[R]nlminb vs optim

nlmib和optim函数在R中的区别是什么？ 我应该先用哪一个？ 哪一个更好！？或者更快？或者更准确？ 我应该相信哪一个

你们可以找到我的完整数据和我要最大化的似然函数。这两个参数相同的函数的答案完全不同，我应该相信哪一个

data <- c(59446625, 184078130, 26296875, 130769230, 110981380, 26113266, 
  32641583, 32641583, 39169899, 78339798, 58618421, 130263160, 
  195394740, 194341800, 64780600, 58302540, 45346420, 19434180, 
  343337180, 19359663, 806652610, 19359663, 204620060, 19183131, 
  25365486, 12682743, 18910112, 63033708, 25156951, 44024664, 503139010, 
  50313901, 31259287, 12485163, 62425816, 81153561, 149600000, 
  49866667, 37400000, 105966670, 261800000, 87266667, 31120562, 
  74689349, 99585799, 124482250, 41079142, 454360210, 74469027, 
  62057522, 105497790, 105497790, 99292035, 31028761, 161349560, 
  37125000, 123750000, 92812500, 30937500, 92676211, 763879940, 
  42871179, 2082314400, 30622271, 24497817, 73493450, 54960087, 
  36613488, 42500000, 12142857, 90613783, 66450108, 736992100, 
  30204594, 331774190, 361935480, 72387097, 916903230, 9.35e+08, 
  66259843, 60236220, 36012839, 258092010, 684243940, 264094150, 
  30010699, 48017118, 35935943, 47914591, 179679720, 23957295, 
  18514194000, 23821656, 83375796, 1905732500, 118688290, 29672073, 
  17803244, 41540903, 29630282, 53334507, 503714790, 41511628, 
  770930230, 35406732, 147528050, 206539270, 88207547, 599811320, 
  117200560, 2051009700, 146500700, 41020195, 75968750, 70125000, 
  99343750, 52593750, 46685160, 192576280, 17506935, 174826870, 
  256412740, 116551250, 64103186, 145689060, 553618420, 17482687, 
  17482687, 52448061, 52303177, 34868785, 23245856, 34868785, 28997243, 
  40596141, 23197795, 34653397, 69306795, 404289640, 432870370, 
  115116280, 201453490, 14389535000, 920930230, 149651160, 521993870, 
  85750679, 280118890, 28544776, 28544776, 79925373, 856343280, 
  11410169, 22820339, 11410169, 39800676, 102344590, 51172297, 
  45363881, 107739220, 56704852, 90727763, 22681941, 39533557, 
  90362416, 67771812, 112953020, 45181208, 33795181, 253294310, 
  22515050, 56287625, 197006690, 22515050, 28106212, 67454910, 
  123667330, 151773550, 263143710, 263143710, 27994012, 94488111, 
  422417440, 166743730, 38778802, 66477946, 105256750, 94177090, 
  138495720, 88637261, 470885450, 1255062400, 398081470, 99520368, 
  204569650, 22115637, 60818003, 110578190, 165540980, 27590164, 
  82770492, 110360660, 77252459, 412769780, 33021583, 961243470, 
  38449739, 2299479500, 82124268, 43828125, 191748050, 263140070, 
  654015540, 98102332, 430560230, 119902850, 801169040, 86920594, 
  70622983, 118901730, 226994220, 86473988, 86473988, 150748560, 
  328416510, 75374280, 322413790, 59109195, 161206900, 145086210, 
  403017240, 42961072, 26850670, 37590938, 75181876, 144716560, 
  117917200, 42878981, 21398601, 171188810, 10665399, 1706463900, 
  159980990, 69106128, 180739100, 143528110, 90369551, 26529004, 
  21223203, 47752207, 47752207, 31834805, 291819040, 42313011, 
  105451130, 42180451, 316353380, 199856250, 42075000, 42075000, 
  115706250, 168089890, 36769663, 236376400, 147078650, 57780899, 
  84097439, 99865709, 115633980, 83992514, 183504670, 62915888, 
  78644860, 83731343, 125597010, 171840970, 41684211, 46952883, 
  208292080, 181917850, 77964793, 88360099, 36383570, 103953060, 
  36383570, 72632552, 31128237, 207521580, 155353850, 315886150, 
  31013514, 217094590, 46520270, 1390439200, 196418920, 98209459, 
  671959460, 221990800, 180690180, 51625767, 309754600, 149714720, 
  216828220, 413006130, 92812500, 77249082, 66949204, 154498160, 
  370795590, 267469440, 113160150, 3039893000, 112884150, 174457320, 
  205369130, 773381010, 588998780, 169017040, 307303710, 5.1e+07, 
  192400720, 303790610, 75947653, 394927800, 151895310, 1503763500, 
  197463900, 86074007, 86074007, 227842960, 71897112, 192400720, 
  55694946, 136295740, 166583680, 161535690, 206967610, 30215440, 
  60430880, 1964669400, 100059450, 1.65e+08)
f.like <- function(p, x)
{
  e <- p[3] * p[1] * p[2]^p[1] * x^(p[3] - 1) * (p[2] + x^p[3])^(-(p[1] + 1))
  -sum(log(e))
}

> nlminb(c(1, 2, 3), f.like, x = data)
$par
[1] 7.458577e+01 1.386598e+04 2.881954e-01

$objective
[1] -Inf

$convergence
[1] 0

$iterations
[1] 39

$evaluations
function gradient 
      65      140 

$message
[1] "X-convergence (3)"

There were 12 warnings (use warnings() to see them)
> optim(c(1, 2, 3), f.like, x = data)
$par
[1]   58.2277186 2902.3301013    0.2398371

$value
[1] 7218.866

$counts
function gradient 
     502       NA 

$convergence
[1] 1

$message
NULL

There were 15 warnings (use warnings() to see them)

数据
出于计算稳定性的原因，建议在表达式中使用日志：

loglik <- function(p, x){
    e <- log(p[3]) + log(p[1]) + log(p[2])*p[1] +
         log(x)*(p[3] - 1) + log(p[2] + x^p[3])*(-(p[1] + 1))
    -sum(e)
}

all.equal(f.like(p=c(1,2,3), x=data),
          loglik(p=c(1,2,3), x=data))
[1] TRUE

我们可以将其与nlminb（）进行比较：


两种方法都发现一些参数在0附近，即在域边界附近。这可能会导致收敛问题

出于计算稳定性的原因，建议在表达式中使用日志：

loglik <- function(p, x){
    e <- log(p[3]) + log(p[1]) + log(p[2])*p[1] +
         log(x)*(p[3] - 1) + log(p[2] + x^p[3])*(-(p[1] + 1))
    -sum(e)
}

all.equal(f.like(p=c(1,2,3), x=data),
          loglik(p=c(1,2,3), x=data))
[1] TRUE

我们可以将其与nlminb（）进行比较：


两种方法都发现一些参数在0附近，即在域边界附近。这可能会导致收敛问题

我怀疑他们两个都不是。您会收到哪些警告？如果您查阅有关
optim
和
nlminb
的帮助，您将看到
optim
已达到迭代限制而未收敛，并且
nlminb
已收敛。如果在每次调用后使用
warnings（）
，您将看到生成了
NaN
。得出你的结论。我怀疑他们两个都没有。您会收到哪些警告？如果您查阅有关
optim
和
nlminb
的帮助，您将看到
optim
已达到迭代限制而未收敛，并且
nlminb
已收敛。如果在每次调用后使用
warnings（）
，您将看到生成了
NaN
。得出结论。回答得好，我在考虑
nlminb
和
optim
之间的性能。我想这很难说。要优化的函数形式可能会起到重要作用。回答得好，我考虑的是
nlminb
和
optim
之间的性能。我想这很难说。要优化的功能形式可能会发挥重要作用。
nlminb(start=c(1, 2, 3), objective=loglik,
       x=data, lower=rep(.01, 3))
$par
[1] 2.653579e+03 6.117484e+05 2.989276e-01

$objective
[1] 7090.686

$convergence
[1] 1

$iterations
[1] 64

$evaluations
function gradient 
     102      247 

$message
[1] "singular convergence (7)"