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{"target":"http://pubannotation.org/docs/sourcedb/PMC/sourceid/4620161","sourcedb":"PMC","sourceid":"4620161","source_url":"https://www.ncbi.nlm.nih.gov/pmc/4620161","text":"Linear mixed-effects modeling (LME)\nAs demonstrated in Chen et al. (2013), linear mixed-effects modeling (LME) can be adopted for group analysis when the HDR is estimated through multiple basis functions. Specifically, the m regression coefficients from each subject associated with the m basis functions are modeled as values corresponding to m levels of a within-subject factor under the LME framework. When no other explanatory variables are present in the model, the LME methodology can be formulated by (2a) with an intercept of 0. That is, the m effects are coded by m indicator variables instead of any conventional contrast coding. Suppose that the m effect estimates associated with the m basis functions from the ith subject are βi1, βi2, …, βim, the LME model can be specified as, βij=αjxij+δi+ϵij,i=1,2,...,n,j=1,2,...,m. where the random effect δi characterizes the deviation or shift of the ith subject's HDR from the overall group HDR, the residual term ϵij indicates the deviation of each effect estimate βij from the ith subject's HDR, and the indicator variables xij take the cell mean coding, xij={1,if ith subject is at jth level,0,otherwise. so that the parameters αj, j = 1, 2, …, m capture the overall group HDR. The significance of the overall HDR at the group level can be tested through LME on the same hypothesis as (2a), (3) H0LME:α1=0,α2=0,...,αm=0.\nIt is of note that the LME approach does not work when other explanatory variables (multiple groups, conditions, or quantitative covariates) are involved because (2a) or (2b) cannot be formulated due to the parameterization constraint through dummy coding. For instance, when there are two groups involved, the typical contrast coding for the two groups renders one dummy variable (e.g., the contrast of one group vs. the other when effect coding is adopted); however, such a coding strategy relies on the existence of an intercept in the model. If the two groups are coded by two indicator variables, the model matrix would become overparameterized.","divisions":[{"label":"title","span":{"begin":0,"end":35}},{"label":"p","span":{"begin":36,"end":1378}},{"label":"label","span":{"begin":1349,"end":1352}}],"tracks":[{"project":"0_colil","denotations":[{"id":"26578853-23376789-358041","span":{"begin":68,"end":72},"obj":"23376789"}],"attributes":[{"subj":"26578853-23376789-358041","pred":"source","obj":"0_colil"}]},{"project":"TEST0","denotations":[{"id":"26578853-32-40-358041","span":{"begin":68,"end":72},"obj":"[\"23376789\"]"}],"attributes":[{"subj":"26578853-32-40-358041","pred":"source","obj":"TEST0"}]},{"project":"2_test","denotations":[{"id":"26578853-23376789-38285030","span":{"begin":68,"end":72},"obj":"23376789"}],"attributes":[{"subj":"26578853-23376789-38285030","pred":"source","obj":"2_test"}]}],"config":{"attribute types":[{"pred":"source","value type":"selection","values":[{"id":"0_colil","color":"#ec9b93","default":true},{"id":"TEST0","color":"#93a4ec"},{"id":"2_test","color":"#beec93"}]}]}}