We present an extension of the Linear Mixed Effects (LME) modeling approach to be applied to the mass-univariate analysis of longitudinal neuroimaging (LNI) data. The proposed method, called spatiotemporal LME or ST-LME, builds on the flexible LME framework and exploits the spatial structure in image data. We instantiated ST-LME for the analysis of cortical surface measurements (e.g. thickness) computed by FreeSurfer, a widely-used brain Magnetic Resonance Image (MRI) analysis software package. We validate the proposed ST-LME method and provide a quantitative and objective empirical comparison with two popular alternative methods, using two brain MRI datasets obtained from the Alzheimer's disease neuroimaging initiative (ADNI) and Open Access Series of Imaging Studies (OASIS). Our experiments revealed that ST-LME offers a dramatic gain in statistical power and repeatability of findings, while providing good control of the false positive rate.