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CPS1937 Xu Sun et al.
                  optimal community solution may be obtained based on any number of leading
                  eigenvectors (see Table 3).

















                   From the community structure, if the respondent and her father’s social class
                  is in the same community, the interaction between them is considered to exist,
                  then the design matrix for the community effect is defined (see Table 4.)


















                   The model with community Effects is parsimonious, the community effect only
                  used 1 degree of freedom, and the DF the new model is 24. Meanwhile,      2
                       2
                  andL substantial  decline,  it  implied  that  the  community  structure  maybe
                  implemented to improve independence model fit (see Table 5.). But, in one
                  case, including the community effect in the log-linear model does not result
                  in a model that fits the observed mobility patterns. So, the second community
                  detection for the the new residual matrix B, B is defined as A-P, A is still the
                  observed mobility table, and then P is defined as the fitted values from the
                  model with the first community Effects that are estimated. After the second
                  community detection, the model fit is improve a great deal, but the log-linear
                  model with two community effect parameters is ill-fitting for the observed
                  mobility table. So the third community detection is implemented.






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