Especificación de casos de uso

The purpose of this analysis is to provide an estimate of the parameter known as the state of mind and a measure of the reliability of its estimation. QoE for web browsing is assessed via metrics derived from the three areas of Network, Application and Content as well as taking in account the random effect of a users’ state of mind.

As mentioned in 4.2.4, state of mind (SOM) has been analysed during the course of our experiments. Users’ states of mind are a random distribution via time and under any circumstances. The model 3 described by Equation(2.52) has been integrated with a random effect for the state of mind.

Table 6-3: Results of model structural assessment based on likelihood test approach (cont.)

Model Df AIC BIC logLik Chisq Chi Df Pr(>Chisq)

Model 1 55 2199.5 2462.5 -1044.8

Model 2 58 2157.1 2434.4 -1025.5 48.438 3 1.718e-10***

Model 3 59 2130.4 2412.5 -1006.2 28.717 1 8.376e-08***

According to the likelihood as described in Table 6-3, Model 3 is one more parameter than model 2. In the favour of the “smaller is better” for both AIC and BIC, model 3 is superior to model 2. In favour of the “larger is better” of log-likelihood (logLik), model 3 is superior to model 2. pvalu e  8 .3 7 6e08 0 .0 0 1 '* * * ' shows a significant test

('*** ') for model 3. Thus, model 3 is superior to model 2.

Figure 6-3: Residuals distribution of Model 3

Figure 6-3 shows a normal Q-Q plot and Q-Q line for model 3. It is roughly normal, and closer than that in model 1. It is approximately independently distributed with a mean of 0 which is much closer to 0 than that found for model 1.

The linear regression between observed and the fitted mean opinion score is shown in the figure with 2

R at roughly 0.9441 (Spearman test) for model 3 giving the respective best fits for the data. 2

The conditional modes of the random effects for each of SOM are presented in Figure 6-4. It indicates normal probability of random variable of SOM and its 95% confidence intervals.

Figure 6-4: Conditional modes of the random effects forSOM factor

Estimated values for random effects of SOM in the Model 3 are shown Table 6-4. Those values are either greater or less than 0, and it concluded that the random effect of

SOM should be introduced into model 3.

Table 6-4: Estimated values of random effect ofSOM

SOM Intercept

Bored 0.0682959

Normal 0.2261464

Stress -0.2944423

The conditional modes of the random effects for each nested combination of (id time: ) are presented in Figure 6-5. It shows the normal probability of random variables of subject and time (id time: ) and its 95% confidence intervals.

Figure 6-5 combines two results into one figure. The first result shows details of random effects estimates from the fitted model 3. This gives a list of b_i that corresponds to each of the 6642 points of {id:time}on the intercept and each level of {D} and {RPS}. Thus, a list of b_i that corresponds to each of 738 discrete points on each Intercept, or each level of D, or each level of RPS. The lowest value of b_i was - 2.429, and the highest value of b_i was 2.38. Therefore the y-axis is a value of the random effects estimates. The highest value of each black line is the upper value of the 95% confidence level, and the lowest value of each black line is the lower value of the 95% confidence level, while the blue dot represents an estimate of the average random value of the random effect of{id:time}.

Then, the estimates of the random effects are applied in a Q-Q plot, thus the x-axis shows a standard normal population on the horizontal axis and the y-axis shows the random effects estimate quantiles. The Q-Q plot is used to compare the shape of the distribution. The linearity of points suggests that the data were normally distributed.

Figure 6-5: Caterpillar plot of normal probability of the conditional modes of the random effects for grouping (id: time) factor from Model 3

Figure 6-6 shows the estimation of fixed effects factors of { ,D RPS Content, } in Model 3. The 95% confidence intervals are estimated by red and green lines in which the first represents the upper confidence interval values and the latter represents the lower bounds.

Figure 6-6: Estimation of fixed effects ofD, RPS and Content and 95% confidence intervals of Model 3

6.4 Discussion and Conclusions

As noted earlier, the data that is collected from users may be a potential source of error because:

1) There is variability between users in how they respond to the experiments that must be accounted for in our analysis.

2) The responses from the same participants are likely to be correlated. For example, if the response from user of (id 1.3) is above the mean of response of the first test at timei , it is likely that (s)he will be above the mean of

response of test 2 at time i1 .

3) We observe 882 responses, but only from 21 users (with a total of 17 different users), if we make inferences about users in general, our effective sample size is 17 rather than 882.

Thus, we have seen the above issues and applied the mixed effect model which has taken the potential source of error into account, as a source of fixed and random effects. The fixed effects explain the response itself, while the random effects explain the variance of the response.

In this chapter, we presented an integration of the human factor of state of mind as well as the uniqueness of individuals themselves during the course of experiments into

model 2. It has become clear that SOM is not easy to capture in a realistic situation although it is needed to support complex analysis from both a psychological and machine learning perspective. SOM changes over time for each individual, this leads to the observation that shows changing MOS scores even though the controllable effects of D and RPS remain fixed. SOM is integrated as a random factor because user’s state of mind change randomly during the experiments between subjects and within each subject. In the scope of our research, SOM is subjectively measured by users’ feedback.

In our terminology, the Contentis considered as objective factor based on download time. However, it is a fact that, content is a user specific factor in terms of particular users. Although, the definition of Content in our experiment has been rather narrowed in comparison to the actual concept of content; however, its effect is still indicated in Section 4.2.5, the content metric for QoE of Web based services. Therefore, that factor is necessary for QoE of Web based services. Both SOM and Content have been integrated in Model 3.

Based on results described in Sections 6.1 and 0, the integration of SOM and Content remains the correlation between fitted values and observed values, giving a value of R0.9716 and 2

0.941

R  . However, more importantly, the integrated

factors improve the model performance based on information criteria where maximum of log likelihood, dimension of model, and effective sample size have been used to assess the result.