Table 5 Measurement invariance across language versions, gender, and income groups of the English version of the TOY8 for the three-year-old subscale

Domain/Model

CFI

ΔCFI

TLI

RMSEA (90%CI)

ΔRMSEA

SRMR

Gross motor

Language version

1a. Configural

0.962

0.963

0.026 (0.019; 0.033)

0.0333

2a. Metric

0.958

-0.004

0.942

0.027 (0.020; 0.034)

-0.001

0.0314

3a. Scalar

0.938

-0.020

0.932

0.032 (0.026; 0.038)

-0.005

0.0309

Gender

1b. Configural

0.952

0.930

0.030 (0.023; 0.036)

0.0438

2b. Metric

0.945

-0.007

0.927

0.030 (0.240; 0.305)

0.00

0.0474

3b. Scalar

0.938

-0.007

0.928

0.030 (0.024; 0.036)

0.00

0.0474

4b. Residual

0.916

-0.022

0.904

0.035 (0.043; 0.041)

-0.005

0.0709

Income

1c. Configural

0.951

0.926

0.027 (0.022; 0.033)

0.0392

2c. Metric

0.941

-0.010

0.918

0.029 (0.023; 0.034)

-0.002

0.0442

3c. Scalar

0.912

-0.029

0.900

0.032 (0.021; 0.035)

-0.003

0.0489

Fine motor

Language version

1d. Configural

0.975

0.959

0.025 (0.014; 0.036)

0.0330

2d. Metric

0.972

-0.003

0.960

0.025 (0.015; 0.035)

0.00

0.0301

3d. Scalar

0.931

-0.041

0.914

0.037 (0.029; 0.045)

-0.012

0.0259

Gender

1e. Configural

0.983

0.973

0.020 (0.006; 0.032)

0.0363

2e. Metric

0.983

0

0.977

0.019 (0.003; 0.029)

0.001

0.0404

3e. Scalar

0.911

-0.072

0.885

0.042 (0.035; 0.050)

-0.023

0.0418

Income

1 f. Configural

0.989

0.982

0.014 (0.01; 0.025)

0.0532

2 f. Metric

0.989

0

0.986

0.012 (0.01; 0.022)

0.002

0.0531

3 f. Scalar

0.975

-0.014

0.974

0.017 (0.05; 0.025)

-0.005

0.0524

Language

Language version

1 g. Configural

0.952

0.946

0.021 (0.019; 0.023)

0.0433

2 g. Metric

0.955

0.003

0.950

0.020 (0.018; 0.022)

0.001

0.0433

3 g. Scalar

0.949

-0.006

0.946

0.021 (0.019; 0.023)

-0.001

0.0475

Gender

1 h. Configural

0.951

0.946

0.021 (0.019; 0.023)

0.0465

2 h. Metric

0.950

-0.001

0.944

0.022 (0.020; 0.024)

0.001

0.0477

3 h. Scalar

0.917

-0.033

0.911

0.028 (0.026; 0.030)

-0.006

0.0538

Income

1i. Configural

0.950

0.941

0.018 (0.017; 0.021)

0.0505

2i. Metric

0.947

-0.003

0.936

0.019 (0.017; 0.021)

-0.001

0.0611

3i. Scalar

0.909

-0.038

0.905

0.024 (0.022; 0.025)

-0.005

0.0657

Cognitive

Language version

1j. Configural

0.962

0.939

0.022 (0.019; 0.023)

0.0337

2j. Metric

0.956

-0.006

0.942

0.025 (0.018; 0.026)

-0.003

0.0403

3j. Scalar

0.932

-0.024

0.912

0.027 (0.019; 0.028)

-0.002

0.0467

Gender

1k. Configural

0.959

0.950

0.021 (0.018; 0.022)

0.0465

2k. Metric

0.950

-0.009

0.942

0.023 (0.019; 0.025)

-0.002

0.0497

3k. Scalar

0.919

-0.031

0.909

0.028 (0.025; 0.031)

-0.005

0.0578

Income

1 l. Configural

0.950

0.920

0.020 (0.019; 0.021)

0.0505

2 l. Metric

0.941

-0.009

0.907

0.024 (0.018; 0.025)

-0.004

0.0611

3 l. Scalar

0.907

-0.034

0.905

0.029 (0.021; 0.031)

-0.005

0.0657

Personal Social

Language version

1 m. Configural

0.953

0.931

0.027 (0.021; 0.034)

0.0277

2 m. Metric

0.943

-0.010

0.921

0.029 (0.023; 0.035)

-0.002

0.0327

3 m. Scalar

0.923

-0.020

0.912

0.031 (0.024; 0.037)

-0.002

0.0423

Gender

1n. Configural

0.950

0.915

0.031 (0.025; 0.038)

0.0289

2n. Metric

0.943

-0.007

0.914

0.032 (0.025; 0.038)

-0.001

0.0308

3n. Scalar

0.917

-0.025

0.891

0.035 (0.030; 0.041)

-0.003

0.0456

Income

1o. Configural

0.937

0.908

0.027 (0.021; 0.032)

0.0371

2o. Metric

0.927

-0.010

0.900

0.029 (0.024; 0.034)

-0.002

0.0542

3o. Scalar

0.910

-0.027

0.878

0.032 (0.022; 0.035)

-0.003

0.0594