need help on normalize scale variable (0-100)

[farah roslan]

I have an independent variable of economic freedom

econfree

of 14 countries from 1998-2016, each of which is graded on a scale from 0 to 100.

Can I know how to standardized or rescaled the variable between 0-1?

Thank you so much for your help!

[Joseph Coveney]

Maybe something like the following?

generate double econfree01 = econfree / 100

[ericmelse]

Farah, I suppose what you are looking for is to standardize percentile ranked data (i.e. sorted or graded from 0-100). Actually, a solution is discussed at a web page of UCLA's Institute for Digital Research and Education (IDRE): How should I analyze percentile rank data?

[farah roslan]

Dear all,

Thank you for your reply.

By the way I have found another similar page of UCLA's Institute for Digital Research and Education (IDRE) : How do I standardized variables in stata? https://stats.idre.ucla.edu/stata/fa...bles-in-stata/ . The economic freedom variable lists the ranked index up to 100 which 40-49.9 =repressed; 50-59.9 =mostly unfree; 60-69.9 = moderately free; 70-79.9 = mostly free ; 80-100= free.

Based two solutions discussed at a web page of UCLA's Institute for Digital Research and Education (IDRE), can I know which one is the most appropriate transformation for my case?

i)

 generate zscore_econfre = invnorm(econfre/100)

or

ii)

egen zeconfre = std(econfre)

list country1 econfre zscore_econfre zeconfre

     +-----------------------------------------------+
     |    country1   econfre   zscore_~e    zeconfre |
     |-----------------------------------------------|
  1. |   Australia      75.6    .6934933    .9206029 |
  2. |   Australia      76.4    .7192288    .9832404 |
  3. |   Australia      77.1    .7421441    1.038048 |
  4. |   Australia      77.4     .752085    1.061537 |
  5. |   Australia      77.3    .7487632    1.053707 |
     |-----------------------------------------------|
  6. |   Australia      77.4     .752085    1.061537 |
  7. |   Australia      77.9    .7688203    1.100685 |
  8. |   Australia        79    .8064212    1.186811 |
  9. |   Australia      79.9    .8380547    1.257278 |
 10. |   Australia      81.1    .8815873    1.351234 |
     |-----------------------------------------------|
 11. |   Australia      82.2    .9230137     1.43736 |
 12. |   Australia      82.6    .9384757    1.468679 |
 13. |   Australia      82.6    .9384757    1.468679 |
 14. |   Australia      82.5    .9345893     1.46085 |
 15. |   Australia      83.1    .9581244    1.507827 |
     |-----------------------------------------------|
 16. |   Australia      82.6    .9384757    1.468679 |
 17. |   Australia        82    .9153651    1.421701 |
 18. |   Australia      81.4    .8927334    1.374723 |
 19. |   Australia      80.3    .8523859    1.288597 |
 20. |       China      53.1    .0777838   -.8410703 |
     |-----------------------------------------------|
 21. |       China      54.8    .1206099    -.707966 |
 22. |       China      56.4    .1611186   -.5826913 |
 23. |       China      52.6    .0652185   -.8802186 |
 24. |       China      52.8    .0702433   -.8645592 |
 25. |       China      52.6    .0652185   -.8802186 |
     |-----------------------------------------------|
 26. |       China      52.5    .0627068   -.8880482 |
 27. |       China      53.7    .0928786   -.7940922 |
 28. |       China      53.6    .0903614    -.801922 |
 29. |       China        52    .0501536   -.9271964 |
 30. |       China      53.1    .0777838   -.8410703 |
     |-----------------------------------------------|
 31. |       China      53.2    .0802983   -.8332404 |
 32. |       China        51    .0250689   -1.005493 |
 33. |       China        52    .0501536   -.9271964 |
 34. |       China      51.2    .0300841   -.9898337 |
 35. |       China      51.9     .047644    -.935026 |
     |-----------------------------------------------|
 36. |       China      52.5    .0627068   -.8880482 |
 37. |       China      52.7    .0677307   -.8723888 |
 38. |       China        52    .0501536   -.9271964 |
 39. |       India      49.7   -.0075199   -1.107279 |
 40. |       India      50.2    .0050133    -1.06813 |
     |-----------------------------------------------|
 41. |       India      47.4   -.0652185   -1.287361 |
 42. |       India        49   -.0250689   -1.162086 |
 43. |       India      51.2    .0300841   -.9898337 |
 44. |       India      51.2    .0300841   -.9898337 |
 45. |       India      51.5    .0376083   -.9663447 |
     |-----------------------------------------------|
 46. |       India      54.2    .1054736   -.7549439 |
 47. |       India      52.2    .0551738   -.9115371 |
 48. |       India      53.9    .0979148   -.7784328 |
 49. |       India      54.1    .1029533   -.7627738 |
 50. |       India      54.4    .1105162   -.7392845 |
     |-----------------------------------------------|
 51. |       India      53.8    .0953963   -.7862626 |
 52. |       India      54.6    .1155616   -.7236254 |
 53. |       India      54.6    .1155616   -.7236254 |
 54. |       India      55.2     .130716   -.6766473 |
 55. |       India      55.7    .1433675    -.637499 |
     |-----------------------------------------------|
 56. |       India      54.6    .1155616   -.7236254 |
 57. |       India      56.2    .1560419   -.5983507 |
 58. |   Indonesia      63.4    .3424664   -.0346152 |
 59. |   Indonesia      61.5    .2923749   -.1833789 |
 60. |   Indonesia      55.2     .130716   -.6766473 |
     |-----------------------------------------------|
 61. |   Indonesia      52.5    .0627068   -.8880482 |
 62. |   Indonesia      54.8    .1206099    -.707966 |
 63. |   Indonesia      55.8    .1459004   -.6296695 |
 64. |   Indonesia      52.1    .0526635   -.9193669 |
 65. |   Indonesia      52.9    .0727564   -.8567294 |
     |-----------------------------------------------|
 66. |   Indonesia      51.9     .047644    -.935026 |
 67. |   Indonesia      53.2    .0802983   -.8332404 |
 68. |   Indonesia      53.2    .0802983   -.8332404 |
 69. |   Indonesia      53.4    .0853288   -.8175811 |
 70. |   Indonesia      55.5    .1383042   -.6531584 |
     |-----------------------------------------------|
 71. |   Indonesia        56    .1509692   -.6140101 |
 72. |   Indonesia      56.4    .1611186   -.5826913 |
 73. |   Indonesia      56.9    .1738289    -.543543 |
 74. |   Indonesia      58.5    .2147016   -.4182686 |
 75. |   Indonesia      58.1    .2044523   -.4495874 |
     |-----------------------------------------------|
 76. |   Indonesia      59.4    .2378467   -.3478016 |
 77. |       Japan      70.2    .5301614    .4978012 |
 78. |       Japan      69.1    .4986868    .4116751 |
 79. |       Japan      70.7    .5446416    .5369495 |
 80. |       Japan      70.9    .5504658    .5526092 |
     |-----------------------------------------------|
 81. |       Japan      66.7    .4316441    .2237632 |
 82. |       Japan      67.6    .4565423    .2942302 |
 83. |       Japan      64.3    .3664894    .0358518 |
 84. |       Japan      67.3    .4482124    .2707416 |
 85. |       Japan      73.3    .6219117    .7405211 |
     |-----------------------------------------------|
 86. |       Japan      72.7    .6037648    .6935427 |
 87. |       Japan        73     .612813    .7170319 |
 88. |       Japan      72.8    .6067755    .7013728 |
 89. |       Japan      72.9    .6097915    .7092023 |
 90. |       Japan      72.8    .6067755    .7013728 |
     |-----------------------------------------------|
 91. |       Japan      71.6    .5709994    .6074166 |
 92. |       Japan      71.8    .5769105    .6230763 |
 93. |       Japan      72.4    .5947659    .6700541 |
 94. |       Japan      73.3    .6219117    .7405211 |
 95. |       Japan      73.1    .6158401    .7248614 |
     |-----------------------------------------------|
 96. |        Laos      35.2   -.3799264   -2.242579 |
 97. |        Laos      35.2   -.3799264   -2.242579 |
 98. |        Laos      36.8   -.3371551   -2.117305 |
 99. |        Laos      33.5    -.426148   -2.375683 |
100. |        Laos      36.8   -.3371551   -2.117305 |
     |-----------------------------------------------|
101. |        Laos        41    -.227545   -1.788459 |
102. |        Laos        42   -.2018935   -1.710162 |
103. |        Laos      44.4   -.1408353    -1.52225 |
104. |        Laos      47.5   -.0627068   -1.279531 |
105. |        Laos      50.3    .0075199   -1.060301 |
     |-----------------------------------------------|
106. |        Laos      50.3    .0075199   -1.060301 |
107. |        Laos      50.4    .0100267   -1.052471 |
108. |        Laos      51.1    .0275764   -.9976635 |
109. |        Laos      51.3    .0325919   -.9820041 |
110. |        Laos        50           0    -1.08379 |
     |-----------------------------------------------|
111. |        Laos      50.1    .0025066    -1.07596 |
112. |        Laos      51.2    .0300841   -.9898337 |
113. |        Laos      51.4       .0351   -.9741743 |
114. |        Laos      49.8   -.0050133   -1.099449 |
115. |    Malaysia      68.2    .4732987     .341208 |
     |-----------------------------------------------|
116. |    Malaysia      68.9    .4930179     .396016 |
117. |    Malaysia        66    .4124631    .1689558 |
118. |    Malaysia      60.2    .2585273   -.2851644 |
119. |    Malaysia      60.1    .2559363   -.2929942 |
120. |    Malaysia      61.1    .2819263   -.2146976 |
     |-----------------------------------------------|
121. |    Malaysia      59.9    .2507596   -.3086533 |
122. |    Malaysia      61.9    .3028555   -.1520601 |
123. |    Malaysia      61.6    .2949919   -.1755493 |
124. |    Malaysia      63.8    .3531179   -.0032968 |
125. |    Malaysia      63.9    .3557872    .0045331 |
     |-----------------------------------------------|
126. |    Malaysia      64.6    .3745435    .0593404 |
127. |    Malaysia      64.8    .3799266    .0750001 |
128. |    Malaysia      66.3    .4206647     .192445 |
129. |    Malaysia      66.4    .4234048    .2002745 |
130. |    Malaysia      66.1    .4151938    .1767853 |
     |-----------------------------------------------|
131. |    Malaysia      69.6    .5129304    .4508234 |
132. |    Malaysia      70.8    .5475515    .5447797 |
133. |    Malaysia      71.5    .5680515     .599587 |
134. | New Zealand      79.2    .8133803    1.202471 |
135. | New Zealand      81.7    .9039912    1.398212 |
     |-----------------------------------------------|
136. | New Zealand      80.9    .8742172    1.335575 |
137. | New Zealand      81.1    .8815873    1.351234 |
138. | New Zealand      80.7    .8668941    1.319915 |
139. | New Zealand      81.1    .8815873    1.351234 |
140. | New Zealand      81.5    .8964733    1.382553 |
     |-----------------------------------------------|
141. | New Zealand      82.3    .9268586     1.44519 |
142. | New Zealand        82    .9153651    1.421701 |
143. | New Zealand      81.4    .8927334    1.374723 |
144. | New Zealand      80.7    .8668941    1.319915 |
145. | New Zealand        82    .9153651    1.421701 |
     |-----------------------------------------------|
146. | New Zealand      82.1    .9191827    1.429531 |
147. | New Zealand      82.3    .9268586     1.44519 |
148. | New Zealand      82.1    .9191827    1.429531 |
149. | New Zealand      81.4    .8927334    1.374723 |
150. | New Zealand      81.2    .8852903    1.359064 |
     |-----------------------------------------------|
151. | New Zealand      82.1    .9191827    1.429531 |
152. | New Zealand      81.6    .9002259    1.390382 |
153. | Phillipines      62.8    .3265609   -.0815933 |
154. | Phillipines      61.9    .3028555   -.1520601 |
155. | Phillipines      62.5    .3186394   -.1050823 |
     |-----------------------------------------------|
156. | Phillipines      60.9    .2767137   -.2303567 |
157. | Phillipines      60.7    .2715085   -.2460161 |
158. | Phillipines      61.3    .2871467   -.1990382 |
159. | Phillipines      59.1    .2301181   -.3712908 |
160. | Phillipines      54.7    .1180854   -.7157956 |
     |-----------------------------------------------|
161. | Phillipines      56.3    .1585797   -.5905212 |
162. | Phillipines        56    .1509692   -.6140101 |
163. | Phillipines        56    .1509692   -.6140101 |
164. | Phillipines      56.8    .1712846   -.5513729 |
165. | Phillipines      56.3    .1585797   -.5905212 |
     |-----------------------------------------------|
166. | Phillipines      56.2    .1560419   -.5983507 |
167. | Phillipines      57.1    .1789206   -.5278839 |
168. | Phillipines      58.2    .2070126   -.4417575 |
169. | Phillipines      60.1    .2559363   -.2929942 |
170. | Phillipines      62.2    .3107378   -.1285712 |
     |-----------------------------------------------|
171. | Phillipines      63.1     .334503   -.0581044 |
172. |   Singapore        87    1.126391    1.813184 |
173. |   Singapore      86.9    1.121677    1.805355 |
174. |   Singapore      87.7     1.16012    1.867992 |
175. |   Singapore      87.8    1.165047    1.875822 |
     |-----------------------------------------------|
176. |   Singapore      87.4    1.145505    1.844503 |
177. |   Singapore      88.2    1.185044     1.90714 |
178. |   Singapore      88.9    1.221227    1.961948 |
179. |   Singapore      88.6    1.205527    1.938459 |
180. |   Singapore        88    1.174987    1.891481 |
     |-----------------------------------------------|
181. |   Singapore      87.1    1.131131    1.821014 |
182. |   Singapore      87.3    1.140688    1.836673 |
183. |   Singapore      87.1    1.131131    1.821014 |
184. |   Singapore      86.1    1.084823    1.742717 |
185. |   Singapore      87.2    1.135896    1.828843 |
     |-----------------------------------------------|
186. |   Singapore      87.5    1.150349    1.852332 |
187. |   Singapore        88    1.174987    1.891481 |
188. |   Singapore      89.4    1.248085    2.001096 |
189. |   Singapore      89.4    1.248085    2.001096 |
190. |   Singapore      87.8    1.165047    1.875822 |
     |-----------------------------------------------|
191. | South Korea      73.3    .6219117    .7405211 |
192. | South Korea      69.7    .5157915    .4586529 |
193. | South Korea      69.7    .5157915    .4586529 |
194. | South Korea      69.1    .4986868    .4116751 |
195. | South Korea      69.5    .5100735    .4429938 |
     |-----------------------------------------------|
196. | South Korea      68.3    .4761045    .3490382 |
197. | South Korea      67.8    .4621135    .3098899 |
198. | South Korea      66.4    .4234048    .2002745 |
199. | South Korea      67.5    .4537622    .2864007 |
200. | South Korea      67.8    .4621135    .3098899 |
     |-----------------------------------------------|
201. | South Korea      68.6    .4845437    .3725268 |
202. | South Korea      68.1    .4704969    .3333785 |
203. | South Korea      69.9    .5215266    .4743126 |
204. | South Korea      69.8     .518657    .4664831 |
205. | South Korea      69.9    .5215266    .4743126 |
     |-----------------------------------------------|
206. | South Korea      70.3    .5330486    .5056314 |
207. | South Korea      71.2    .5592369    .5760978 |
208. | South Korea      71.5    .5680515     .599587 |
209. | South Korea      71.7    .5739523    .6152461 |
210. |   Sri Lanka      64.6    .3745435    .0593404 |
     |-----------------------------------------------|
211. |   Sri Lanka        64    .3584588    .0123626 |
212. |   Sri Lanka      63.2    .3371551   -.0502746 |
213. |   Sri Lanka        66    .4124631    .1689558 |
214. |   Sri Lanka        64    .3584588    .0123626 |
215. |   Sri Lanka      62.5    .3186394   -.1050823 |
     |-----------------------------------------------|
216. |   Sri Lanka      61.6    .2949919   -.1755493 |
217. |   Sri Lanka        61     .279319   -.2225271 |
218. |   Sri Lanka      58.7    .2198346   -.4026092 |
219. |   Sri Lanka      59.4    .2378467   -.3478016 |
220. |   Sri Lanka      58.4    .2121372   -.4260982 |
     |-----------------------------------------------|
221. |   Sri Lanka        56    .1509692   -.6140101 |
222. |   Sri Lanka      54.6    .1155616   -.7236254 |
223. |   Sri Lanka      57.1    .1789206   -.5278839 |
224. |   Sri Lanka      58.3    .2095742    -.433928 |
225. |   Sri Lanka      60.7    .2715085   -.2460161 |
     |-----------------------------------------------|
226. |   Sri Lanka        60    .2533471   -.3008237 |
227. |   Sri Lanka      58.6    .2172673   -.4104391 |
228. |   Sri Lanka      59.9    .2507596   -.3086533 |
229. |    Thailand      67.3    .4482124    .2707416 |
230. |    Thailand      66.9    .4371536    .2394228 |
     |-----------------------------------------------|
231. |    Thailand      66.6    .4288945    .2159336 |
232. |    Thailand      68.9    .4930179     .396016 |
233. |    Thailand      69.1    .4986868    .4116751 |
234. |    Thailand      65.8     .407011    .1532967 |
235. |    Thailand      63.7    .3504514   -.0111263 |
     |-----------------------------------------------|
236. |    Thailand      62.5    .3186394   -.1050823 |
237. |    Thailand      63.3    .3398095   -.0424451 |
238. |    Thailand      63.5    .3451255   -.0267857 |
239. |    Thailand      62.3    .3133694   -.1207416 |
240. |    Thailand        63    .3318534    -.065934 |
     |-----------------------------------------------|
241. |    Thailand      64.1     .361133    .0201922 |
242. |    Thailand      64.7    .3772335      .06717 |
243. |    Thailand      64.9    .3826221    .0828297 |
244. |    Thailand      64.1     .361133    .0201922 |
245. |    Thailand      63.3    .3398095   -.0424451 |
     |-----------------------------------------------|
246. |    Thailand      62.4    .3160034   -.1129118 |
247. |    Thailand      63.9    .3557872    .0045331 |
248. |     Vietnam      40.4   -.2430069   -1.835437 |
249. |     Vietnam      42.7   -.1840171   -1.655355 |
250. |     Vietnam      43.7   -.1585797   -1.577058 |
     |-----------------------------------------------|
251. |     Vietnam      44.3   -.1433675    -1.53008 |
252. |     Vietnam      45.6   -.1105162   -1.428295 |
253. |     Vietnam      46.2   -.0953963   -1.381317 |
254. |     Vietnam      46.1   -.0979148   -1.389146 |
255. |     Vietnam      48.1    -.047644   -1.232553 |
     |-----------------------------------------------|
256. |     Vietnam      50.5    .0125335   -1.044641 |
257. |     Vietnam      49.8   -.0050133   -1.099449 |
258. |     Vietnam      50.4    .0100267   -1.052471 |
259. |     Vietnam        51    .0250689   -1.005493 |
260. |     Vietnam      49.8   -.0050133   -1.099449 |
     |-----------------------------------------------|
261. |     Vietnam      51.6    .0401168   -.9585152 |
262. |     Vietnam      51.3    .0325919   -.9820041 |
263. |     Vietnam        51    .0250689   -1.005493 |
264. |     Vietnam      50.8    .0200544   -1.021152 |
265. |     Vietnam      51.7    .0426256   -.9506854 |
     |-----------------------------------------------|
266. |     Vietnam        54    .1004337   -.7706032 |
     +-----------------------------------------------+

.

[Maarten Buis]

Neither will solve your original question. The first one seems completely wrong to me (a graded scale is not a percentile rank score). The second is often called z-standardization. This can be ok, but it depends on what you want to do. As I said, it does not answer your original question.

[Nick Cox]

Not my field but my guess is that the economic freedom index is intended to be used to compare countries and compare time variations. Standardizing it in any way just throws away the useful information.

[farah roslan]

Dear all,

I have read in the economic freedom index (https://www.heritage.org/index/about) that

Each of the twelve economic freedoms within these categories is graded on a scale of 0 to 100. A country’s overall score is derived by averaging these twelve economic freedoms, with equal weight being given to each.

.

Yes, I now understand that the first option is wrong. However, I still have some doubt should I use the second option or just use the non-standardized one? I am intended to see does it will affect share of biomass capacity installation.

i) ordinary data (econfree)

 xtreg lhydro_share pc2 lgdp1 elec1 fdi1 econfre fit subsidy i.year, fe 

Fixed-effects (within) regression               Number of obs     =        266
Group variable: country1                        Number of groups  =         14

R-sq:                                           Obs per group:
     within  = 0.4809                                         min =         19
     between = 0.0001                                         avg =       19.0
     overall = 0.0011                                         max =         19

                                                F(25,227)         =       8.41
corr(u_i, Xb)  = -0.9833                        Prob > F          =     0.0000

------------------------------------------------------------------------------
lhydro_share |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         pc2 |  -.0655707   .0270567    -2.42   0.016    -.1188851   -.0122564
       lgdp1 |   .3450528   .0786028     4.39   0.000     .1901685    .4999372
       elec1 |   .0020581   .0017316     1.19   0.236     -.001354    .0054702
        fdi1 |   .0071978   .0058163     1.24   0.217    -.0042631    .0186587
     econfre |   .0019474   .0040192     0.48   0.628    -.0059724    .0098672
         fit |   .0692202   .0351108     1.97   0.050     .0000355    .1384049
         subsidy |   .1838791    .039527     4.65   0.000     .1059925    .2617658
             |
       year1 |
       1999  |  -.0210305   .0663552    -0.32   0.752    -.1517813    .1097204
       2000  |  -.0577933   .0669544    -0.86   0.389    -.1897249    .0741383
       2001  |  -.0805049   .0669943    -1.20   0.231    -.2125152    .0515054
       2002  |  -.0788503   .0678297    -1.16   0.246    -.2125066     .054806
       2003  |  -.0991864    .068539    -1.45   0.149    -.2342405    .0358676
       2004  |  -.1448507    .069693    -2.08   0.039    -.2821787   -.0075227
       2005  |  -.2259492   .0714347    -3.16   0.002     -.366709   -.0851893
       2006  |  -.2428903    .073753    -3.29   0.001    -.3882183   -.0975624
       2007  |   -.289154   .0807087    -3.58   0.000     -.448188     -.13012
       2008  |  -.3155979   .0812343    -3.89   0.000    -.4756676   -.1555283
       2009  |  -.3591335   .0798298    -4.50   0.000    -.5164357   -.2018313
       2010  |   -.456135   .0829548    -5.50   0.000     -.619595   -.2926751
       2011  |  -.5076699   .0847434    -5.99   0.000    -.6746543   -.3406855
       2012  |  -.5956082   .0869465    -6.85   0.000    -.7669335   -.4242828
       2013  |  -.6799752   .0888697    -7.65   0.000    -.8550903   -.5048602
       2014  |  -.7509083   .0911867    -8.23   0.000    -.9305889   -.5712277
       2015  |  -.8017971   .0941076    -8.52   0.000    -.9872333   -.6163609
       2016  |  -.8367132   .0954974    -8.76   0.000    -1.024888   -.6485385
             |
       _cons |  -7.711727   1.964041    -3.93   0.000    -11.58181   -3.841644
-------------+----------------------------------------------------------------
     sigma_u |  2.4353473
     sigma_e |  .17484565
         rho |  .99487192   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(13, 227) = 40.07                    Prob > F = 0.0000

ii) standardizing econfree

 
 egen zeconfre = std(econfre)

. xtreg lhydro_share pc2 lgdp1 elec1 fdi1 zeconfre fit subsidy i.year, fe 

Fixed-effects (within) regression               Number of obs     =        266
Group variable: country1                        Number of groups  =         14

R-sq:                                           Obs per group:
     within  = 0.4809                                         min =         19
     between = 0.0001                                         avg =       19.0
     overall = 0.0011                                         max =         19

                                                F(25,227)         =       8.41
corr(u_i, Xb)  = -0.9833                        Prob > F          =     0.0000

------------------------------------------------------------------------------
lhydro_share |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         pc2 |  -.0655707   .0270567    -2.42   0.016    -.1188851   -.0122564
       lgdp1 |   .3450528   .0786028     4.39   0.000     .1901685    .4999372
       elec1 |   .0020581   .0017316     1.19   0.236     -.001354    .0054702
        fdi1 |   .0071978   .0058163     1.24   0.217    -.0042631    .0186587
    zeconfre |   .0248723   .0513335     0.48   0.628    -.0762788    .1260234
         fit |   .0692202   .0351108     1.97   0.050     .0000355    .1384049
         subsidy |   .1838791    .039527     4.65   0.000     .1059925    .2617658
             |
       year1 |
       1999  |  -.0210305   .0663552    -0.32   0.752    -.1517813    .1097204
       2000  |  -.0577933   .0669544    -0.86   0.389    -.1897249    .0741383
       2001  |  -.0805049   .0669943    -1.20   0.231    -.2125152    .0515054
       2002  |  -.0788503   .0678297    -1.16   0.246    -.2125066     .054806
       2003  |  -.0991864    .068539    -1.45   0.149    -.2342405    .0358676
       2004  |  -.1448507    .069693    -2.08   0.039    -.2821787   -.0075227
       2005  |  -.2259492   .0714347    -3.16   0.002     -.366709   -.0851893
       2006  |  -.2428903    .073753    -3.29   0.001    -.3882183   -.0975624
       2007  |   -.289154   .0807087    -3.58   0.000     -.448188     -.13012
       2008  |  -.3155979   .0812343    -3.89   0.000    -.4756676   -.1555283
       2009  |  -.3591335   .0798298    -4.50   0.000    -.5164357   -.2018313
       2010  |   -.456135   .0829548    -5.50   0.000     -.619595   -.2926751
       2011  |  -.5076699   .0847434    -5.99   0.000    -.6746543   -.3406855
       2012  |  -.5956082   .0869465    -6.85   0.000    -.7669335   -.4242828
       2013  |  -.6799752   .0888697    -7.65   0.000    -.8550903   -.5048602
       2014  |  -.7509083   .0911867    -8.23   0.000    -.9305889   -.5712277
       2015  |  -.8017971   .0941076    -8.52   0.000    -.9872333   -.6163609
       2016  |  -.8367132   .0954974    -8.76   0.000    -1.024888   -.6485385
             |
       _cons |  -7.587399    1.92469    -3.94   0.000    -11.37994   -3.794856
-------------+----------------------------------------------------------------
     sigma_u |  2.4353473
     sigma_e |  .17484565
         rho |  .99487192   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(13, 227) = 40.07                    Prob > F = 0.0000

. 
end of do-file

Thank you for your kind help. I really appreciate this.

[Joseph Coveney]

can I know which one is the most appropriate transformation for my case?

As far as the second one

egen zeconfre = std(econfre)

you do realize, right, that you're subtracting a constant and then dividing by a constant, that it's a linear combination of the original scores?

It's the same with what I suspected that you wanted at first

summarize econfre, meanonly
generate double econfre01 = (econfre - r(min)) / (r(max) - r(min))

again, subtracting a constant and then dividing by a constant, which yields a linear combination.

(Try

graph matrix econfre zeconfre econfre01, half

to see what I mean.)

For all that effort, or even for the little effort of what's in my first post, it doesn't seem worth it to linearly transform the score into a range that your colleagues aren't used to.

With regard to

generate zscore_econfre = invnorm(econfre/100)

I'm with Nick.

[Nick Cox]

Otherwise put, the economic freedom index is based on components each on a 0 to 100 scale. So far, so good. That doesn't mean that you best use it in analysea by scaling it further.

[farah roslan]

Dear Joseph and Nick,





Yes, you are right. I shall use the ordinary variable and not scaling it further.

Thank you for your thoughtful feedback.

Have a nice day ahead!

[farah roslan]

Dear all,


I have last question, is it worth to log the economic freedom index variable to interpret it as an elasticity?

[Maarten Buis]

Does a percent more freedom make sense, i.e. is your index measured on a ratio scale with a fixed 0 point and where the distance between values is meaningful? I suspect your index is strictly speaking ordinal. You can probably get away with adding it linearly to your model, i.e. treat it as if it were measured on an interval scale. However, elasticity would be too much for my taste (though notoriously tastes differ).