strong	124.509	38	<.001	.995	−.003	.033 [.027–.040]	−.006
Estonia
Configural	116.955	6	<.001	.996		.094 [.800–.110]
Weak	118.751	12	<.001	.996	.000	.065 [.055–.076]	−.029
Strong	311.634	42	<.001	.990	−.006	.056 [.050–.061]	−.009
France
Configural	105.361	6	<.001	.994		.093 [.078–.108]
Weak	92.977	12	<.001	.995	+.001	.059 [.048–.071]	−.034
Strong	266.046	42	<.001	.987	−.008	.053 [.047–.059]	−.006
Germany
Configural	66.486	6	<.001	.995		.084 [.066–.102]
Weak	49.271	12	<.001	.997	+.002	.046 [.033–.060]	−.038
Strong	250.396	42	<.001	.982	−.015	.059 [.052–.066]	+.013
Partial strong	136.768	38	<.001	.992	−.005	.043 [.035–.050]	−.003
Ireland
Configural	136.305	6	<.001	.994		.112 [.096–.129]
Weak	117.613	12	<.001	.995	+.001	.071 [.060–.083]	−.041
Strong	302.272	42	<.001	.987	−.008	.060 [.054–.066]	−.011
Italy
Configural	90.465	6	<.001	.995		.102 [.084–.121]
Weak	99.735	12	<.001	.995	.000	.073 [.061–.087]	−.029
Strong	150.705	42	<.001	.993	−.002	.044 [.036–.051]	−.029
Japan
Configural	134.913	6	<.001	.991		.121 [.104–.139]
Weak	102.297	12	<.001	.994	+.003	.072 [.059–.085]	−.049
Strong	239.764	42	<.001	.986	−.008	.057 [.050–.064]	−.015
Korea
Configural	59.904	6	<.001	.998		.069 [.054–.086]
Weak	58.323	12	<.001	.999	.001	.046 [.034–.058]	−.023
Strong	374.008	42	<.001	.989	−.010	.065 [.059–.071]	+.019
Partial strong	242.069	36	<.001	.993	−.006	.055 [.049–.062]	+.009
The Netherlands
Configural	60.941	6	<.001	.997		.081 [.063–.100]
Weak	74.174	12	<.001	.996	−.001	.061 [.048–.075]	−.020
Strong	224.406	42	<.001	.989	−.007	.056 [.049–.063]	−.005
Poland
Configural	29.587	6	<.001	.999		.049 [.032–.067]
Weak	59.505	12	<.001	.998	−.001	.049 [.037–.062]	.000
Strong	208.863	42	<.001	.991	−.007	.049 [.043–.056]	.000
Slovak Republic
Configural	102.937	6	<.001	.998		.103 [.086–.121]
Weak	106.906	12	<.001	.998	.000	.072 [.060–.085]	−.031
Strong	213.481	42	<.001	.996	−.002	.052 [.045–.059]	−.020
Spain
Configural	160.601	6	<.001	.986		.125 [.108–.142]
Weak	142.012	12	<.001	.988	+.002	.081 [.069–.093]	−.044
Strong	272.084	42	<.001	.979	−.009	.057 [.051–.064]	−.024
Sweden
Configural	19.070	6	<.001	.999		.042 [.022–.065]
Weak	23.160	12	<.001	.999	.000	.028 [.009–.045]	−.014
Strong	309.409	42	<.001	.971	−.028	.073 [.065–.080]	+.045
Partial strong	110.016	38	<.001	.992	−.007	.040 [.031–.048]	+.012
United Kingdom
Configural	106.198	6	<.001	.995		.081 [.068–.095]
Weak	86.582	12	<.001	.997	+.002	.050 [.040–.060]	−.031
Strong	363.668	42	<.001	.985	−.012	.055 [.050–.060]	+.005
Partial strong	169.435	38	<.001	.995	−.002	.037 [.031–.043]	−.013
United States
Configural	87.444	6	<.001	.994		.100 [.082–.119]
Weak	73.386	12	<.001	.996	+.002	.061 [.048–.075]	−.039
Strong	168.389	42	<.001	.991	−.005	.047 [.040–.055]	−.014

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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