runs test for evaluation of model fit

• To: mathgroup at smc.vnet.net
• Subject: [mg57173] runs test for evaluation of model fit
• From: Csukas Attila <attila at biking.taiiku.tsukuba.ac.jp>
• Date: Fri, 20 May 2005 04:43:06 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Dear Everybody,

I am facing to a new problem and if it is possible would like to ask
some help from experts as you are.
I have observed values (second in the brackets) for three ids (first in
the brackets) and also have predicted values (third in the brackets)
estimated by a model. I would like to use runs test to prove that the
model fitted well, that is there is no significant difference between
observed and predicted values for each id.

Does anybody know how can it be done? Any help is appreciated! Thanks

Out[10]=
{{id,obs,pred},{2,116.9,116.486},{2,122.1,122.073},{2,126.1,127.074},{2,

131.1,131.598},{2,137.1,135.899},{2,141.1,140.88},{2,148.3,149.053},{2,
161.2,160.338},{2,165.9,166.697},{2,

167.8,168.316},{2,168.,168.617},{2,170.1,168.67},{4,120.8,121.477},{4,

128.2,127.612},{4,134.5,133.438},{4,138.9,139.369},{4,145.2,146.045},{4,
153.7,154.016},{4,163.7,162.616},{4,

170.1,169.62},{4,172.1,173.697},{4,174.4,175.536},{4,177.3,176.255},{4,

177.3,176.518},{7,111.8,110.578},{7,115.5,116.887},{7,122.1,122.456},{

7,126.8,127.377},{7,132.4,131.743},{7,136.4,135.698},{7,139.1,139.616},{

7,145.3,144.669},{7,152.1,152.685},{7,161.,160.428},{7,163.2,163.488},{
7,164.1,164.176}}

but I have difficulties with the application for the above data. Hints
I have found on W-W are the next:

In[1]:=
x = Table[Random[Integer],{n = 25}]

Out[1]=
{1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0}

In[2]:=
{{n1 = Tr@x, n0 = n - n1},  r = Length@Split@x}

Out[2]=
{{14,11},12}

In[3]:=
N@{m = 1 + 2*n0*n1/n, sd = Sqrt[(m-1)(m-2)/(n-1)]}

Out[3]=
{13.32,2.41059}

In[6]:=
f[r_,n0_,n1_] := If[EvenQ@r,
With[{k = r/2 - 1},2*Binomial[n0-1,k  ]*Binomial[n1-1,k  ]],
With[{k = (r-1)/2},  Binomial[n0-1,k  ]*Binomial[n1-1,k-1] +
(**)                 Binomial[n0-1,k-1]*Binomial[n1-1,k  ]]];
rf=Table[{r,f[r,n0,n1]},{r,2,2Min[n0,n1]+Boole[n0??n1]}]

Out[7]=
{{2,2},{3,23},{4,260},{5,1365},{6,

7020},{7,22230},{8,68640},{9,145860},{10,300300},{11,450450},{12,648648}
,{?_
13,702702},{

14,720720},{15,566280},{16,411840},{17,231660},{18,115830},{19,45045},{2
0,?_
14300},{21,3575},{22,572},{23,78}}

In[8]:=
{#, # === Tr@rf[[All,2]]}&@Binomial[n,n1]

Out[8]=
{4457400,True}

```

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