I am trying to implement a Linear Mixed-Effects Model in Matlab. I have many repeated measures of some features in a longitudinal data set of 51 people. I considered a random intercept that varies by subject, and all the other features as fixed-effects.
These are the results that I got:
Linear mixed-effects model fit by REML
Model information:
Number of observations 1432
Fixed effects coefficients 41
Random effects coefficients 51
Covariance parameters 2
Formula:
Linear Mixed Formula with 41 predictors.
Model fit statistics:
AIC BIC LogLikelihood Deviance
-37617 -37392 18852 -37703
Fixed effects coefficients (95% CIs):
Name Estimate SE tStat DF pValue Lower Upper
'(Intercept)' 0.058824 0.00432 13.617 1391 9.9401e-40 0.05035 0.067299
'walknums' 3.7027e-15 1.7968e-09 2.0607e-06 1391 1 -3.5248e-09 3.5248e-09
'spd_MED' 1.3314e-14 1.5799e-09 8.4271e-06 1391 0.99999 -3.0992e-09 3.0993e-09
'spd_IQR' -5.2216e-15 7.2452e-10 -7.207e-06 1391 0.99999 -1.4213e-09 1.4213e-09
'TimesOut' 6.9186e-17 1.2472e-08 5.5474e-09 1391 1 -2.4466e-08 2.4466e-08
'timeout_mins' -5.3738e-16 1.528e-10 -3.5169e-06 1391 1 -2.9974e-10 2.9974e-10
'cpu_sessions' -5.37e-14 1.858e-08 -2.8902e-06 1391 1 -3.6448e-08 3.6448e-08
'cpu_time' -1.3575e-15 6.3484e-10 -2.1383e-06 1391 1 -1.2453e-09 1.2453e-09
'TransNum' 6.4053e-16 1.4996e-10 4.2712e-06 1391 1 -2.9418e-10 2.9418e-10
'SensorNum' 2.0057e-16 6.1782e-11 3.2465e-06 1391 1 -1.212e-10 1.212e-10
'TST__Total_Sleep_Time_' 1.7449e-17 2.9183e-10 5.9794e-08 1391 1 -5.7247e-10 5.7247e-10
'TTIB__Total_Time_in_Bed_' 2.2715e-16 1.9261e-10 1.1793e-06 1391 1 -3.7785e-10 3.7785e-10
'LATENCY' -8.2113e-16 7.567e-10 -1.0851e-06 1391 1 -1.4844e-09 1.4844e-09
'WASO__Wake_After_Sleep_Onset_' 3.2435e-16 1.2723e-10 2.5494e-06 1391 1 -2.4958e-10 2.4958e-10
'MIB__Motion_In_Bed_' 2.2456e-16 8.3319e-10 2.6952e-07 1391 1 -1.6344e-09 1.6344e-09
'UP_TIMES__Times_up_at_night_' 1.7083e-13 2.053e-08 8.3209e-06 1391 0.99999 -4.0273e-08 4.0273e-08
'BATHROOM_VISITS' -2.1346e-13 2.8767e-08 -7.4202e-06 1391 0.99999 -5.6432e-08 5.6431e-08
'TIME_TO_BED' 7.1692e-20 5.5363e-15 1.2949e-05 1391 0.99999 -1.086e-14 1.0861e-14
'INITIAL_LATENCY' -1.1546e-15 6.1742e-10 -1.87e-06 1391 1 -1.2112e-09 1.2112e-09
'time_walking' -9.5444e-17 2.3914e-11 -3.9911e-06 1391 1 -4.6912e-11 4.6912e-11
'timeout_MED' -4.0725e-16 1.4192e-10 -2.8695e-06 1391 1 -2.784e-10 2.784e-10
'cpu_time_MED' -1.2468e-15 6.3405e-10 -1.9664e-06 1391 1 -1.2438e-09 1.2438e-09
'TTIB_TST_ratio' -4.8356e-13 1.823e-07 -2.6526e-06 1391 1 -3.5761e-07 3.5761e-07
'WASO_TST_ratio' -3.2172e-14 1.6291e-08 -1.9748e-06 1391 1 -3.1958e-08 3.1958e-08
'UP_TIMES_TST_ratio' 1.2565e-12 4.374e-06 2.8727e-07 1391 1 -8.5804e-06 8.5804e-06
'BATHROOM_UP_TIMES_ratio' 1.7295e-13 3.2722e-08 5.2856e-06 1391 1 -6.4189e-08 6.4189e-08
'HOF_walknums' -3.6037e-18 2.0277e-11 -1.7772e-07 1391 1 -3.9776e-11 3.9776e-11
'HOF_spd_MED' -9.2077e-17 1.138e-11 -8.0912e-06 1391 0.99999 -2.2324e-11 2.2323e-11
'HOF_spd_IQR' 3.1001e-17 6.3941e-12 4.8484e-06 1391 1 -1.2543e-11 1.2543e-11
'HOF_TimesOut' 2.8602e-17 1.1486e-09 2.4903e-08 1391 1 -2.2531e-09 2.2531e-09
'HOF_timeout_mins' 6.6336e-19 1.8415e-13 3.6022e-06 1391 1 -3.6125e-13 3.6125e-13
'HOF_cpu_sessions' 3.3945e-15 1.43e-09 2.3738e-06 1391 1 -2.8052e-09 2.8052e-09
'HOF_cpu_time' 3.2927e-18 1.4125e-12 2.3311e-06 1391 1 -2.7709e-12 2.7709e-12
'HOF_TransNum' -1.6505e-19 1.4104e-13 -1.1703e-06 1391 1 -2.7668e-13 2.7668e-13
'HOF_SensorNum' -8.3677e-20 1.743e-14 -4.8007e-06 1391 1 -3.4192e-14 3.4192e-14
'HOF_TST__Total_Sleep_Time_' -1.6576e-19 1.1649e-13 -1.4229e-06 1391 1 -2.2851e-13 2.2851e-13
'HOF_LATENCY' 1.0214e-17 7.1938e-12 1.4198e-06 1391 1 -1.4112e-11 1.4112e-11
'HOF_WASO__Wake_After_Sleep_Onset_' -4.0384e-19 2.3504e-13 -1.7182e-06 1391 1 -4.6108e-13 4.6108e-13
'HOF_MIB__Motion_In_Bed_' -5.9631e-18 6.7789e-12 -8.7966e-07 1391 1 -1.3298e-11 1.3298e-11
'HOF_UP_TIMES__Times_up_at_night_' -7.9758e-15 1.8101e-09 -4.4062e-06 1391 1 -3.5508e-09 3.5508e-09
'HOF_BATHROOM_VISITS' 2.6271e-14 5.384e-09 4.8795e-06 1391 1 -1.0562e-08 1.0562e-08
Random effects covariance parameters (95% CIs): Group: subject_ID_left (51 Levels)
Name1 Name2 Type Estimate Lower Upper
'(Intercept)' '(Intercept)' 'std' 0.030846 0.029737 0.031997
Group: Error
Name Estimate Lower Upper
'Res Std' 1.543e-07 1.2435e-07 1.9147e-07
- Does this mean that none of my features is significant for the prediction of the result vector?
- Should I take all of them out of my model, or should I consider other combinations?
- Should I consider any other random effect?
Thank you for your help!
Best Answer
You ask three questions following your model output.
Regarding the first question, the fact that the non-intercept covariates are not significant does not mean that they are useless for prediction. If your dataset is not very large (you have 51 people and 41 predictors), then fitting a model this large and isolating the effects of the different covariates will be difficult. If some are not informative, they can obscure the importance of others, just like in fixed effects models.
Regarding the second question, you should try other combinations. Try to focus on the variables that you think should be the most informative first. Firstly, do you expect them to come in as a main effect, and secondly, could you expect some kind of interaction between them?
You might consider another random effect if there is another grouping that the individuals can be placed into, like they belong to a set of 15 different schools, for example. Otherwise, I would first focus on trying to improve the structure of your fixed effects model.