Table 7 Measurement invariance across language version, gender and income groups of the English version of the TOY8 for the five-year-old subscale

Model

CFI

ΔCFI

TLI

RMSEA (90%CI)

ΔRMSEA

SRMR

Gross motor

Language version

1a. Configural

0.977

0.957

0.026 (0.019; 0.034)

0.0183

2a. Metric

0.974

-0.003

0.959

0.025 (0.018; 0.032)

0.001

0.0154

3a. Scalar

0.890

-0.084

0.867

0.046 (0.040; 0.051)

-0.021

0.0189

Gender

1b. Configural

0.969

0.942

0.031 (0.024; 0.038)

0.0209

2b. Metric

0.968

-0.001

0.952

0.027 (0.021; 0.034)

0.004

0.0228

3b. Scalar

0.940

-0.028

0.933

0.033 (0.028; 0.039)

-0.006

0.0229

Income

1c. Configural

0.969

0.949

0.024 (0.018; 0.030)

0.0252

2c. Metric

0.966

-0.003

0.955

0.022 (0.017; 0.028)

-0.002

0.0224

3c. Scalar

0.849

-0.117

0.855

0.040 (0.036; 0.044)

-0.018

0.0239

Fine motor

Language version

1d. Configural

0.952

0.930

0.027 (0.023; 0.031)

2d. Metric

0.946

-0.006

0.931

0.027 (0.023; 0.031)

0.00

0.0220

3d. Scalar

0.853

-0.093

0.837

0.042 (0.039; 0.045)

-0.015

0.0294

Gender

1e. Configural

0.950

0.928

0.028 (0.024; 0.032)

0.0279

2e. Metric

0.949

-0.001

0.936

0.026 (0.022; 0.030)

0.002

0.0291

3e. Scalar

0.879

-0.070

0.866

0.038 (0.035; 0.041)

0.012

0.0300

Income

1 f. Configural

0.943

0.917

0.024 (0.021; 0.028)

0.0278

2 f. Metric

0.940

-0.004

0.927

0.023 (0.020; 0.026)

0.001

0.0288

3 f. Scalar

0.871

-0.069

0.868

0.031 (0.028; 0.034)

-0.008

0.0284

Language

Language version

1 g. Configural

0.953

0.947

0.020 (0.018; 0.022)

0.0257

2 g. Metric

0.945

-0.008

0.939

0.021 (0.020; 0.023)

0.001

0.0268

3 g. Scalar

0.835

-0.110

0.827

0.036 (0.035; 0.037)

-0.015

0.0288

Gender

1 h. Configural

0.950

0.943

0.021 (0.019; 0.022)

0.0325

2 h. Metric

0.949

-0.001

0.942

0.022 (0.020; 0.023)

-0.001

0.0326

3 h. Scalar

0.946

-0.003

0.944

0.021 (0.019; 0.022)

0.001

0.0330

Income

1i. Configural

0.953

0.946

0.016 (0.015; 0.018)

0.0259

2i. Metric

0.945

-0.008

0.940

0.017 (0.016; 0.018)

-0.001

0.0265

3i. Scalar

0.874

-0.071

0.871

0.025 (0.024; 0.026)

-0.008

0.0265

Cognitive

Language version

1j. Configural

0.982

0.972

0.015 (0.019; 0.020)

0.0212

2j. Metric

0.979

-0.003

0.972

0.015 (0.010; 0.020)

0.00

0.0254

3j. Scalar

0.876

-0.103

0.858

0.034 (0.030; 0.038)

-0.019

0.0210

Gender

1k. Configural

0.977

0.965

0.017 (0.012; 0.022)

0.0245

2k. Metric

0.981

0.004

0.975

0.014 (0.009; 0.019)

0.003

0.0217

3k. Scalar

0.974

-0.007

0.9698

0.016 (0.011; 0.021)

-0.002

0.0231

Income

1 l. Configural

0.979

0.969

0.013 (0.008; 0.018)

0.0216

2 l. Metric

0.981

0.003

0.0975

0.012 (0.007; 0.016)

0.001

0.0222

3 l. Scalar

0.877

-0.104

0.870

0.026 (0.023; 0.030)

-0.014

0.0225

Personal social

Language version

1 m. Configural

0.972

0.951

0.032 (0.026; 0.038)

0.0203

2 m. Metric

0.967

-0.005

0.949

0.033 (0.029; 0.039)

-0.001

0.0171

3 m. Scalar

0.902

-0.065

0.879

0.051 (0.046; 0.056)

-0.018

0.0183

Gender

1n. Configural

0.960

0.930

0.039 (0.033; 0.045)

0.0303

2n. Metric

0.960

0.000

0.942

0.035 (0.030; 0.040)

0.004

0.0310

3n. Scalar

0.945

-0.015

0.936

0.037 (0.032; 0.042)

-0.002

0.0311

Income

1o. Configural

0.956

0.923

0.034 (0.029; 0.039)

0.0261

2o. Metric

0.946

-0.010

0.926

0.034 (0.029; 0.038)

0.00

0.0266

3o. Scalar

0.925

-0.021

0.907

0.032 (0.027; 0.0038)

-0.002

0.0302