# Stylistic Change and Fashion in Women's Dress: Regularity Or Randomness?

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John W. G. Lowe and Elizabeth D. Lowe (1984) ,"Stylistic Change and Fashion in Women's Dress: Regularity Or Randomness?", in NA - Advances in Consumer Research Volume 11, eds. Thomas C. Kinnear, Provo, UT : Association for Consumer Research, Pages: 731-734.

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http://acrwebsite.org/volumes/6341/volumes/v11/NA-11

Utilizing historical data from 1789 to 1935 on six persistent dimensions of women's evening dress, a mathematical model derived elsewhere (Lowe and Lowe 1982) was tested against new data extending to 1983 to determine its predictability. The fashion process in women's dress appears to be predictable, but just barely.

The problem to be addressed in this paper is: how predictable is fashion change? me fashion process is rather ubiquitous, influencing activities ranging from medical practice and social theory to the purchasing of a vast array of consumer products. The extent to which fashion operates in any of these realms is a matter of degree, but one can argue that the fashion process achieve. its greatest dominance in the area of women's dress. Nor is it a new phenomenon; as William Shakespeare wrote, "Fashion wears out more clothes than the man."

METHODOLOGY AND DATA BASE

Utilizing fashion publications, a year-to-year record of dress exist, stretching back to the French Revolution. Data include metrical remeasurements of six persistent dimensions of women's formal evening attire, including skirt length and width, waist length and width, and decolletage length and width. Data for the period 1789 to 1936 were compiled by two anthropologists, Alfred Kroeber and Jane Richardson (Richardson and Kroeber 1940). Using the same method of selecting fashion plates and obtaining measurements, we extended the data base to 1980. A 5-year overlap of data from 1939 to 1935 passed statistical tests for comparability.

All six dress dimensions were converted to ratios of the dimensions, divided by the total height of the figure to provide comparability of data. The total height was measured from the center of the mouth to the tip of the toe bearing weight or to the center of the skirt if no feet were visible, thus eliminating problems associated with changing hair styles. Briefly stated, skirt length was measured from the mouth to hem of the skirt at center front; waist length from mouth to narrowest part at waist along center front; decolletage length from mouth to middle of neckline at center front. Skirt width was measured as the diameter of the skirt at the hem; waist width as the width at the minimum area of the waist; and decolletage width as the distance between inside edges of the dress at the shoulder line. A number of measurements were taken every year for each dress dimension and means were computed.

Limitations

This study focuses on women's formal evening dress, presumably that area of women's dress where stylistic change plays its greatest role and continuity with the past is strongest.

The data set consists of haute couture plates, not actual consumer choices. The yearly means for each dress dimension are not measures of what the population at large was wearing but rather depict a kind of ideal, what the purveyors of high fashion thought women ought to be wearing. Obviously the measures are related, but the data examined here may best be thought of as an underlying conceptual structure on which local and idiosyncratic transformations are made according to taste, and, as this structure alters, so too do individual and local behavior. The few studies that have been made, comparing the two (for instance Jack and Schiffer 1948), indicate that fashion change in New York City, Muncie, Indiana, or Butte, Montana follows the same general trajectory as the nigh fashion ideal, though attenuated and perhaps lagged in time.

The fashion process may he thought of as consisting of two components: (I) mechanisms which generate new innovations and select among them, and (2) a diffusion process governing the spread of ne; forms. Each has its regularities, at least of a statistical nature. In this country, for example, southern California is a recurrent spawning ground for fashions in popular culture. In this paper, however, we will concentrate on regularities in the first component, the generation of new conceptual patterns from old ones.

Another important limitation must be noted. We deal only with quantitative change in persistent features of women's dress. Fashion also consists of a vast array of particular elements - padded shoulders, Dill' ox hats, ruffled sleeves and so forth - that rise and fall in popularity and continuously replace one another through time. These, too, are of interest, but are outside the scope of this investigation.

THE MODEL

Utilizing the historical data from 1789 to 1936 and building on some of Kroeber's (Kroeber 1919, 1944, 1948, 1957) ideas concerning stylistic change, it is possible to derive a dynamic, mathematical model that governs the transformation of the six dress dimensions through time. The model is developed on the basis of four assumptions.

(I) Inertia operates. Spurred by the desire for novelty, there is a tendency to move on to new values of the dimensions rather than return to old ones, hence, for change in any particular direction to continue. If skirts have been progressively rising for the last few years, they tend to continue to rise. Because of inertia, an entity once set in motion remains in motion; thus, a variable will overshoot its equilibrium point, giving rise to oscillations.

(2) However, a resistance to that motion occurs, so that large year-to-year jumps in one direction engender forces favoring movement back the other way; the larger the jump, the stronger the opposing force. This part of the model embodies a mathematical expression of the principle of cultural continuity or that tendency for culture not to change too rapidly.

(3) The dress dimensions are not independent, rather, they affect one another in such a was that there exists a set of ideal proportions between them, e.g., as skirts get shorter, they should also get narrower, else the result appears ridiculous. A kind of aesthetic grammar is created whose rules are by no means always obeyed, but when they are not, a restoring force is created, attempting to return the system to a state of ideal balance. Not all the dimensions affect one another, hut most do; of the 30 possible dyadic interactions, we see evidence of 24. This component is statistically the weakest of the four assumptions, but in a sense is the most critical, for unlike the other three, it maintains the system in equilibrium.

(4) Finally noise, or a random, totally unpredictable component, is also an inherent part of the model. The conceptualization is stochastic/probabilistic and leaves room for the human capacities of innovation and choice, but such choices are bounded by a multitude of constraints and biases.

As with many economic time series, error proves to be multiplicative and a logarithmic transformation of the variables is required. By careful choice of the reference or zero points, heteroscedasticity can be alleviated, the effect of physical constraints such as floor length minimized, and interaction between dimensions expressed as linear relations ( Table 1).

VARIABLES USED IN FINAL MODEL OF FASHION CHANGE

Utilizing these assumptions and ordinary least squares, a final model was formulated (Lowe and Lowe 1982).

Where:

x_{i}(t) = the value of the i'th dimension at time t

Vx_{i}(t) = x_{i}(t) - x_{i}(t-1)

V^{2}x_{i}(t) = Vx_{i}(t) - Vx_{i}(t-1) = x_{i}(t) - 2x_{i}(t-1) + x_{i}+(t-2) y_{i}, c_{i}, a_{ij}, and b_{i} are constants (parametric values) estimated by ordinary least squares

e_{i}(t) = the residual tena, random white noise

Support for the model arises from high R2 values, statistically significant evidence of interaction and resistance to motion, as well as residual errors which pass multiple tests for randomness. Because the system is linear, its dynamic behavior is relatively easy to ascertain. The solution is a series of stochastic cycles with periods about a century or more in length. Also, the equilibrium position appears reasonable, lying near the mean values for each of the dimensions.

ANALYSIS

This paper revolves around how well the above model performs in the period 1937 to the present, and in particular, how well does it predict ensuing events. One possibility is to perform the same regression operations using the same variables as in the 1936 model (that is, based on the period from 1789 to 1936) for the entire data set, and compare results.

First, we find essentially identical R2 values, <R2> = 71.2 and <R22> = 71.8 where <R21> = the average for all six dimensions in the 1936 model and <R22> = the average in the 1980 model (based on the period from 1937 to 1980). If the basic model were simply a statistical artifact, then the addition of new data would considerably decrease the explained variance and therefore the R2 values.

Second, the residuals of the 1980 model pass several tests for randomness: the Durbin-Watson test, the runs test, an examination of the first 20 autocorrelates and partial autocorrelations, and the Kolmogorov-Smirnov test of the cumulative spatial density function (Fuller 1976; Hanushek and Jackson 1977; Wonnacott and Wonnacott 1979). It is desirable to utilize several tests because randomness is a simple, but elusive, property and numerous examples exist of series that are random in certain respects but not all respects (Shannon 1975). All tests were passed, i.e., exhibited no statistically significant deviation for randomness, with the exception of waist width, which failed the runs test. The implication is an overall lack of systematic misrepresentation of the data. Truly random residuals suggest that all the structure and predictability existing in the data have been successfully extracted.

On the other hand, several of the regression coefficients in the 1980 model are by no means identical to their values in the original model, and a few, in fact, change signs, a result inconsistent with the idea of invariant rules of proportion. The temporal record is sufficiently long, 192 years, that it is feasible to divide the series into halves and look for statistical differences in the parametric values. The result i; that in a significant number of regression coefficients (8 out of 42), the difference in parametric values exceeds the .05 probability level. It appears that the stylistic grammar is not totally invariant. Therefore, as T ' X we should not expect to see a convergence to "true" parametric values. These findings indicate that some sort of rule relaxation or alteration is taking place, and therefore, updating may be advantageous in making predictions, and for the most part it is indeed.

Perhaps the most straightforward way to test the efficacy of the 1936 model is to use it to predict subsequent values of the six dimensions and compare these to the actual values. What we wish to predict is Vx, the projected change in a dimension, not V-x, the rate of that change. Is Vx positive or negative, will, for example, skirts rise next year, and if so, by how much? Calculating the projected value, Vxt+l, is easily achieved by adding Vxt to both sides of the equations in Table 2, since

V^{2}x_{t+1} = x_{t+1} - Vx_{t} (2)

V^{2}x_{t+1} + Vx_{t} = Vx_{t+1} (3)

FINAL REGRESSION RELATIONSHIPS FOR EACH DIMENSION

A COMPARISON OF THE MEAN SQUARE PREDICTION ERRORS

Because the model is stochastic, that is, noise or unpredictability is an inherent part of the process, the ability to project future values decays very rapidly with lead time. Hence we will only attempt to forecast one year ahead.

One statistic of interest is the mean square prediction error, E2, the square of the difference between the predicted value and the actual value, E^{2} = <Vx_{t+1} - Vx_{t+1}>^{2}. The more accurate the prediction, the closer E2 approaches zero.

In the majority of cases updating helps; it diminishes the mean square predictive error, E2. In four out of six dimensions, we find that E2 for a model updated every 10 years is smaller than E2 using the parametric values in the 1936 formulation (Table 3). On the other hand, updating every four years did little good and often resulted in a higher prediction error. On the whole, there fore, parametric change seems to be fairly slow.

The expectation is that E2 = e2 where e2 is the estimated residual variance in the original model and as such represents the degree of uncertainty in making a prediction. On the whole E2 > e2, and in two instances, skirt length and decolletage length, E2 is significantly larger (p < .05). However, in both series, the variance in Vx, o^{2}_{Vx} = <(Vx)^{2}> is substantially larger for the period 1937 to 1980 compared to 1789 to 1936. Apparently the greater the "activity" in a dimension, xi, the larger its residual variance, e2. The variability in e2 through time comes about for two reasons.

(1) The focus of fashion shifts attention from one dimension to another; perhaps one year the legs are emphasized through short, narrow skirts while the next year lowered waistlines dominate the silhouette. The situation is not unlike the financial markets where through time stocks in different companies will seize investor interest and as a result fluctuate in their volatility.

(2) Stylistic change is not a closed system. The impact of external events, especially socio-political unrest, tends to result .n an increase in e2. Far instance, the residual variance is large during the Napoleonic era and around W.W.I. External disturbances do not normally result in directed change. It is not necessarily true that skirts go up during wars or down with the Dow Jones average, hut economic and political events increase the residual variance and so operate to agitate the system, thus leading to more extreme values. the manner in which external events are reflected in the stylistic process suggests a model for large-scale stylistic change. High, sustained residual error results eventually, if not immediately, in new configurations. T,'l this case a new aesthetic grammar may emerge, one perhaps even involving" different set of features or dimensions

Qualitative Predictions

Using the regression models it is also possible to make qualitative predictions, to forecast the direction of change for each dimension. There we find, on the average, 60% accuracy with the 1936 model. The overall accuracy rises to 697. for the model updated by 10-year intervals. Flipping a coin would of course provide a 50% accuracy. Therefore, the model results in a fairly thin edge, a rather modest gain in predictability, though if one could forecast pork bellies or gold futures with the same kind of accuracy, he/she could become very weal thy indeed. And because so many trials are involved, the probability of achieving a 62% degree of accuracy by chance is quite minute, less than one in 10,000. Finally, -t is apparent that errors cluster. The sequence is characterized by fairly long stretches when the model works quite well, interspersed with intervals in which it seems to break down. So, an intelligent forecaster would weight or value his predictions accordingly.

Time Series Versus Regression Models

Might not a simpler formulation be more predictive? One popular device for achieving predictions given a fairly long temporal record is Box-Jenkins modelling (Box and Jenkins 1976). For each series, dealing with VXt produces a simple stationary model. For skirt length, waist length, skirt width, and decolletage width, Vxt is best fit by a first order autoregression process; and in the case of decolletage length and waist width, the best fit is a first order moving average process. Both classes of time series models essentially treat only the cultural continuity, or resistance to change, aspect in the regression model discussed earlier. With a first order autoregression process, the subsequent value of Vx depends only on its present value plus a random, unpredictable component. With a first order moving average process, the subsequent value of Vx is determined by a geometrically weighted sum of past values plus a random component. These models do not involve interaction between the dimensions and are much simpler, requiring the estimation of far fewer parameters.

With such modelling, updating does little good an normally results in worse estimates (that is, greater E) - refer to Table 3). The implication is that the change through time is largely restricted to the interactive, aesthetic grammar part of the model (as well as magnitude of the random portion). Like grammatical constructions in language, the aesthetic proportions alluded to earlier tend to be culture specific, do not diffuse easily, and are relatively stable in time. But alteration over the centuries can and does take place.

For the majority of the dimensions, a time series model does not predict as well as an updated regression model. For the skirt and decolletage dimensions the mean square predictive error is larger with a time series model than with an updated regression model; in the other two cases, waist length and width, it is somewhat smaller (refer to Table 3). Likewise the ability to predict direction is better with Box-Jenkins models for waist length and width and worse for the other dimensions. Hence, for the two waist dimensions in which updating the regression mode does not help, the Less complex Box-Jenkins models also give better predictions. It seems therefore that structural change occurs to a difFerential extent. In fact, this structural change is most apparent and explicable in the case of waist width. For that dimension the difference between E2 values (the mean square predictive error) is most pronounced when an updated regression model is compared to either an updated regression model Dr the simpler time series formulation. It is waist width which fails the runs test, and in fact, using the regression model, from 1947 to 1980 the predicted value is always negative. The structural change that ensued is presumably associated with the failure of the corset is return, which is perhaps related to the changing ole of women in the workplace and society at large.

SUMMARY

The central conclusion is that the fashion process in women's dress is predictable, but just barely. Whether or not this predictability would increase or decrease if we dealt with actual consumer choices is a matter for speculation. Likewise, we have dealt here only with quantitative changes which necessarily tramples underfoot subtleties in the stylistic process. But despite a certain degree of apparent structural transformation and irreducible noise, the predictability of stylistic change in women's evening wear seems beyond dispute. There is an important difference between prediction and understanding. Time series models of the Box-Jenkins variety rarely offer much insight or understanding, hut often provide the most reliable predictions. For the majority of the dress dimensions, however, they do not. They do provide a baseline against which more complex models may he measured and what we find is that introducing the concept of inertia and interaction between dress dimensions does on the whole increase not only our understanding of the stylistic process, but also our ability to forecast it.

REFERENCES

Box, George E. P. and Jenkins, Gwilym J. (1976), Time Series Analysis: Forecasting and Control, revised ed., San Francisco: Holden-Day.

Fuller, Wayne A. (1976), Introduction to Statistical Time Series, New York: Wiley.

Hanushek, Eric A. and Jackson, John E. (19??), Statistical Methods for Social Scientists, New York: Academic Press.

Jack, Nancy Koplin and Schiffer, Betty (1948), "The Limits of Fashion Control," American Sociological Review, 13, 730-738.

Kroeber, Alfred L. (1919), "On the Principle of Order in Civilization as Exemplified by Changes of Fashion," American Anthropologist, 21, 235-263.

Kroeber, Alfred L. (1944), Configurations of Culture Growth, Berkeley, Calif.: The Regents of the University of California.

Kroeber, Alfred L. (1948), Anthropology: Culture Patterns and Processes, New York: Harcourt, Brace.

Kroeber, Alfred L. (1957), Style and Civilizations, Ithaca, N.Y.: Cornell University Press.

Lowe, John W. G. and Lowe, Elizabeth D. (1982), "Cultural Pattern and Process: A Study of Stylistic Change in Women's Dress," American Anthropologist, ( 3), 521-554.

Richardson, Jane and Kroeber, Alfred 1). (1940), "Three Centuries of Women's Dress Fashions: A Quantitative Analysis," Anthropological Records, 5(2), 111-153.

Shannon, Robert E. (1975), Systems Stimulation: The Art and Science, Englewood Cliffs, N.J.: Prentice -Hall, Inc.

Wonnacott, Ronald J. and Wonnacott, Thomas H. (1979), Econometrics, 2nd ed ., New York: Wiley.

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