Random walk effects in behavioral data

Abstract

IZtrnk of Sweden ?'el centenary Fund and Uni7,ersity o j StokholttlThis paper deals with random walk models and their possible application to psychological and sociological data. Such data may present a combination of apparent regularity and great difficulty of causal explanation. Random walk, implying the summation of individually small shocks or effects could account for both properties. A s a special case a binary structure consisting of two interacting entities, each also influenced by an exogenous factor, is considered and ways of looking a t the behavior of such systems suggested. Conventional techniques of analyzing variability rely heavily on stratification, e.g.. by social class, as a means of determining the effects of environment. This method often performs rather poorly, and the outcome is put in the same perspective, and related to different conceptions of environment. Finally, developmental data and developmental correlations are examined from the same point of view. Gy3 APPEARANCE OF ORDERm G E ASU +mall units alike often >how a L high degr ( b e of stability and therefore predictability in some behavior judged agaiiiit the variation observed among units. This i i trur iri psychological research when individual diffcwmces are itudied and fitted into dcvclopmcrital patterns, arid no less true in sociological research in so far a\ it dcah \\ ith aggregate bchavior and largescdc manifcdations of pcrsiitenw and change. Thw Durkheim (1952, 51) noting the distinctive, and criduririg character of suividc rates cwnrluded that tlicir i t ability (through timc) and variability (among units) slionc,d that they spring from a ''unified and definite" causal em, \$how prrniaiwtiw I T ould ot2icriviic bc incxplicablc.Hcw arc phmomeria that sccm natural targets for a psyrhologi5t or soc*iologist \\ ho has set his heart on systematic. thcory. Ytlt, cvery behavioral irirntiit i5 also a\rztrc of the limited degrccb of i u (~e s i that hah follo~vcd vc.nturcs into hard thcory. Why is there this strange combination of opaquciie+ with the appearance of la\\ fulness arid predic.tability? To give a cwmpletc a n s w r is clcarlj. beyond anvoric's reach but it is p o 4 b l c to invoke a i a partial explanation a qirnpl(1 t j pe of stochastic process, random \\ allr. \Iore specifically, this nil1 wrv(' two purpo5cs. The first is the usual one, to provide a (*ompart scheme into \\ hich observational data can be fitted. The serond is less eomrnoii and borders on a mctathcwrctical function. This i i to use the> itatistical liypothrsis as a gcncml assumption about tlic true structurr underlying thc class of phenomcna one is invchtigating, and t h m to aik what light cuhtomary resvarch mrthods I \ ill shed on the structure. It will be >howl that the random walk model fits some of the known facts in bcliavioral rcscarc*h reasonably well and explains fiiidirigs of apparrnt regularity arid also their stubborn r to cfforts at causal interpretation.Random w d k is a udl-knon n clemcwt in the thcory of probability and stochastic procchs...