Table 6 Measurement invariance across language versions, gender, and income groups of the English version of the TOY8 for the four-year-old subscale

Model

CFI

ΔCFI

TLI

RMSEA (90%CI)

Δ RMSEA

SRMR

Gross motor

Language version

1a. Configural

0.958

0.928

0.029 (0.023; 0.035)

0.0269

2a. Metric

0.954

-0.004

0.920

0.031 (0.025; 0.037)

-0.002

0.0222

3a. Scalar

0.785

-1.690

0.697

0.060 (0.55; 0.065)

-0.029

0.0308

Gender

1b. Configural

0.957

0.926

0.029 (0.023; 0.035)

0.0235

2b. Metric

0.952

-0.005

0.931

0.028 (0.022; 0.033)

0.001

0.0286

3b. Scalar

0.941

-0.011

0.926

0.029 (0.024; 0.034)

-0.001

0.0271

Income

1c. Configural

0.952

0.925

0.023 (0.018; 0.028)

0.0269

2c. Metric

0.947

-0.005

0.930

0.022 (0.018; 0.027)

0.001

0.0285

3c. Scalar

0.863

-0.084

0.852

0.033 (0.029; 0.036)

-0.011

0.0315

Fine motor

Language version

1d. Configural

0.970

0.957

0.028 (0.022; 0.033)

0.0293

2d. Metric

0.966

-0.004

0.958

0.027 (0.022; 0.033)

0.001

0.0305

3d. Scalar

0.901

-0.065

0.894

0.043 (0.039; 0.048)

-0.016

0.0314

Gender

1e. Configural

0.977

0.965

0.025 (0.021; 0.029)

2e. Metric

0.978

0.001

0.972

0.023 (0.019; 0.026)

0.002

0.0259

3e. Scalar

0.980

0.002

0.978

0.020 (0.017; 0.024)

0.003

0.0288

4e. Residual

0.945

-0.035

0.939

0.033 (0.029; 0.038)

-0.013

0.0374

Income

1 f. Configural

0.981

0.971

0.019 (0.015; 0.022)

0.0247

2 f. Metric

0.979

-0.002

0.975

0.017 (0.014; 0.021)

0.002

0.0268

3 f. Scalar

0.965

-0.014

0.964

0.021 (0.018; 0.024)

-0.004

0.0277

Language

Language version

1 g. Configural

0.952

0.944

0.023 (0.021; 0.024)

0.0399

2 g. Metric

0.943

-0.009

0.935

0.024 (0.023; 0.026)

-0.001

0.0420

3 g. Scalar

0.912

-0.031

0.921

0.028 (0.024; 0.031)

-0.004

0.0591

Gender

1 h. Configural

0.950

0.942

0.023 (0.021; 0.024)

0.0522

2 h. Metric

0.950

0.00

0.944

0.022 (0.021; 0.024)

0.001

0.0528

3 h. Scalar

0.946

-0.004

0.941

0.023 (0.022; 0.024)

0.00

0.0529

4 h. Residual

0.912

-0.034

0.923

0.029 (0.023; 0.031)

-0.006

0.0601

Income

1i. Configural

0.950

0.942

0.019 (0.017; 0.020)

0.0433

2i. Metric

0.944

-0.006

0.937

0.019 (0.018; 0.021)

0.00

0.0445

3i. Scalar

0.918

-0.026

0.913

0.023 (0.022; 0.024)

-0.004

0.0440

Cognitive

Language version

1j. Configural

0.953

0.947

0.020 (0.018; 0.021)

0.0410

2j. Metric

0.949

-0.004

0.944

0.020 (0.019; 0.022)

0.00

0.0463

3j. Scalar

0.899

0.893

0.028 (0.027; 0.029)

-0.008

0.0672

Gender

1k. Configural

0.953

0.947

0.021 (0.020; 0.022)

0.0359

2k. Metric

0.952

-0.001

0.948

0.021 (0.019; 0.022)

0.00

0.0360

3k. Scalar

0.952

0.00

0.949

0.021 (0.019; 0.022)

0.00

0.0360

4k. Residual

0.951

-0.001

0.949

0.021 (0.019; 0.022)

0.00

0.0379

Income

1 l. Configural

0.951

0.944

0.017 (0.016; 0.019)

0.0310

2 l. Metric

0.943

-0.008

0.938

0.018 (0.017; 0.019)

-0.001

0.0307

3 l. Scalar

0.924

-0.019

0.921

0.020 (0.019; 0.022)

-0.002

0.0316

Personal Social

Language version

1 m. Configural

0.983

0.965

0.027 (0.019; 0.036)

0.0212

2 m. Metric

0.982

-0.001

0.968

0.026 (0.018; 0.034)

0.001

0.0293

3 m. Scalar

0.890

-0.092

0.850

0.056 (0.050; 0.063)

-0.030

0.0297

Gender

1n. Configural

0.981

0.960

0.029 (0.021; 0.038)

0.0229

2n. Metric

0.979

-0.002

0.964

0.028 (0.020; 0.036)

0.001

0.0269

3n. Scalar

0.945

-0.034

0.927

0.040 (0.033; 0.046)

-0.012

0.0263

Income

1o. Configural

0.981

0.960

0.025 (0.017; 0.032)

0.0214

2o. Metric

0.972

-0.009

0.956

0.026 (0.020, 0.032)

-0.001

0.0286

3o. Scalar

0.925

-0.047

0.913

0.036 (0.031; 0.042)

-0.010

0.0293