Description Usage Arguments Details Value References See Also Examples

Implements the maximum likelihood algorithm of Ludwig and Titterington (1994) for linear regression of three dimensional data with correlated uncertainties.

1 | ```
titterington(x, alpha = 0.05)
``` |

`x` |
an |

`alpha` |
cutoff value for confidence intervals |

Ludwig and Titterington (1994)'s 3-dimensional linear regression
algorithm for data with correlated uncertainties is an extension of
the 2-dimensional algorithm by Titterington and Halliday (1979),
which itself is equivalent to the algorithm of York et al. (2004).
Given *n* triplets of (approximately) collinear measurements
*X_i*, *Y_i* and *Z_i* (for *1 ≤q i ≤q n*),
their uncertainties *s[X_i]*, *s[Y_i]* and *s[Z_i]*,
and their covariances cov[*X_i,Y_i*], cov[*X_i,Z_i*] and
cov[*Y_i,Z_i*], the `titterington`

function fits two
slopes and intercepts with their uncertainties. It computes the
MSWD as a measure of under/overdispersion. Overdispersed datasets
(MSWD>1) can be dealt with in the same three ways that are
described in the documentation of the `isochron`

function.

A four-element list of vectors containing:

- par
4-element vector

`c(a,b,A,B)`

where`a`

is the intercept of the`X-Y`

regression,`b`

is the slope of the`X-Y`

regression,`A`

is the intercept of the`X-Z`

regression, and`B`

is the slope of the`X-Z`

regression.- cov
`[4x4]`

-element covariance matrix of`par`

- mswd
the mean square of the residuals (a.k.a 'reduced Chi-square') statistic

- p.value
p-value of a Chi-square test for linearity

- df
the number of degrees of freedom for the Chi-square test (2

*n*-4)- tfact
the

*100(1-α/2)\%*percentile of the t-distribution with*(n-2k+1)*degrees of freedom

Ludwig, K.R. and Titterington, D.M., 1994. Calculation
of *^{230}*Th/U isochrons, ages, and errors. Geochimica et
Cosmochimica Acta, 58(22), pp.5031-5042.

Titterington, D.M. and Halliday, A.N., 1979. On the fitting of parallel isochrons and the method of maximum likelihood. Chemical Geology, 26(3), pp.183-195.

York, D., Evensen, N.M., Martinez, M.L. and De Basebe Delgado, J., 2004. Unified equations for the slope, intercept, and standard errors of the best straight line. American Journal of Physics, 72(3), pp.367-375.

1 2 3 4 5 6 7 8 9 | ```
d <- matrix(c(0.1677,0.0047,1.105,0.014,0.782,0.015,0.24,0.51,0.33,
0.2820,0.0064,1.081,0.013,0.798,0.015,0.26,0.63,0.32,
0.3699,0.0076,1.038,0.011,0.819,0.015,0.27,0.69,0.30,
0.4473,0.0087,1.051,0.011,0.812,0.015,0.27,0.73,0.30,
0.5065,0.0095,1.049,0.010,0.842,0.015,0.27,0.76,0.29,
0.5520,0.0100,1.039,0.010,0.862,0.015,0.27,0.78,0.28),
nrow=6,ncol=9)
colnames(d) <- c('X','sX','Y','sY','Z','sZ','rXY','rXZ','rYZ')
titterington(d)
``` |

```
$par
a b A B
0.6523258 -1.1448293 0.6287848 -0.8317666
$cov
a b A B
a -0.0014659472 0.002534783 -0.0002053377 0.000577532
b 0.0025347834 -0.029356631 -0.0025913430 0.006835091
A -0.0002053377 -0.002591343 0.0015645768 -0.003932355
B 0.0005775320 0.006835091 -0.0039323548 0.010804817
$df
[1] 8
$mswd
b
-19.35144
$p.value
[1] 1
$type
[1] "titterington"
```

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