BEBR FACULTY WORKING PAPER NO. 89-1592 An Empirical Comparison of Probit and ID3 Methods For Accounting Classification Research The Ulraiy of the OCT t | 1989 cf Urt)an«-CJwmpalgn John S. Chandler Ting-peng Liang Ingoo Han College of Commerce and Business Administration Bureau of Economic and Business Research University of Illinois Urbana-Champaign BEBR FACULTY WORKING PAPER NO. 89-1592 College of Commerce and Business Administration University of Illinois at Urbana- Champaign August 1989 An Empirical Comparison of Probit and ID3 Methods for Accouunting Classification Research John S . Chandler Associate Professor Ting-peng Liang Assistant Professor Ingoo Han Ph.D. Student Department of Accountancy The authors thank James Gentry for his helpful comments on earlier versions of the paper. This research was partially supported by the Department of Accountancy of the University of Illinois at Urbana- Champaign. ABSTRACT This paper investigates some properties of applying Probit and ID3 methods to the analysis of accounting classification problems. The particular accounting problem examined is the LIFO/FIFO choice. Both original and hold- out samples are used to study the effects of the training sample size and the nature of the data set on the accuracy of classification. The results indicate that (1) Probit and ID3 identify different factors that affect LIFO/FIFO choice;' (2) in hold-out tests, ID3 performs better when the sample size of the input data set is small relative to the total population; whereas Probit performs better when the sample size is relatively large; and (3) ID3 performs better when the input data set is dominated by nominal variables; whereas Probit performs better otherwise. Digitized by the Internet Archive in 2011 with funding from University of Illinois Urbana-Champaign http://www.archive.org/details/empiricalcompari1592chan Page 1 1. INTRODUCTION In the past decade, Probit has been one of the primary methods in studying accounting classification problems such as LIFO/FIFO choices or bankruptcy prediction (e.g., Dopuch and Pincus 198S; Hagerman and Zmijewski 1979; Lee and Hsieh 1985). Although Probit has been argued to be theoretically superior to both multivariate discriminant analysis (MDA) and ordinary least square regression (e.g., Dietrich and Kaplan 1982: Ohlson 19S0) 1 in classification research, limitations exist when nominal variables are involved. In this case, dummy variables must be used to represent different values of the nominal variables, which may result in a violation of the normality assumption that the relationship between the dependent variable and independent variables is a cumulative normal distribution function (Aldrich and Nelson 19S4). In addition, the assumption that the dependent variable is a linear function of the independent variables may be questionable when nominal variables exist. Recently, nonparametric classification techniques have been considered as alternatives to traditional parametric methods in classification problems. For example. Marais. Patell. and Wolfson (1984) applied a recursive partitioning algorithm (RPA) to commercial loan classification and found it to be "a viable competitor to parametric methods such as polytomous Probit even when the assumptions underlying the parametric model are satisfied. " Frydman, Altman, and Kao (19S5) also report that RPA outperforms discriminant analysis in most original sample and hold-out comparisons. In addition to the feature of making no assumption on data distributions, non-parametric methods usually derive a decision tree that shows the interaction of variables. After proper transformation, decision rules suitable for developing expert systems or rule-based decision support systems can be derived from the decision tree. Counter-arguments also exist. In a recent study, for example, Noreen (19SS) shows that (1) the rejection regions for the Probit test statistics are not well-specified for small samples, and (2) the ordinary least square regression seems to perform at least as well as Probit for the cases considered. Page 2 which may make the resulting model easier to use and to understand. The primary purpose of this paper is to investigate the properties of another nonparametric algorithm, the ID3 method, in analyzing accounting problems. ID3 algorithm is an inductive learning technique that derives decision models from data. It originated from Hunt, Martin, and Stone's work (1966) on conceptual learning and was later implemented and expanded by Quinlan (1979. 1982). The primary difference between ID3 and RPA is that the former uses a criteria derived from information theory to determine the relative importance of independent variables and constructs decision trees accordingly; whereas the latter minimizes the observed expected cost of misclassification. Recent studies on ID3 have provided evidence that it can outperform expert judgment and discriminant analysis (e.g., Braun and Chandler 1987, Messier and Hensen 1988). In this paper, we use both original and hold-out samples to investigate its sensitivity to training sample size and the nature of the data set. The particular accounting problem studied was the LIFO/FIFO decision. Our empirical results include the following. First, ID3 and Probit identify different factors that affect LIFO/FIFO choice. This raises a concern about the effect of research methods on the interpretation of research findings. Second, in hold-out tests, ID3 performs better when the sample size of the input data set is small relative to the total population; whereas Probit performs better when the sample size is relatively large. Third, ID3 performs better when the input data set is dominated by nominal variables; whereas Probit performs better otherwise. The remainder of this article is organized as follows. Section 2 describes the ID3 algorithm. Section 3 briefly reviews some methodological issues in LIFO/FIFO research. Section 4 discusses the first experiment that compares the internal validity of the models (i.e., the degree to which the cases in the data set from which the model was derived are correctly classified by a model). Section 5 presents the results of the second Page 3 experiment in which hold-out samples are used to examine the external validity of the resulting models (i.e., the degree to which hold-out cases are correctly interpreted by a model). Section 6 concludes the findings and discusses some implications. 2. THE ID3 ALGORITHM The input to ID3 is a data set consisting of observed data of N cases (called training sample data). For each case, the input data include its actual group classification and values associated with a finite number of factors potentially affecting its group classification. The function of the algorithm is to induce a model from the observed data, which is capable of identifying the relationships between the factors and the actual classification. Instead of relying on sample distribution statistics, the algorithm uses entropy to measure the relative information content attributed to each factor and generates a decision tree model. The factor with the highest information content is considered the more important factor and selected as the root node of the tree. Other factors are then examined based on their relative information content. In this section, we shall discuss the measurement of information content and the model construction process of the ID3 algorithm. 2.1. A Measurement of Information Contents— Entropy Entropy was originally developed to measure the amount of information transmitted in a communication process (Shannon and Weaver 1949). It indicates the observational variety and has a value range from zero to one (Krippendorff 19S6). Entropy is zero when all observations are of the same kind (i.e., no variety), and is one when observations have equal opportunities to be classified as any one of the classes (i.e., maximum degree of variety). Entropy assumes nothing about the nature of the frequency or probability distribution and are, thus, nonparametric. When applying entropy to classification problems, the entropy of a variable shows the extent to which the accuracy of a classification can be improved (or the uncertainty can be reduced) by Page 4 introducing the variable. The purpose of the ID3 algorithm is to construct a decision tree capable of classifying all cases in the input data set. Mathematically, entropy is a logarithmic function of related frequencies or probabilities. Consider a data set of N cases, with each case described by a number of variables and a category. A given variable X classifies the N cases in k categories, C-., ..., Ci , and has m values, Vi, ..., V m . For a particular value, V-, of X, there is a probability of p-- that V- classifies a case into class C-. The entropy of X = V- is H(Vj) = - £ P H log2 Pj: (1) The entropy of X, the weighted sum over all of its m values, is H(X) = g -§- H(V ; ) (2) Where N- = number of cases where X = V-. i l For numerical variables, the calculation of entropy by ID3 includes two steps. First, a value is chosen to split the range of values for that variable into two regions: high and low. Second, the entropy of the variable is computed based on that split value. This process is performed for each possible split. The value that minimizes entropy is selected as the split value for the variable. In other words, for each case W- (1 < i < N), ID3 divides X values into two subsets (V-i, .. , V-) and (V- , -,, .. , V^), which allows ID3 to compute the entropy resulting from the split. If the division of (Vi, .. ,V+) and (V\ , -., .. , V^) has the the lowest entropy, then we split the variable at S, where S = (V t + V t+1 )/2 (3) Insert Table 1 Here Page 5 Table 1, for example, shows a set of highly simplified LIFO/FIFO data including one nominal variable and one integer variable. For the variable of industry type, in the lumber industry, six firms use FIFO and no firm uses LIFO; while in the metal industry one firm uses FIFO and seven firms use LIFO. Based on equations (1) and (2), the entropy of the variable industry type can be calculated in the following: H(Industry=lumber) = - | log 2 | - jj log 2 Q = H(Industry=metal) = - g log 2 | - 1 log 2 | = 0.54 H(Industry) = £ * + ^ * 0.54 = 0.308 Since net sales is an integer variable, we need to find the split with the minimum entropy. Among the thirteen possible splits in the example, the optimum split is 450 million which divides the values of net sales into two groups: (63, .. , 400) and (500, .. , 2300). The first group includes five FIFO firms and no LIFO firm; whereas the second group includes two FIFO firm and seven LIFO firms. Its entropy is H(Net sales) = - - £ (| log 2 | + 1 log 2 1 ) = 0.491 The values of 0.308 and 0.491 indicate the resulting varieties after introducing industry type and net sales into the classification model, respectively. 2.2. Model Construction Process Since lower entropy implies lower level of variety and lower uncertainty, the ID3 algorithm considers the variable with the lowest uncertainty as the most important one and gives it higher priority in constructing models. Its model construction process begins with the whole input data set from which the root node of the classification tree can be constructed. This includes several steps. First, the entropy of each variable is calculated based on the input data. Second, the variable with the minimum entropy is chosen as the root node of the tree. If the variable is nominal and has m levels, then the tree will have m branches at the first level and all input cases will be divided into m Page 6 groups according to their values of the root variable. For numerical variables, the tree will have two branches containing cases whose values are higher than and lower than the split value, respectively. After splitting the original cases, each of the m groups of input cases is considered a separate data set. If all cases in the group are in the same category, then no further analysis on the group is needed. This indicates that the preceding variable is capable of classifying those cases completely. The category to which these cases belongs becomes a leaf node of the h'< Otherwise, entropies of the variables will be calculated again based on the cases in the subgroup and the variable with ill- minimum entropy will be attached to the branch. The ca>c-s in the moup will be lurther split based on the value of the selected variable. This process continues until no further improvement is possible. In the previous example, the entropy of industry type is lower than that of net sales. Therefore, the industry type forms the root node, which divides the firms into lumber and metal groups. Since all firms in the lumber group use FIFO, no further analysis is possible and the leaf node of this branch is FIFO. In the metal group, one firm uses FIFO and seven firms use LIFO. A further analysis splits the net sales of the firms into two groups: (500, .. , 1000) and (1420, .. , 2300). The first group includes one FIFO and two LIFO firms, while the second one includes five LIFO firms and no FIFO firm. The split value is 1210 and the entropy is calculated to be 0.344. Since the two firms in the first group are not of the same class, we can further classify them into two categories: firms with net sales less than 825 (LIFO firms) and firms with net sales higher than 825 (FIFO firms). All firms in the second group are LIFO firms and cannot be further decomposed. The process stops when all firms in the same group are using the same inventory method. Figure 1 shows the resulting decision tree. Page 7 Insert Figure 1 Here 2.3 A Comparison of ID3 and Probit Probit method uses statistical inference procedures to derive a linear model from a set of input data. The model estimates the likelihood that, given the input data, the case falls in a particular class. It has several assumptions. First, the dependent variable is categorical. Second, the relationship between the dependent variable and the independent variables is a cumulative normal distribution. Third, no two or more independent variables are perfectly correlated. Fourth, there is no serial correlation of the dependent variable among the cases. Based on these assumptions, Probit estimates the parameters of the linear model by the Maximum Likelihood Estimation (MLE) procedures (see for example [Aldrich and Nelson 1985] for a detailed discussion). ID3 is different from Probit in at least the following aspects. First, the ID3 algorithm makes no assumption on data distribution. In fact, the algorithm treats continuous variables as discrete and uses a recursive decomposition process to divide their values into several discrete ranges. Probit, on the other hand, assumes that the relationship between the dependent and independent variables is a cumulative normal distribution function. Therefore, it seems that the ID3 algorithm is more appropriate when the normality assumption is likely to be violated, and Probit is more appropriate otherwise. Second, the ID3 algorithm generates decision tree models in which the weakness of a factor may not be compensated by the strength of the other. Probit models, however, assume a linear compensatory relationship among independent variables. This implies that ID3 may be more appropriate when the problem involves nominal variables that make a linear model inappropriate. Page 8 Third, the model construction process of ID3 is essentially an exhaustive decomposition process, which tries to cover every instance; whereas the Probit method focuses on optimizing the probability of correct classification. Therefore, ID3 seems to be more likely to overfit the sample data and hence may be more sensitive to the noise in the input data set. Finally, the entropy function is a logarithmic function generally biased toward variables with more levels and against variables with less levels (Mingers 1987). In other words, variables with more levels are more likely to be given higher priority in the model construction process. Probit models do not have this bias in processing numerical variables, but may be in favor of attributes with less levels when dummy variables are used in handling nominal variables. Given these differences, it would be interesting to know whether these two methods have different properties when they are applied to accounting classification problems. How different will the models derived from different methods? Do different models have different internal and external validities? Which method is better? When and why does a particular method outperform the other? In the remaining sections, we describe two experiments investigating these issues in the context of LIFO/FIFO choices. 3. BACKGROUND OF LIFO/FIFO RESEARCH Choice of inventory accounting methods has been a research issue for the past decade. Theoretically, the LIFO method has tax advantages when inflation exists and is considered more attractive than the FIFO method. In practice, however, a majority of firms still adopt FIFO as their primary inventory accounting method. As a result, much research has been conducted to investigate the factors affecting the adoption of a certain method (e.g., Biddle [1980], Cushing and LeClere [19SS], Dopuch and Pincus [19SS], Lee and Hsieh [19S5], Morse and Richardson [1983]). Page 9 Previous literature has examined at least three potential explanations of LIFO/FIFO choice: Ricardian costs, agency costs, and political costs (Lee & Hsieh 1985). The Ricardian hypothesis assumes that the inventory method choice is based on a firm's comparative advantage in tax minimization associated with the production- investment opportunity set. A particular method (e.g., LIFO) will be adopted if its tax savings exceed the implementation costs. Therefore, LIFO may be the optimal choice for some firms; whereas FIFO is the optimal choice for others. The agency cost hypothesis assumes that some firms remain on FIFO to report higher earnings because of managers' concerns about the impact of a LIFO switch on the securities market or their compensation contracts (e.g., Abdel-Khalik 1985; Ricks 1982). Managers are willing to forego potential tax savings to obtain other benefits. The political costs hypothesis assumes that a method will be chosen if its political costs exceed the potential tax savings. For example, the dominating firm in an industry may choose LIFO to reduce its reported earnings to avoid being the target of the anti-trust laws. Probit has been the major method used in previous studies to test these hypotheses. Empirical findings, however, are inconclusive in many aspects. For example, the relative frequency of price increases was found significantly different between LIFO and FIFO firms by Lee and Hsieh [1985]; but the effect was insignificant in Dopuch and Pincus [19SS]. The inconsistency in previous research findings may be due to several reasons. (1) Data effects — the data collected for hypothesis testing in different studies may have different characteristics. In terms of long-term LIFO and FIFO firms, for example, Lee and Hsieh (1985) chose firms using a certain method consecutively for more than seven years; whereas Dopuch and Pincus (19S8) used 20 years as the criterion. Page 10 (2) Variable effects — variables selected for examination may be different in different studies. There are usually more than one variable that can be used to test a theory. For example, both net sales and total asset can be used as surrogate variables for firm size. In addition, the correlation between variables may make it difficult to clearly relate the significance of a variable to a single theory. (3) Method effects — the Probit method used for hypothesis testing may have limitations that prevent it from providing unbiased results. In generally, there are three potential biases in Probit models. First, the effect of nominal variables may be underestimated. Using dummy variables to handle nominal factors dilutes the overall effect of the factor. This bias is particularly significant in a multivariate analysis when the nominal variable has many levels. In LIFO/FIFO studies, for example, industry type was found significant in univariate analysis but insignificant in multivariate analysis (Lee and Hsieh 1985). Second, the linear compensatory model assumption may be inappropriate in studying LIFO/FIFO decisions. The linear compensatory model is appropriate only if we assume that the manager uses a weighted-sum strategy to make LIFO/FIFO decision. Otherwise, we need to consider other functional forms. The decision tree model derived from ID3 may be an appropriate alternative form for other strategies such as conjunctive selection, disjunctive selection, or elimination by aspects. Third, the cumulative normal assumption may be violated, which results in unreliable parameter estimations. There arc at least two factors that may cause the violation of the normality assumption: nature of data and training sample size. When the decision is primarily affected by nominal variables or the data distribution is extremely skewed, the normality assumption is likely to be violated. When the size of the input data is small, the normality assumption is also likely to be violated. Based on the discussion in the previous section, the ID3 algorithm does not have these biases Page 11 (although it certainly may have some other biases) and can be a promising alternative to Probit in investigating the inventory accounting decision. In order to compare the ID3 and Probit methods, we conducted two experiments. In the first study, we examined the data and variable effects of Probit models, and compared the internal validity of the ID3 and Probit models. In the second experiment, we used hold-out samples to examine how training sample size and the nature of data affected the external validity of these methods. 4. THE FIRST EXPERIMENT The first experiment focuses on comparing the models resulting from ID3 and Probit. Data collected from the COMPUSTAT data base and DRI tape are analyzed by both Probit and ID3 methods. The results are then compared with previous empirical findings. Our primary purpose is to examine the methodological issues such as the variable and method effects. Therefore, we have no intention of arguing whether previous LIFO/FIFO research findings are appropriate. 4.1 Data Collection Data collection included two stages. An initial data base consisting of eighteen variables was constructed. This data base was then used to compile six data sets for the experiments. 4.1.1 Initial data base Based on theories and previous research findings, eighteen explanatory variables considered having effect on LIFO/FIFO choices were selected, which included one nominal and seventeen numerical variables. This set of variables was chosen to reflect the following concerns. (1) Nature of industry -- Some industries have unique environments in favor of a Page 12 certain inventory accounting method. Most previous research uses two-digit SIC codes to represent the nature of industry. This variable has been found significant in Eggleton, Penman, and Twombly (1976) and the univariate analysis of Lee and Hsieh (1985). (2) Firm size — The benefits of using LIFO are expected to be more significant for larger firms. It was found important in Morse and Richardson (1983), Abdel-Khalik (1985), Cushing and LeClere (1988), and Dopuch and Pincus (1988). Three variables were used as surrogates for firm size in our study: net sales, net income, and total assets. (3) Inflation and its variability— Higher and stable inflation rates arc expected to generate higher tax benefits from using LIFO. We used the average growth of input price to measure inflation rate, and used coefficient of variation (CV) of input price 2 and CV of growth of input price to measure price variability. (4) Inventory and its variability -- A stable and non-decreasing inventory level is expected to generate the maximum tax savings from LIFO adoption. We used average inventory to measure the inventory level and CV of inventory to measure inventory variability. In general, inventory variability may be affected by the variabilities of demand and production. Firms with lower demand or production variability more easily maintain a stable inventory level. We used net sales growth, CV of net sales growth, and relative frequency of net sales growth to measure demand variability; and used CV of net income and CV of net sales to measure the operational variability of a firm. (5) Inventory controllability - Tax savings obtained from using LIFO depends on the inventory controllability of a firm. The ability to control inventory is a favorable factor for a firm to adopt LIFO. We used two ratios, inventory/net sales and Coefficient of Variation (CV) = Standard deviation / mean. Page 13 inventory/total assets, to measure the inventory controllability. (6) Capital intensity -- Lee and Hsieh (1985) argue that capital-intensive firms have higher fixed-to-variable-cost ratios and should have a stronger incentive to use LIFO. We included gross capital intensity in our variable set. (7) Debt/equity ratio — A higher debt/equity ratio may force the firm's manager to increase current earnings by adopting LIFO. We included long-term debt/equity ratio as its surrogate measure. Table 2 lists the seventeen numerical variables and indicates those tested in Lee &: Hsieh (1985) and Dopuch and Pincus (1988). Please note that our point is not to determine the best set of explanatory variables for LIFO/FIFO studies but to develop a set of LIFO/FIFO data on which the impact of different methodologies can be investigated. Insert Table 2 Here After determining the variables, data were collected from the COMPUSTAT database. The inflation data were collected from the DRI tape. Since many firms switched from FIFO to LIFO in 1974 in response to the oil crisis, we set 1975 as the starting year to obtain samples. The criterion for selection was that the firms must have used LIFO or FIFO firms consecutively for at least ten years. Initially, 220 FIFO firms and 60 LIFO firms were identified. Three of them were later eliminated because of missing data. These firms were distributed in 23 industries, as listed in Table 3. Table 4 shows the means and standard deviations of LIFO and FIFO firms for the numerical variables. Insert Tables 3 and 4 Here Page 14 4.1.2 Testing data sets Since more than one surrogate variable may reflect the same theoretical factor in our initial data base, high correlations among them exist. In order to test the variable and method effects in classification research, we compiled six data sets of different variables from the intial data set. Each resulting data set still has 280 cases. The procedures for composing these data sets are as follows. First, three sets of data with eight numerical variables each were selected after considering the multicollinearity issue. This allowed us to examine the effect of using different surrogate variables in model construction. Second, the nominal variable industry type was added to the three sets to form another three data sets. This allowed us to examine the effect of nominal variables in model construction. Table 5 lists the variables included in each data set. Insert Table 5 Here 4.2 Data Analysis For each data set, two analyses were applied to construct models from data. First, Probit was applied to examine the effect of including different variables on hypothesis testing. The results, as shown in Tables 6 and 7, indicate that the variable effect does exist when Probit is applied. For example, long-term debt/equity is significant in model 1 but insignificant in models 2 and 3. In addition, when CV of net sales was replaced by CV of net sales growth, the significance levels of CV of inventory reduced (models 1 and 3 in Table 6). Insert Tables 6 and 7 Here Another effect we observed is the impact of nominal variables. By comparing the models in Tables 6 and 7, we find that three variables becomes significant because Page 15 of the existence of a nominal variable (industry type): net sales, long-term debt/equity, and growth of input price. However, the significance of gross capital intensity decreases (models 1 and 3 in Tables 6 and 7). All the dummy variables for different industries were not statistically significant. In summary, the results in Tables 6 and 7 suggest that the addition or deletion of a variable may change the significance levels of other variables and hence affect the reliability of hypothesis testing. In the second analysis, ID3 method was applied to the data sets that included industry type 3 . The resulting decision-tree models are shown in Figures 2, 3, and 4. Assuming the variables included in the decision rules to be significant factors, we find three differences between Probit and ID3 models. First, the factors selected by the different methods were different. For example, industry type was considered the most significant one in ID3 models but insignificant in Probit models. Inventory/net sales was very significant in Probit model (model 1 in Table 7); but only appeared in industries 2600, 3600, and 3700 for the ID3 method. Second, different factors were identified by ID3 for different industries. For instance, long-term debt/equity was found important in printing, publishing, and allied industries (SIC code 2700), but irrelevant in the lumber (2400) or chemical (2800) industries. This implies that ID3 is capable of identifying the industry-specific nature of inventory accounting choices. Third, the ID3 models are relatively less sensitive to the addition or deletion of variables. A large portion of the decision trees remains the same in Figures 2, 3, and 4. Insert Figures 2, 3, and 4 Here In addition to the differences in model format and variables included in a model, the classification accuracy of the resulting models is also important. Table 8 shows a 3 The software used to run the ID3 algorithm is called ACLS, which stands for Analog Concept Learning System. Page 16 comparison of the classification accuracy between the models constructed by Probit and ID3. Here the classification accuracy is measured by the percentage of the cases in the input data set that is correctly classified by the model. Generally speaking, Probit models with industry type outperformed those without industry type; and ID3 models outperformed Probit models in terms of the percentage of firms correctly classified. Since the ID3 algorithm tries to cover all sample data in the process of model construction, the perfect classification is no surprise. In fact, this level is usualh r achieved unless conflicting data exist in the samples. A potential problem associated with the high classification accuracy of ID3 is that it may overfit the input data and hence may be heavily influenced by the noise present in the input data set. Therefore. it is necessary to conduct another experiment to compare the prediction accuracy, i.e., the accuracy when the models are applied to hold-out samples, and the circumstances in which a particular method is more appropriate. Insert Table 8 Here 5. THE SECOND EXPERIMENT The second experiment uses hold-out samples to compare the external validity of Probit and ID3. In order to examine the situations where a particular method is better, two factors that may affect the applicability of a particular method were investigated: nature of the data set and training sample size. The experimental design included three independent variables: data analysis method (METHOD), characteristics of the data set (DATA), and training sample size (SIZE). They were organized into a 2*2 >3 factorial design. The methods investigated were Probit and ID3. The characteristics of the data set also had two levels: one was dominated bv a nominal variable, the other was not. A Page 17 data set is said to be dominanted by a nominal variable if the variable alone can correctly classify a significant portion (e.g., 70%) of the input cases. The training sample sizes included three levels: large/small (L/S), medium/medium (M/M), and small/large (S/L). Large/small means using a large portion of the samples to derive the model for predicting a small number of holdouts. Medium/mediun means using about half of the samples to predict another half. Small/large means using a small portion of the samples to predict the remaining samples. The dependent variable was the prediction accuracy of the model derived in a particular setting. It was defined as follows: # of hold-out cases correctly predicted Prediction Accuracy = Total # of hold-out cases The hypotheses tested in this experiment can be formulated as follows. (1) Effect of data characteristics Since Probit and ID3 are substantially different in many aspects, we anticipate that they will have different performance in analyzing different types of data. In particular, we expect ID3 to perform better when a nominal factor has significant effect on the decision outcome and Probit to perform better otherwise. That is, Hl.l: In a situation where actual classification is dominated bv a nominal •j variable, ID3 performs better than Probit. HI. 2: In a situation where actual classification is not dominated by a nominal variable, Probit performs better than ID3. (2) Effect of training sample size The normality assumption usually is true only when the training sample size is large. Since ID3 makes no assumption on data distribution, we expect ID3 to be less sensitive to the decrease of sample size. That is, Page IS H2: The decrease in the size of training sample set has more effect on Probit than on ID3. 5.1. Data Collection The data sets used to test the hypotheses were colic < tod through a two-step process. First, two sets of data with different characteristics were compiled from the initial data set constructed in the pilot study. One was composed of firms in the industries not dominated by a particular inventory accounting method, whereas the other consisted of firms in the industries dominated by a single method. They represented different effects of the nominal variable industry type. The effect of the industry SIC code was relatively low in the first set and high in the second. The degree of industry dominance used to differentiate these two sets was 3/4. In other words, industries with more than three-fourths of their firms using the same method were classified as industry-dominated (DOM). The rest were classified as non-industry- dominated (NDOM). If we define the degree of industry dominance as the percentage of the firms in the data set whose actual inventory method can be correctly classified by observing the industry type only, these two data sets have different degrees of industry dominance. They are 67.5% and 99.4% respectively. The industries with less than five firms in the original data set were eliminated to avoid potential biases in the next stage of the experiment. Table 9 lists the two-digit SIC codes and number of firms included in these data sets. Insert Table 9 Here In the second step of the process, thirty data subsets with three different sizes were randomly sampled from each of the two data sets. The sample sizes of these subsets were divided into three levels: large, medium, and small. The large subset Page 19 included roughly two-third of the samples, the medium subset included one-half of the samples, and the small subset included one-third of the samples in the data set. Table 10 shows the sample sizes of these subsets. Since the industry-dominated and non- dominated data sets had different number of firms, their subsets also had different number of firms. These subsets were used as training data from which decision models were derived. The samples not included in a training subset formed a counterpart, a testing subset, for evaluating the prediction accuracy of the model derived from the training subset. Insert Table 10 Here 5.2. Data Analysis For each pair of training and testing data subsets, the following analysis was performed. First, Probit was used to derive a linear model from the training set. Second, the model was used to predict the LIFO/FIFO choices of the firms in the testing set and to calculate the prediction accuracy of the model. Third, ID3 was used to analyze the same training data sets and derive decision-tree models. Fourth, the resulting models were used to predict the corresponding testing data sets to provide comparable results. This analysis was conducted over all sixty pairs of data subsets. Table 11 shows the means and variances of prediction accuracy under various settings. Table 11- (a) shows the statistics involving a single factor. Table ll-(b) shows the statistics involving the interaction of two factors (SIZE-DATA and METHOD*DATA). Table ll-(c) shows the statistics involving the interaction of all three factors. The average prediction accuracy ranges from 0.60SS to 0.9000. Page 20 Insert Table 11 Here One-way, two-way, and three-way analyses of variance (ANOVA) were performed to test the hypotheses. The results of one-way ANOVA, as illustrated in Table 12, show that DATA (the characteristics of the data set) had significant effect on the prediction accuracy (p=0.01%, R = 0.7062). Both methods performed better in dealing with DOM (the industry-dominated data set). This result is no surprise. It could be because that DOM was less noisy. For example, the degree of industry dominance was by definition much higher in DOM than in NDOM, which increased the prediction accuracy. The result indicates that the less noisy a data set is, the more accurate the resulting model will be. The effects of METHOD and SIZE were not significant at the 5% level. Insert Table 12 Here Since the insignificance of METHOD and SIZE could be attributed to the overwhelming DATA effect, a two-way ANOVA was conducted on DOM and NDOM data sets separately. The results, as shown in Table 13, indicate that METHOD was significant in both DOM (p=4.93%) and NDOM (p=0.01%), whereas SIZE and the interaction of SIZE and METHOD were significant in DOM only (p= 0.17% and p=2.53% respectively). Combining these findings and the descriptive statistics in Table ll-(b), we found that the ID3 algorithm outperformed Probit in DOM (0.S910 versus 0.8633) but was significantly worse in NDOM (0.6192 versus 0.7244). This confirms the hypotheses on data characteristics. 111. I and HI. 2. In DOM, the prediction accuracy decreased significantly (p=0.17%) when rhe sample size decreased. The same trend was observed in NDOM, but the effect was not significant at the 5% level (p=7.14%). The Page 21 significance of SIZE * METHOD in DOM indicate that the reduction of sample size had different effect on different methods. In order to further understand the details of the interaction among factors, a three-way ANOVA was conducted. Insert Table 13 Here Table 14 illustrates the results of the three-way ANOVA. The main effects of all three factors became significant in the analysis. In other words, they all had significant effect on the prediction accuracy of the derived model. In addition, the interactions of SIZE and METHOD and of METHOD and DATA were also significant at p=3.S9% and 0.01% respectively. The effect of SIZE * DATA and the interaction of the three factors were not significant at the 5% level, but the latter was significant at 10% level (p=8.47%). Insert Table 14 Here The significance of the interaction between SIZE and METHOD again supports our previous argument that the reduction of sample size had a different effect on both methods. Combining this result with the statistics in Table ll-(c), we found that the prediction accuracy had two sharp decreases. In DOM. its accuracy decreased from 0.7666 in L/S to 0.7000 in M/M. In NDOM. the accuracy decreased from 0.S91S in M/M to 0.S092 in S/L. This effect, as portrayed in Figure 5, was not seen in the ID3 case, although the accuracy did reduce slightly when the training sample size decreased. The result confirms hypothesis H2 that Probit is more sensitive to the reduction of training sample size. The significance of METHOD * DATA indicates that the characteristics of data set affected the prediction accuracy. This is consistent with the results of two-way ANOVA that supports hypotheses Hl.l and HI. 2. Page 22 Insert Figure 5 Here 6. IMPLICATIONS AND CONCLUSION In this paper, we have presented a non-parametric method for accounting research and two experiments examining some methodological issues. In the first experiment, we found that selection of variables affected the significance of variables and hence the interpretation of research findings. In order to reduce inconsistent findings in classification research, therefore, special attention must be paid to the selection of variables to be included in a study. In addition, if previous findings in different research are to be compared, the effect due to variable selection must be considered. In the second experiment, we found that data characteristics, training sample size, and data analysis method had significant effect on the performance of the resulting model of LIFO/FIFO choice. In addition, the interaction between data characteristics and method, and between sample size and method were also significant. The implications of these findings are two-fold. First, concerning research on LIFO/FIFO choice, the effect of different data analysis methods and the dominance of industry SIC-code need to be investigated. As observed in the first study, the industry SIC-code was considered the most important factor in the decision model derived by ID3, but was insignificant in the model derived by Probit. Most previous research adopted Probit and tended to seek firm-specific economic reasons to explain the LIFO/FIFO decision. This may have been subject to the limitation of Probit in handling discrete variables, as discussed in Sections 2 and 3. Therefore, studies using methods different from Probit or focused on industry-level that use either industry-specific data or data aggregated by industry will be desirable. Page 23 Second, concerning accounting classification research in general, classification algorithms other than statistical methods may provide more reliable results under certain circumstances. Researchers need to consider all alternative methods available in order to increase the reliability of the results. The ID3 algorithm studied in this article is only a representative of AI methods. Other algorithms and new versions of ID3 may provide different results. Of course, there is no one universally best methodology. Therefore, selection of methodology becomes very important to the validity of the results. If a choice is to be made between Probit and ID3, data characteristics and sample size are two major factors that need to be considered. In general, Probit performs better when the effect of nominal variables in the data set is less significant and ID3 performs better otherwise. This is due to their assumptions on data distribution and criteria for constructing decision models. The normality assumption of Probit makes it more sensitive to the decrease of sample size and difficult to handle nominal variables. Its hurdle level, where a sharp decrease of accuracy occurs, is higher than that of ID3. Lack of the normality assumption in ID3, however, causes its poor performance in handling large number of samples with dominant continuous variables; but its repetitive decomposition algorithm allows it to handle nominal variables well. From this brief analysis, we have compared the effect of using Probit and ID3 in studying the LIFO/FIFO choice and shown that Probit and ID3 are complementary methods for accounting classification research. Due to the exploratory nature of the work and the complexity of the issue, further research needs to be conducted to fully understand the choice of methodology for accounting research. Directions include at least the following: (1) Other data characteristics. In this work, we only examined the degree of dominance of a single nominal variable. The cases of multiple nominal variables and Page 24 other criteria for classifying data characteristics will need to be investigated. (2) Other accounting problems. The results were obtained from the LIFO/FIFO choice data. Further work may be done in studying other accounting classification problems. Bankruptcy prediction from financial reports, for example, may also include both nominal and numerical variables and have similar effects. (3) Other methodologies. As stated previously, ID3 is only a representative of AI methods. There are other AI methods, such as Michalski's AQ approach (Michalski and Chilausky, 1980), and algorithms outside AI area that may also be useful for accounting research and need to be examined. Page 25 8. REFERENCES Abdel-Khalik, A.R. (1985), "The Effect of LIFO-Switching and Firm Ownership on Executives 1 Pay," Journal of Accounting Research . Autumn, pp. 427-447. 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Frydman, H., Altman, E.I., and Kao, D.L (19S5), "Introducing Recursive Partitioning for Financial Classification: The Case of Financial Distress," Journal of Finance , Vol. XL, No. 1, pp. 269-291. Hagerman, R.L. and M.E. Zmijewski (1979), "Some Economic Determinants of Accounting Policy Choice," Journal of Accounting and Economics , August, pp. 141-161. Halperin, R.M. and Lanen, W.N. (19S7), "The Effects of the Thor Power Tool Decision on the LIFO/FIFO Choice," The Accounting Review . April, pp. 378-384. Page 26 Hunt, E.B., J. Martin, and P. Stone (1966), Experiments in Induction . New York: Academic Press. Hunt, H.G. (1985), "Potential Determinants of Corporate Inventory Accounting Decisions," Journal of Accounting Research , Autumn. Krippendorff, K. (1986) Information Theory: Structural Models for Qualitative Data . Beverly Hills: Sage Publications. Lee, C. and D. Hsieh (1985), "Choice of Inventory Accounting Methods: Comparative Analysis of Alternative Hypotheses," Journal of Accounting Research . Autumn, pp. 468- 485. Marais, M.L., J.M. Patell, and M.A. Wolfson (1987), "The Experimental Design of Classification Models: An Application of Recursive Partitioning and Bootstrapping to Commercial Bank Loan Classifications," Supplement to the Journal of Accounting Research , pp. 87-114. Messier, W.F., Jr. and J.V. Hansen (1988), "Inducing Rules for Expert Systems Development: An Example Using Default and Bankruptcy Data," Management Science . December, pp. 1403-1415. Michalski, R.S. and R.L. Chilausky (1980), "Learning By Being Told and Learning From Examples: An Experimental Comparison of the Two Methods of Knowledge Acquisition in the Context of Developing Expert Systems for Soybean Disease Diagnosis," International Journal of Policy Analysis and Information Systems , 4:2, pp. 125-161. Mingers, J. (1987), "Expert Systems — Rule Induction With Statistical Data," Journal of Operational Research Society , 3S:1, pp. 39-47. Morse, D. and G. Richardson (1983), "The LIFO/FIFO Decision," Journal of Accounting Research . Spring, pp. 106-127. Noreen, N. (1988), "An Empirical comparison of Probit and OLS Regression Hypothesis Tests," Journal of Accounting Research . Spring, pp. 119-133. Ohlson, J. (1980), "Financial Ratios and the Probabilistic Prediction of Bankruptcy," Journal of Accounting Research . 18:1, pp. 109-131. Quinlan, J (1979). "Discovering Rules From Large Collections of Examples: A Case Study," in D. Michie (ed.), Expert Systems in tJii! Micro Electronic Age , Edinburgh, Scotland: Edinburgh University Press. Quinlan, J.R. (1982), "Semi-autonomous Acquisition of Pattern-bn^rl Knowledge," in D. Michie (ed.), Introductory Readings m Expert Systems . London: George &: Breack. Ricks, W. (19S2), "The Market's Response to the 1974 LIFO Adoptions," Journal of Accounting Research . Autumn, Part I, pp.367-3S7. Shannon, C.E. and W. Weaver (1949), The Mathematical Theory of Communicatio n. Urbana, IL: The University of Illinois Press. Page 27 Sunder. S. (1973), "Relationship between Accounting changes and Stock Prices: Problems of Measurement and Some Empirical Evidence," Journal of Accounting Research (Supplement), pp. 1-45. Industry Type Net Sales Accounting Method Lumber 200 FIFO Lumber 152 FIFO Lumber 312 FIFO Lumber 600 FIFO Lumber 63 FIFO Lumber 400 FIFO Metal 1000 FIFO Metal 500 LIFO Metal 1521 LIFO Metal 2300 LIFO Metal 1420 LIFO Metal 650 LIFO Metal 2000 LIFO Metal 1500 LIFO Note: 1. Net sales are in millions of dollars. Table 1. A Sample Data Set Variable Name This Lee & Dopuch&: Paper Hsieh Pincus Net sales * * * Total assets * * CV of net sales * Relative frequency of sales grow •th * Net sales growth * CV of net sales growth * Inventory * CV of inventorv * * * Inventory/Net sales * * * Inventory/Total assets * * * Net income * CV of net income * Long-term debt/Equity * * * Gross capital intensity * * * CV of input price * * Growth of input price * * CV of growth of input price * se Table 2. Numerical variables Included in the Initial Data Set SIC CODE DESCRIPTION FIFO FIRMS LIFO FIRMS 2000 FOOD AND KINDRED PRODUCTS 6 2200 TEXTILE MILL PRODUCTS 3 3 2300 APPAREL AND OTHER FINISHED 2400 2500 2600 2700 2800 2900 3000 3100 3200 "300 3500 3600 3700 3800 3900 5000 5100 5300 5900 14 5 I 3 10 13 PRODUCTS MADE FROM FABRICS AND SIMILAR MATERIALS LUMBER AND WOOD PRODUCTS, EXCEPT FURNITURE FURNITURES AND FIXTURES PAPER AND ALLIED PRODUCTS PRINTING, PUBLISHING, AND ALLIED INDUSTRIES CHEMICALS AND ALLIED PRODUCTS PETROLEUM REFINING AND RELATED INDUSTRIES RUBBER AND MISCELLANEOUS PLASTIC PRODUCTS LEATHER AND LEATHER PRODUCTS STONE, CLAY, GLASS, AND CONCRETE PRODUCTS PRIMARY METAL INDUSTRIES FABRICATED METAL PRODUCTS, EXCEPT MACHINERY AND TRANSPORTATION EQUIPMENT INDUSTRIAL AND COMMERCIAL MACHINERY AND COMPUTER EQUIPMENT ELECTRONIC AND OTHER ELECTRICAL EQUIPMENT AND COMPONENTS EXCEPT COMPUTER EQUIPMENT TRANSPORTATION EQUIPMENT MEASURING, ANALYZING, AND CONTROLLING INSTRUMENTS; PHOTOGRAPHIC, MEDICAL AND OPTICAL GOODS; WATCHES AND CLOCKS MISCELLANEOUS MANUFACTURING INDUSTRIES WHOLESALE TRADE -DURABLE GOODS WHOLESALE TRADE - NONDURABLE GOODS GENERAL MERCHANDISE STORES MISCELLANEOUS RETAILS 8 14 60 15 20 12 11 1 6 1 2 3 4 3 4 1 2 7 3 1 2 2 4 1 3 TOTAL 217 60 Table 3. Distribution of Sample Firms FIFO FIRMS LIFO FIRMS VARIABLES MEANS ST. DEV MEANS ST. DEV Net sales $341M $885M $1,247M $3,079M CV of net sales .3954 .2073 .3089 .1114 Net sales growth .1410 .1165 .0992 .1114 CV of net sales growth 3.723 11.36 3.155 7.418 Relative frequency of sales growth .7839 .1798 .7852 .1556 Total assets $220M $650M $1,023M $2,781M Inventory $ 69M $ 171M $ 148M $ 315M CV of inventory .4144 .2265 .2776 .1164 Net income $ 30M $ 97M $ 92M $ 284M CV of net income .4498 20.516 1.051 7.2037 Long-term debt/ Equity .5094 .7222 .3643 .2637 Inventory/net sales .2126 .0910 .1636 .0727 Inventory/total assets .3081 .1211 .2627 .1263 Gross capital intensity .3141 .2164 .4649 .2SS0 CV of input price .1961 .0304 .20S6 .0542 Growth of input price .0679 .0132 .0734 .0171 CV of growth of input price .6285 .4146 .6230 .3096 Table 4. Means and Standard Deviations for LIFO and FIFO firms CO CO *J y "y CO -o flj o — : ^ «j <. Q *— ^ ^— ^ c-i cs ^» ~v y CO -o o «5 £ «3 Q 1 — » ^-^ f— 1 1— 1 "y o CO o >«;< d ,< -tj nJ Q^ V <-« /-■ 3 2; y X rt «3 > CN * * * * * * OO CO CO i— ( C"> *# lOVOr-l CN r- CO MOO ! cs o .— < CO CO CN rH co ! * * ^ r>- cn —< o o O CN O .-H CO r- 1 <£> CO o lO n°oo lO W C7> -^ CO CO m co * * * * * * * co o o CN CN * omcs —■ CN CN CN O ^ CN r-J ,-! o t-t CO CO y y CO CO CO co co o O 3 cr y co fi ~ *J CU _, ■ u > Es .2 3 **- "V ^ o to Or' O o .x a, « g g O..S "3 •* J *j <-»-< w-j S 3 O J 5 J^ *» "* > a fr- §*° EL O O o J3 **• G s £ > o « 8 n ft > > 2 2> CO iO o co CN OS iO & -a o o y o ►J y "S y > > > "* rt nj "co ** *» I s a J£ _y y 3 S 3 ,x y y c '2 '3 .5?bbu3 ^COOO y o y >> Eh 3 a •— « hO a 'S =3 O 2 y co «3 P s o 1-1 fa y > — y Q y o 3 n * * * * * * * » * * * * * * ♦ * y — > U3 CO CO y y CO CO co a y 53 -S 3 cr y - y "3 3 1 "3.S. 3 o cs. ~ *-• ■*- ^j ■" > ^^^ — _. . ^ o 2 bO o o y *S «>> o> o ci y > >% Oh O U J C w ^ o y co Q X CO y y -O "y .S CO > ■- C- Variable Name Model 1 Model 2 Model 3 (Data set 4) (Data set 5) (Data set 6) Industry type Coefficients < 0.01 &; insignificant Net sales ' 1.781* — 1.783* CV of net sales .993 1.291 CV of net sales growth -1.119 Total assets CV of inventory Long-term debt/equity Inventory/net sales Inventory/total assets Gross capital intensity Growth of input price CV of growth of input price Log Likelihood Ratio 127.27 115.94 128.30 Note: * ... Significant at least at 5% level. ** ... Significant at least at 1% level. *** . Significant at least at .1% level. — 1.450 — -2.742*** -3.082*** -3.154*** -3.188*** -3.017*** -2.837*** -3.193*** — -3.221*** — -1.097 — 1.471 1.254 1.331 2.191* 2.121* 2.319* 1.328 1.333 1.3S0 Table 7. Models Derived From Data Sets Including Industry Type Situation Model 1 Model 2 Model 3 Probit Method (No Industry Type) 83.03 81.59 82.67 Probit Method (With Industry Type) 86.28 87.00 S5.92 ID3 Method (With Industry Type) 100.0 100.0 100.0 Table 8. Percentage of Correct Classification Non-industry-dominated Industry-dominated Sic code FIFO LIFO SIC code FIFO LIFO 22 26 27 28 30 34 35 39 50 59 Total 3 3 10 13 3 8 14 6 12 6 78 3 2 3 4 4 7 7 2 4 3 39 20 23 24 33 36 37 38 51 Total 6 14 5 1 60 15 20 11 132 1 7 3 1 2 1 15 Table 9. Composition of Two Data Sets for The Second Experiment Non- industry-dominated Industry-dominated Train Test Total Train Test Total Large Medium* Small 78 58 39 39 58 78 117 116 117 98 78 49 49 78 98 147 146 147 * One was randomly held out to make the training and testing sample sizes equal. Table 10. Sizes of the Training and Testing Data Subsets Factor Level N Mean Variance SIZE L/S M/M S/L 40 40 40 .7969 .7771 .7518 .0150 .0155 .0150 METHOD ID3 Probit 60 60 .7552 .7953 .0209 .0091 DATA NDOM DOM 60 60 .6718 ,8787 .0060 .0031 (a) Means and Variances by Factor Levels Factor Level NDOM DOM N Mean Variance N Mean Variance L/S 20 .6948 .0077 20 .8990 .0012 SIZE M/M 20 .6630 .0035 20 .8911 .0010 S/L 20 .6576 .0065 20 .8459 .0056 ID3 30 .6193 .0033 30 .8910 .0011 METHOD Probit 30 .7244 .0031 30 .8663 .0049 (b) Means and Variances by Factor Levels and Data Sets SIZE METHOD NDOM DOM N Mean Variance N Mean Variance L/S ID3 Probit 10 10 .6230 .7666 .0028 .0020 10 10 .9000 .8980 .0010 .0016 M/M ID3 Probit 10 10 .6261 .7000 .0016 .0027 10 10 .8940 .8918 .0012 .0010 S/L ID3 Probit 10 10 .6088 .7064 .0060 .0024 10 10 .8827 .8092 .0011 .0078 (c) Means and Variances by Experimental Cells Table 11. Means and Variances of the Prediction Accuracy Factor Source DF SS MS F P(%) R 2 SIZE Model 2 .0410 .0205 1.35 26.36 .0225 Error 117 1.7764 .0152 Total 119 1.8174 METHOD Model 1 .0484 .0484 3.23 7.5 .0266 Error 118 1.7690 .0150 Total 119 1.8174 DATA Model 1 1.2835 1.2835 283.7** .01 .7062 Error 118 .5339 .0045 Total 119 1.8174 * ... Significant at .01% level Table 12. One-way ANOVA Results Source DF SS MS F P (7o) R 2 SIZE 2 .0162 .0081 2.8 7.14 .5524 METHOD 1 .1655 .1655 56.8** .01 SIZE*METHOD 2 .0126 .0063 2.2 12.55 ERROR 54 .1574 .0029 TOTAL 59 .3517 ** ... Significant at .01% level (a) Two-way ANOVA on the Non-industry-dominated Data Source DF SS MS F P (%) R 2 SIZE 2 .0328 .0164 7.23** .17 .32S2 METHOD 1 .0092 .0092 4.04* 4.93 SIZE*METHOD 2 .0179 .0089 3.94* 2.53 ERROR 54 .1224 .0023 TOTAL 59 .1822 * ... Significant at 5% level ** ... Significant at 1% level (b) Two-way ANOVA on the Industry-dominated Data Table 13. Two-way ANOVA Results Source DF SS MS F P(%) R 2 SIZE 2 .0410 .0205 7.9** .06 .8460 METHOD 1 .0484 .0484 18.7** .01 DATA 1 1.2835 1 L.2835 495.4** .01 SIZE*METHOD 2 .0173 .0087 3.4* 3.S9 SIZE*DATA o .OOSO .0040 1.5 21.85 METHOD*DATA 1 .1263 .1263 48.75** .01 SIZE*METHOD* 2 .0131 .0066 2.53 8.47 DATA ERROR 103 .2798 .0026 TOTAL 119 1.8174 * ... Significant at 5% level ** ... Significant at .1% level Table 14. Three-way ANOVA Results lumber FIFO Figure 1. A Sample Decision Tree Figure 2. Decision Tree for Model 1 < 605M Net sales > 605M FIFO LIFO 33 < .5514 CV of net sales > .5514 < .3833 < .3130 < 48^r CV of net sales Net sales > .3833 > 48M 34 CV of inventory >.3130 LIFO FIFO FIFO LIFO LIFO FIFO < .308 Long term debt/equity < .353i > .30 < .2291 iross capital intensity >19M 35 Gross capital intensity > .2291 2.3534 N CV of net sales < .19 > .1907 FIFO FIFO LIFO FIFO FIFO LIFO < .11 LIFO 36 < 39M. CV of inventory < .101 Net sales > .119 Inventory/net sales >.101 CV of net sales < .1251 Net sales 37 LIFO FIFO 2 414 Inventory/net sales LIFO FIFO LIFO FIFO FIFO Figure 2. Decision tree for Model 1 (cont'd) < .2034 FIFO CV of net sales .2034 -.3097 LIFO >.3097 FIFO 39 Net sales FIFO LIFO < 15M <.3369 Net sales >15M FIFO LIFO SIC CV of net sales < .248 50 Long-term debt/equity >3369 FIFO FIFO 51 53 < 2.227M Net sales > 2.227M FIFO LIFO FIFO 59 < .073 Growth of input prices >.073 FIFO LIFO Figure 2. Decision Tree for Model 1 (conclusion) Figure 3. Decision Tree for Model 2 < .2604 SIC LIFO FIFO LIFO FIFO FIFO LIFO FIFO FIFO LIFO FIFO FIFO FIFO LIFO LIFO FIFO LIFO > .9176 > FIFO < .2837 CV of net sales > .28 Inventory/net sales >.2784 LIFO FIFO FIFO LIFO FIFO Figure 3. Decision Tree for Model 2 (cont'd) < .2034 FIFO CV of net sales .2034 -.3097 LIFO >.3097 FIFO 39 Total asset FIFO LIFO < 11M <.3369 Total asset >11M FIFO LIFO SIC CV of net sales < .248 50 Long-term debt/equity >3369 FIFO FIFO 51 53 < 1.5547M Total asset > 1.554M FIFO LIFO FIFO 59 < .073 Growth of input prices > .073 FIFO LIFO Figure 3. Decision Tree for Model 2 (conclusion) FIFO Growth of input price <.0567 >.0567 FIFO < 1 .22 Inventory/net sales FIFO LIFO Long-term debt/equity > .051 > .401 CV of net sales growth < .127 < .3084 Long-term debt/equity CV of inventory > .89 < .1235. CV of inventory > .1235 LIFO LIFO LIFO FIFO FIFO Net sales <6,857M CV of net sales Net sales > 601 M Figure 4. Decision Tree for Model 3 <605M SIC Net sales <.3130 CV of inventory >605M < 2.725 Long-term debt/equity > 2.725 < 1 .66 >.3130 <.308 Long-term debt/equity >.308 > 19M Gross capital intensity > .3! CV of net sales >.2777 Net sales <39M < .1014 Inventory/net sales >39M <.3132 > .1 01 4 CV of inventory < .1 251 Net sales >414M Inventory/net sales > .1 251 FIFO LIFO LIFO FIFO LIFO FIFO LIFO FIFO FIFO FIFO LIFO FIFO LIFO FIFO LIFO FIFO LIFO FIFO LIFO FIFO LIFO FIFO FIFO Figure 4. Decision Tree for Model 3 (cont'd) SIC >.141 CV of net sales < .141 < 1.36 <18M CV of net sales growth > 1.36 Net sales >18M Net sales >295M Net sales > .2108 Inventory/net sales < .98 Long-term debt/equity CV of net sales > .248 Net sales < 2,227 CV of net sales growth LIFO LIFO FIFO FIFO FIFO LIFO FIFO LIFO LIFO FIFO FIFO FIFO LIFO FIFO LIFO FIFO Figure 4. Decision Tree for Model 3 (conclusion) Accuracy 90.. 80.. 70 60 50 L/S -o- M/M DOM NDOM S/L Sample Size Labels : O ID3 q Probit FIGURE 5. prediction Accuracies of ID3 and Probit