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help for ^spell^
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Identification of spells or runs of similar values
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^spell^ [varname] [^if^ exp] [^in^ range]
[ ^,^ { ^f^cond^(^fcondstr^)^ | ^c^ond^(^condstr^)^ | ^p^cond^(^pcondstr^)^
>  }
^by(^byvarlist^) ce^nsor^(^censorvarlist^) e^nd^(^endvar^)^
^s^eq^(^seqvar^) sp^ell^(^spellvar^) replace resort^ ]

Description
-----------

^spell^ examines the data, treated as sequences or series, to identify
spells or runs, and generates new variables:

(1) indicating distinct spells (0 for not in spell, or integers 1 up);

(2) giving sequence in spell (0 for not in spell, or integers 1 up); and

(3) indicating whether observations occur at the end of spells (0 or 1).

By default, these variables will be called ^_spell^, ^_seq^ and ^_end^.

Remarks
-------

There are four ways of defining spells in ^spell^.

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First, given

^spell^ varname

a new spell starts whenever varname changes.

Second, a new spell starts whenever some condition defining the first
observation in a spell is true. A spell ends just before a new spell
starts. Such a condition may be specified by the ^fcond( )^ option.

observation        time
1                  1
2                  2
3                  3
4                  7
5                  8
6                  9

Suppose we wish to divide ^time^ into spells of consecutive values,
in this case observations 1-3 and 4-6. A new spell starts when

^(time - time[_n - 1]) > 1^

which works for ^_n == 1^ as well because ^time[0]^ is treated as missing.
Spells started by earthquakes, eruptions, accidents or other traumatic
events may often be defined in this way.

Third, spells are defined by some condition being true for every observation
in the spell. A spell ends when that condition becomes false. Such a
condition may be specified by the ^cond( )^ option.

observation         varname
1                    0
2                   10
3                   11
4                   12
5                    0
6                   13
7                    0
8                   14

Observations 2, 3, 4; 6; and 8 form 3 spells for the condition
"varname > 0".

Observations 4; 6; and 8 form 3 spells for the condition
"varname >= 12".

Fourth, a special but useful case of the previous kind is
^cond(^varname > 0 & varname < .^)^, that is, values of varname are
positive (but not missing). Given daily data, spells of rain are
defined by there being some rainfall every day. As a convenience,
such conditions may be specified by ^pcond(^varname^)^, or
more generally, ^pcond(^expression^)^.

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The order of the data when ^spell^ is called is taken to define position
in the sequence. No explicit time or other ordering variable is
required, but if any such exist, the user should ensure that data are in
correct order before ^spell^ is called.

Spells are deemed to end at the last observation (under ^by( )^, at the
last of each distinct group of observations).

Under ^if^ or ^in^, for identifying spells, observations are sorted so
below.

Missing values may be ignored by using ^if^ to exclude them. They are
not ignored by default, as a convenience to users wishing to explore
patterns of missing values. Recall that numeric missing ^.^ is treated
as larger than any positive number. Thus be careful to exclude missing
values where appropriate.

Conditions in terms of ^_n^ and ^_N^ are interpreted as follows. First,
if ^if^ and/or ^in^ is specified, only those observations satisfying those
conditions are considered, so that for example ^_N^ refers to the last such
observation. Second, if ^by( )^ is specified, ^_n^ and ^_N^ refer to distinct
groups defined by byvarlist. Third, ^spell^ respects the sort order of
observations when it is invoked. These rules may operate together, in this
order.

Two situations require particular care, because ^spell^ works
best when the appropriate order of observations is defined unambiguously
by a single criterion. The natural order of observations may depend on two
or more variables, as when there are separate variables for year and month.
The desired output may be sometimes best achieved by working with a
combined variable which contains, say, year + (month - 0.5) / 12 or
^ym(^year^,^month^)^.

In some problems with tied values, ^spell^ may or may not place them in
the same spell. The sequence variable will differ and the end variable
may differ. There may be insufficient information to determine a unique
sort order.

Given the earlier example, modified here,

observation        time
1                  1
2                  2
3                  2 <--- value changed from 3
4                  7
5                  8
6                  9

and the same ^fcond( )^, which observations are put in positions 2 and 3
is arbitrary. By default, they will be assigned ^_seq^ of 2 and 3 and
^_end^ of 0 and 1, even though they are identical.

Options
-------

^fcond(^fcondstr^)^ specifies a true or false condition that defines the
start of a spell: to be precise, the first observation in a spell.
A new spell starts whenever this condition is true.

If varname is specified, and neither ^fcond( )^ nor ^cond( )^ is
specified, ^fcond( )^ defaults to "varname != varname[_n-1]".

^cond(^condstr^)^ specifies a true or false condition that defines the
spell.

^pcond(^pcondstr^)^ is equivalent to

^cond(^(pcondstr) > 0 & (pcondstr) < .)^)^

That is, some expression pcondstr evaluates to a positive number
(but not missing).  Commonly, the expression is just the name of
a numeric variable.

Only one of ^fcond( )^, ^cond( )^ and ^pcond( )^ may be specified.

^by(^byvarlist^)^ specifies one or more variables that subdivide the
data into groups. For example, the byvarlist could specify
individual people. A further condition on a spell is then that
the variable or variables in a byvarlist remain constant.

With ^by( )^, ^spell^ sorts data first by byvarlist and then by the
order of the data when called. It then identifies spells. See also
^resort^ below.

^censor(^censorvarlist^)^ defines two new variables that are 1 if the
spell is left- or right-censored and 0 otherwise. A left-censored
spell starts at the first relevant observation (so it might have
started earlier, except that we have no data to determine that). A
right-censored spell ends at the last relevant observation (so it
might have ended later, except that we have no data to determine
that). ^censor( )^ should specify two new variable names, separated
by white space (e.g. ^censor(cl cr)^), for indicating left-censored
and right-censoring. As a special case, ^censor(.)^ indicates that
_cl and _cr should be tried as new variable names.

^end(^endvar^)^ defines a new variable that is 1 at the end of each
spell and 0 otherwise. ^_end^ is tried as a variable name if this
option is not specified.

^seq(^seqvar^)^ defines a new variable that is the number of
observations so far in the spell. ^_seq^ is tried as a variable name
if this option is not specified.

^spell(^spellvar^)^ defines a new variable that is the number of spells
so far. All observations in the first spell are tagged with 1, all
in the second with 2, and so on. ^_spell^ is tried as a variable name
if this option is not specified. Under ^by( )^, a separate count is
kept for distinct values of byvarlist.

^replace^ indicates that any variables created by ^spell^ may overwrite
existing variables with the same names.

^resort^ restores the original sort order of the observations after
identifying spells. (The default if ^by( )^, ^if^ or ^in^ is invoked
is to sort the data so that comparable and relevant observations are
put together.)

Examples
--------

. ^spell party^

Spells are distinct jobs (panel data):

. ^spell job, by(id)^

Number of spells (panel data):

. ^egen nspells = max(_spell), by(id)^

To define spells of consecutive values of ^time^:

. ^spell, f(_n == 1 | (time - time[_n - 1]) > 1) by(id)^

Rainfall spells:

. ^spell, p(rain)^

For spells in which rainfall was at least 10 mm every day:

. ^spell, c(rain >= 10) e(hrend) s(hrseq)^

To get information on spell lengths (# observations):

. ^su hrseq if hrend^
. ^tab hrseq if hrend^

Length of each spell in a new variable:

. ^spell^ ...
. ^egen length = max(_seq), by(_spell)^

. ^spell^ ... ^, by(id)^
. ^egen length = max(_seq), by(id _spell)^

Duration (length in time) of each spell in a new variable:

. ^egen _tmax = max(time), by(_spell)^
. ^egen _tmin = min(time), by(_spell)^
. ^gen duration = _tmax - _tmin^

Cumulative totals of varname:

. ^sort _spell _seq^
. ^qui by _spell : gen _tot = sum(^varname^) if _seq^

Sums of varname:

. ^egen total = sum(^varname^), by(_spell)^

Authors
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Nicholas J. Cox, University of Durham, U.K.
n.j.cox@@durham.ac.uk

Richard Goldstein
richgold@@ix.netcom.com

Acknowledgements
----------------