Comparison between models

This section will make some comparison between these two models by using the testing criteria, RMSE, MAD, and MAPE. The fit curve can offer a growth trend of one technology; therefore, the fitting performance is also an important part to do the technology forecasting. These data sets can be classified according to length, the saturation level, and the growth rate during 10% to 90% penetration level. This section will use the estimated value of these three models to draw the curve in order to see the fit performance through figures. The fitting performance between models also can be performed in other way. The testing criteria will be listed by a tabular form.

These criteria which used to test the fitting performance will be described first, and they will help the researcher easily to find which model is better than others through the number form.

Now the long data sets (e.g. Microwave oven, Room air conditioner, and Color TV sets) will be discussed first. The extended logistic model can compare with other two existent models by drawing each projected curve (Figure 4.1 to 4.3). Although these three models all look close to the original data points in these three data, some difference between models can also be found through projected curves. The penetration of microwave oven shows a bi-logistic form for the growth lagging at 1980-1985; therefore, these models all overestimate the penetration in that stage (Figure 4.1). This phenomenon makes Gompertz underestimate the introduction and saturation level, but Fisher-Pry and extended logistic model are more close to data points than Gompertz.

Microwaver Oven

Figure 4. 1 The penetration and estimate value in Microwave Oven data.

Room Air Conditioner

1970 1975 1980 1985 1990 1995 2000 Year

Figure 4. 2 The penetration and estimate value in Room air conditioner data.

Saturation level plays an important role in order to make forecasts precisely.

However, Fisher-Pry supposes a saturation level at 100%. In the case of room air

conditioner, extended logistic and Gompertz perform better than Fisher-Pry model according to the projected curve (Figure 4.2). Fisher-Pry obviously overestimates the trend in introduction and saturation level. This case shows that Fisher-Pry is only appropriate to some data sets whose saturation level reached 100%. The data set of color TV sets shows a rapid growth, and it only takes 6 years from 10% to 90%.

These three forecasting models all looks better in fitting performance, because most of data points fall in between 90% to 100% (Figure 4.3). Consequently, the only way to check the fitting performance is to look the criterion.

Color TV

0 10 20 30 40 50 60 70 80 90 100

1960 1970 1980 1990 2000

Year

Penetration Penetration

Fisher-Pry Extended Logistic Gompertz

Figure 4. 3 The penetration and estimate value in Color TV data.

After checking these long data sets, the extended logistic model shows the trend that it fits better than other two models (Table 4.3). The extended logistic model performs better than Gompertz and Fisher-Pry model in all data sets.

Table 4. 3 The comparison between long data sets.

Microwave oven Room air

conditioner color TV Gompertz and

Extended Logistic Extended Logistic Extended Logistic Extended Logistic Fisher-Pry and

Extended Logistic Extended Logistic Extended Logistic Extended Logistic Now the short data sets will be discussed in order to compare the performance between models. The data set of space heater grows slowly after reaching 60% of penetration. Fisher-Pry seems to lose its fit ability in this case, but Gompertz and extended logistic model still have good fit ability (Figure 4.4). The reason is that Gompertz and extended logistic model can change it capacity. If the right capacity is chosen, the fitting performance will be better.

Space Heater

0 10 20 30 40 50 60 70 80 90 100

1975 1980 1985 1990 1995 2000 Year

Penetration Penetration

Fisher-Pry Extended Logistic Gompertz

Figure 4. 4 The penetration and estimate value in Space heater data.

VideoTape Recorder

0 10 20 30 40 50 60 70 80 90 100

1975 1980 1985 1990 1995 2000

Year

Penetration Penetration

Estimate(FP) Extended Logistic Gompertz

Figure 4. 5 The penetration and estimate value in Space heater data.

Same situation happened in two cases below, videotape recorder and radio cassette (Figure 4.5 to 4.6). The case of videotape recorder shows a standard sigmoid form, and grows slower after 1993. The extended logistic and Gompertz model both have good fitting performance in this case, and Fisher-Pry still meets the same problem. Although the case of radio cassette does not look like a sigmoid curve, the extended logistic model also can fit this case well, and so does Gompertz model. The extended logistic decide the capacity from the observed data points, but Gompertz model needs to decide the capacity manually. Although both extended logistic and Gompertz model have good fitting performance, the extended logistic can avoid deciding capacity in order to decrease the personal bias.

Radio Cassette

1960 1965 1970 1975 1980 1985 1990 Year

Penetration Penetration

Fisher-Pry Extended Logistic Gompertz

Figure 4. 6 The penetration and estimate value in Radio Cassette data.

CD Player

1986 1988 1990 1992 1994 1996 1998 2000

Year

Penetration Penetration

Fisher-Pry Extended Logistic Gompertz

Figure 4. 7 The penetration and estimate value in CD player data.

The case of CD player has the least number of data points in these 7 data sets (Figure 4.7). The extended logistic model shows the better fitting performance than other two forecasting models. The reason that extend logistic performs better is that it

can adjust the capacity according to data points, not adjust it artificially. Fisher-Pry has the worst performance than other models, and Gompertz model can adjust its fitting performance by changing the capacity. However, changing the capacity may affect projections when Gompertz model is used in this case.

This research tests the short data sets (Space Heater, Video Tape Recorder, Radio Cassette, and CD player), and this step is to inspect whether the extended logistic model also fit well in short data sets. Because most of the short data sets do not reach 100% saturation level, this research will set the possible upper limit. For example, Space heater will reach the saturation level about 80%; therefore, 0.8 is the possible upper limit. Therefore, the extended logistic model performs better than other two models in these four short data sets (Table 4.4).

Table 4. 4 The comparison between short data sets.

Space Heater Video Tape Recorder

Radio

Cassette CD player Gompertz and

The classification of data sets in this thesis has been introduced at Chapter 3 (Table 3.1), and the shape of curve can simply divided into three forms, symmetric (Microwave Oven, and Room Air Conditioner), asymmetric (Color TV, and Video Tape Recorder), and flexible (Space Heater, Radio Cassette, and CD Player). The extended logistic model fits well in different kinds of points of inflection (Table 4.5), and judgmental criteria are according to the measurements (Table 4.6). The most factor that influence the Fisher-Pry model is upper limit. Because Fisher-Pry model

assumed that old products or technologies will complete substitute by new technologies, it will make large biases in fitting some data sets whose saturation level are less than 100%.

Table 4. 5 The rank of models in symmetric, asymmetric, and other data sets

Symmetric Asymmetric Flexible

Microwave

Table 4. 6 The criterion between models in durable goods.

Model MAD RMSE MAPE

Fisher-Pry 3.491 3.8629 0.1821

Gompertz 4.1594 4.9 0.1082

Microwave Oven (28)

Extended 3.3284 3.7454 0.1253

Fisher-Pry 3.4078 3.8123 0.3195

Gompertz 1.34 1.8 0.068

Room Air Conditioner(33)

Extended 1.267 1.5957 0.076

Fisher-Pry 1.2104 1.3689 0.2336

Gompertz 1.0088 1.1472 0.0818

Color TV(33)

Extended 0.5167 0.6059 0.1426

Fisher-Pry 4.1426 4.7339 0.1412

Gompertz 1.2302 1.5921 0.0309

Space Heater(21)

Extended 0.213 0.7862 0.0189

Fisher-Pry 7.0779 7.9655 0.7375

Gompertz 2.3444 2.8108 0.1893

Video Tape Recorder(21)

Extended 1.9434 2.4643 0.1043

Fisher-Pry 2.794 3.4465 0.1014

Gompertz 1.3965 1.6142 0.041

Radio Cassette(21)

Extended 1.3313 1.6252 0.047

Fisher-Pry 5.4321 6.2623 0.2104

Gompertz 2.5618 2.8868 0.0799

CD Player (12)

Extended 0.7339 0.9895 0.019