why does fitlme with a random effect gives the same results to fitlme without the random effect

considering the data attached.

tbl = readtable('t.txt');

mdl1 = fitlme(tbl, 'y ~ g + (1|match)')

mdl1 = 
Linear mixed-effects model fit by ML

Model information:
    Number of observations            1134
    Fixed effects coefficients           2
    Random effects coefficients        567
    Covariance parameters                2

Formula:
    y ~ 1 + g + (1 | match)

Model fit statistics:
    AIC       BIC       LogLikelihood    Deviance
    2914.1    2934.2    -1453            2906.1  

Fixed effects coefficients (95% CIs):
    Name                   Estimate     SE          tStat      DF      pValue        Lower       Upper    
    {'(Intercept)'}        -0.087584    0.036597    -2.3932    1132      0.016864    -0.15939    -0.015779
    {'g'          }         -0.20722    0.051756    -4.0038    1132    6.6391e-05    -0.30877     -0.10567

Random effects covariance parameters (95% CIs):
Group: match (567 Levels)
    Name1                  Name2                  Type           Estimate      Lower    Upper
    {'(Intercept)'}        {'(Intercept)'}        {'std'}        1.5011e-06    NaN      NaN  

Group: Error
    Name               Estimate    Lower     Upper  
    {'Res Std'}        0.87144     0.8363    0.90805

mdl2 = fitlme(tbl, 'y ~ g')

mdl2 = 
Linear mixed-effects model fit by ML

Model information:
    Number of observations            1134
    Fixed effects coefficients           2
    Random effects coefficients          0
    Covariance parameters                1

Formula:
    y ~ 1 + g

Model fit statistics:
    AIC       BIC       LogLikelihood    Deviance
    2912.1    2927.2    -1453            2906.1  

Fixed effects coefficients (95% CIs):
    Name                   Estimate     SE          tStat      DF      pValue        Lower       Upper    
    {'(Intercept)'}        -0.087584    0.036597    -2.3932    1132      0.016864    -0.15939    -0.015779
    {'g'          }         -0.20722    0.051756    -4.0038    1132    6.6391e-05    -0.30877     -0.10567

Random effects covariance parameters (95% CIs):
Group: Error
    Name               Estimate    Lower     Upper  
    {'Res Std'}        0.87144     0.8363    0.90805

Why do they give exactly the same outputs? Presumebly the first model should be equivalent to a paird t-test

[h, p] = ttest(tbl.y(tbl.g == 1), tbl.y(tbl.g == 0))

h = 1

p = 1.0788e-04

[Peng Li]

Using other software (JMP), they clearly give different results:

upper panel without random effect, and lower panel with the random effect. The one with the random effect gives a p value the same to ttest.

Answer 1

[Ive J]

This shows the model fits well with only fixed effect and there is no variance left for random effects. Also, your observations (sample size) to group ratio is relatively small. Either increase your sample size (which I guess not possible with your current design), or simply use fitlm instead.

[Peng Li]

thanks for your answer. It is essentially a matched design, so theoretically, a matched test or mixed model (if including covariates) should be the right choice i suppose?

The JMP outputs gave different results between the models with and without random effect. And we figured out that, somehow, in JMP, it allows a negative variance of the random effect (by checking the condition "Unbounded Variance Components". If uncheck it, the variance of random effect was 0, and all became the same to matlab output, but the p value, which was due to different ways to calculate the DF i think.