help for ewm

The Entropy Weight Method (EWM)

ewm is a command about evaluation by the entropy weight method (EWM).

Syntax

ewm varlist [if] [in] , [ score(newvar) undes(varlist) by(varlist)
norm(method) shift(#) smooth(#) raw pv base list keep ]

score(newvar) is optional, creats a new variable which is the comprehensive score evaluated by ewm. The default new name is "EW_Score".

undes(varlist) is optional, defines undesirable variable sets. These variables should be the subset of varlist.

by(varlist) is optional, defines group (time) variable(s). The option is applied to panel, longitudinal or multidimensional data.

norm(method) is optional, specifies normalization method such as MM, MX, L1 or L2. The default method is the Min-Max normalization (i.e. norm(MM)).

shift(#) is optional, adds a number (range is (0, 1]) to standardized values. This option is not allowed with smooth(#).

smooth(#) is optional, smooths standardized values with a parameter (range is (0, 1)). The formula is a+(1-a)*x , a~(0,1).

raw is optional, uses raw data to calculating the comprehensive score. The default is using the Min-Max normalized data.

pv is optional, uses proportional data to calculating the comprehensive score. This option is not allowed with option raw.

base is optional, uses the maximum and minimum values of the base period for standardization; must be set with by(varlist).

list is optional, lists the entropy weight of varlist (their suffixes are _EW).

keep is optional, keeps the entropy weight variables of varlist (their suffixes are _EW). The default is dropped.

*** Important Notes:

1. Option shift(#), smooth(#) or base should work if option norm(method) is "MM" or "MX".

2. The formulas for normalization methods in option norm(method) are as follows:

(1) MM, i.e. max-min normalization, (Xi-Xmin)/(Xmax-Xmin) or (Xmax-Xi)/(Xmax-Xmin) (for undesirable variables) ;

(2) MX, i.e. maximization, Xi/Xmax or 1-Xi/Xmax (for undesirable variables) ;

(3) L1, i.e. sum normalization, Xi/SUM(Xi) or 1-Xi/SUM(Xi) (for undesirable variables) ;

(4) L2, i.e. vector normalization, Xi/SUM(Xi^2) or 1-Xi/SUM(Xi^2) (for undesirable variables) .

3. The command ewm may generate some variables named with preffixes or suffixes as follows:

EW_ , _EW , _SCOR , _ET , _MNRM , _MAXM , _MINM , _pc , _NMS , _EJ .

So, you should avoid to including variables names with these prefixes or suffixes.

Examples

1. Basic command example (the comprehensive score evaluated based on the Min-Max Normalized data):

. ewm x1-x10

. mat list r(EW)

. mat list r(EW) format(%6.4f)

2. Basic command example (the comprehensive score evaluated based on the raw data):

. ewm x1-x10, raw

. dis r(ew)

. local ew=r(ew)

3. Basic command example (the comprehensive score evaluated based on the proportional data, their sum is 1):

. ewm x1-x10, pv

6. Example of various normalization methods:

. ewm x1-x10, norm(MX) list

. ewm x1-x10, norm(L1) list

. ewm x1-x10, norm(L2) list

5. Extended command example:

. ewm x1-x10, sc(new_sc) undes(x3 x6 x8) list keep

. ewm x1-x10, sc(new_sc) shift(0.01) list keep

. ewm x1-x10, sc(new_sc) smooth(0.01) list keep

6. Example of panel, longitudinal or multidimensional data:

. ewm x1-x10, by(year) list keep

. ewm x1-x10, by(year) base list keep

Saved Results

Matrices

r(EW) Entropy weight matrix

Macros

r(ew) Entropy weight ; if option by(varlist) is not set

Authors

Dejin Xie, School of Economics and Management, Nanchang University, China.

E-mail: xiedejin@ncu.edu.cn.

Also see

Help: egen, entropyetc (if installed).