“…Initially, a program called PMF2 utilizes a unique algorithm (Paatero, 1997) for solving the factor analytic task. PMF2 has been used in a number of recent factor analytic studies (Anttila et al, 1995;Huang et al, 1999;Polissar et al, 1996Polissar et al, , 1998Polissar et al, , 1999Polissar et al, , 2001Prendes et al, 1999;Xie et al, 1999a;Lee et al, 1999Lee et al, , 2002Lee et al, , 2003Paterson et al, 1999;Chueinta et al, 2000;Ramadan et al, 2000;Anderson et al, 2001Anderson et al, , 2002Claiborn et al, 2002;Miller et al, 2002;Qin et al, 2002;Begum et al, 2004;Buzcu et al, 2003;Gao et al, 2003;Kim et al, 2003aKim et al, , b, 2004Larsen and Baker, 2003;Maykut et al, 2003;Qin and Oduyemi, 2003;Hien et al, 2004;Kim and Hopke, 2004a Subsequently, an alternative approach that provides a flexible modeling system, the multilinear engine (ME), has been developed for solving the various PMF factor analysis least-squares problems (Paatero, 1999). ME has already been applied to a number of environmental problems (Xie et al, 1999b;Paatero and Hopke, 2002;Hopke et al, 2003;Kim et al, 2003c;Paatero et al, 2003;Ramadan et al, 2003;Chueinta et al, 2004).…”