I am looking to determine if there are regional differences in single common measurement across time, using R.
The data is of annual frequency for 51 years (1961 to 2011) for seven regions.
The variable measured is per capita emissions.
Plotting the data visually suggests that not all regions exhibit the same trend (some appear constant, others increase/decrease while yet others look like their trends may be increasing - getting steeper).
What statistical test(s) should be used to determine if the slopes of these regional time-series trends are indeed different from each other? The measurements are likely not independent of each other within Region (behaviour is sticky), but we might presume that they are between Region...
If it helps, my dataset (in wide mts
R format) is below.
Thanks!
Year Europe Indus.Asia Lat.Am NAfr.WCAsia NAm.Oceania SSA SSE.Asia
1961 1 0.3330287 0.08342768 0.2988371 0.1970832 0.6036110 0.2771904 0.1491002
1962 2 0.3399356 0.08739431 0.3050448 0.1957801 0.6072381 0.2774883 0.1519685
1963 3 0.3497737 0.09234678 0.3064860 0.1967561 0.6188448 0.2808335 0.1513993
1964 4 0.3506815 0.09567696 0.2994094 0.1964786 0.6400042 0.2846973 0.1527038
1965 5 0.3517937 0.10081783 0.2971080 0.1959702 0.6371043 0.2882228 0.1495615
1966 6 0.3655056 0.10409945 0.3022665 0.1959077 0.6513748 0.2845789 0.1506697
1967 7 0.3751051 0.10359561 0.3085563 0.1962348 0.6527076 0.2934402 0.1529256
1968 8 0.3847365 0.10244660 0.3181694 0.2015809 0.6682721 0.2886078 0.1558793
1969 9 0.3838484 0.10135446 0.3214369 0.2004127 0.6670239 0.2939225 0.1563187
1970 10 0.3936929 0.10550931 0.3190227 0.2011312 0.6736572 0.3029824 0.1582456
1971 11 0.3911788 0.10782480 0.3005018 0.2061686 0.6810935 0.3015153 0.1555705
1972 12 0.3888467 0.10796591 0.2995851 0.2042940 0.6862982 0.2964260 0.1543937
1973 13 0.4042535 0.11137749 0.2966723 0.1998279 0.6666261 0.2920530 0.1576311
1974 14 0.4114716 0.11116291 0.3081587 0.2041539 0.6770527 0.2975302 0.1573771
1975 15 0.4088594 0.11213601 0.3195318 0.2093902 0.6990652 0.2992955 0.1605997
1976 16 0.4124370 0.11137034 0.3329371 0.2110148 0.7338768 0.2997060 0.1594188
1977 17 0.4125538 0.11234512 0.3337914 0.2126674 0.7226528 0.3039447 0.1620297
1978 18 0.4198469 0.11851035 0.3397066 0.2194563 0.7101107 0.3064783 0.1637319
1979 19 0.4232864 0.12057965 0.3380299 0.2209554 0.6810473 0.3040716 0.1602157
1980 20 0.4218926 0.12148329 0.3505814 0.2280130 0.6721993 0.3029758 0.1621418
1981 21 0.4172976 0.12375568 0.3494269 0.2311256 0.6807635 0.3051217 0.1660875
1982 22 0.4223521 0.13089340 0.3373198 0.2317372 0.6819238 0.3058660 0.1661771
1983 23 0.4261567 0.13512950 0.3316797 0.2311859 0.6781721 0.2947787 0.1713330
1984 24 0.4327464 0.13905190 0.3364816 0.2352414 0.6853792 0.2891287 0.1726075
1985 25 0.4327769 0.14014033 0.3448070 0.2415244 0.6955721 0.2943122 0.1725749
1986 26 0.4384473 0.14360094 0.3596229 0.2449454 0.6966196 0.2941324 0.1753695
1987 27 0.4409924 0.14773305 0.3481004 0.2412722 0.6998172 0.2942876 0.1750773
1988 28 0.4418265 0.14960314 0.3485329 0.2437859 0.6900106 0.2968633 0.1778406
1989 29 0.4447421 0.15081434 0.3546949 0.2384495 0.6866791 0.3024815 0.1810750
1990 30 0.4304627 0.15639769 0.3570101 0.2413544 0.6841630 0.3049107 0.1816244
1991 31 0.4142964 0.15557267 0.3595744 0.2363494 0.6824669 0.3054693 0.1803897
1992 32 0.4099102 0.16369167 0.3620947 0.2492692 0.6920663 0.3002969 0.1849306
1993 33 0.3970080 0.17536967 0.3649345 0.2463124 0.6811545 0.3011804 0.1872747
1994 34 0.3827137 0.18347220 0.3754718 0.2482677 0.7008975 0.2940523 0.1884567
1995 35 0.3823503 0.19545531 0.3861121 0.2491750 0.6987574 0.2967518 0.1917361
1996 36 0.3844043 0.20075046 0.3952523 0.2507883 0.6990538 0.3023953 0.1937828
1997 37 0.3812992 0.20906418 0.3934072 0.2484025 0.6972838 0.3041432 0.1930203
1998 38 0.3798254 0.21622077 0.3870048 0.2545955 0.7007982 0.3047103 0.1946998
1999 39 0.3773650 0.22288219 0.4024141 0.2563572 0.7167966 0.3103474 0.1975481
2000 40 0.3792981 0.23270136 0.4036371 0.2594711 0.7132213 0.3080760 0.1984123
2001 41 0.3740450 0.23275714 0.4023274 0.2531616 0.7031493 0.3120869 0.1994249
2002 42 0.3778445 0.23755244 0.4036734 0.2609872 0.7121247 0.3163197 0.1958088
2003 43 0.3830538 0.24061360 0.4048166 0.2666359 0.7032099 0.3208936 0.2019877
2004 44 0.3879519 0.24239370 0.4106120 0.2687964 0.7123248 0.3294516 0.2035080
2005 45 0.3927197 0.24813350 0.4215930 0.2742297 0.7061623 0.3348791 0.2080581
2006 46 0.3947798 0.25229643 0.4313497 0.2810117 0.7046364 0.3409603 0.2142793
2007 47 0.3980420 0.25871431 0.4414887 0.2843196 0.7053338 0.3409665 0.2222694
2008 48 0.3975002 0.26601418 0.4477263 0.2842824 0.6871963 0.3479022 0.2245092
2009 49 0.4016810 0.27165581 0.4399089 0.2869924 0.6803058 0.3448820 0.2265546
2010 50 0.3940681 0.27902452 0.4439119 0.2939435 0.6725924 0.3563978 0.2337000
2011 51 0.3887767 0.28328307 0.4481589 0.3020620 0.6633836 0.3586240 0.2358033