Accepted Solutions
Thank you again for your reply, @Caozheng0115 -san
You can specify any positive costs. In non-parametric estimates, the cumulative costs are calculated. In parametric estimations, costs are used as weights for log likelihood function. (If you would like to know the mathematical details, I would like to explain it more, so please reply so.)
I am very afraid that I misunderstood your situation and that I might have failed to explain "time-varying effect". In your last example, the "Site" column is not "time-varying effect". "Time-varying" effects are effects whose values changes within each ID. In the following data, the Site column is a time-varying effect.
I am also afraid that I misunderstand the difference in robots. I assumed that all robots are the same version, type and grade, so I did not set the "ID" as a grouping effect or a model effect. (For example, if ID=001, ID=002 and ID=003 are C-3PO, R2-D2 and BB-8 in Star Wars, respectively, these three robots are completely different kinds. So, I think we should set the ID column into Grouping column and also include it to a model effect.)
In your last example, the "Site" is completely confounded with the "ID". So, we cannot separate the effect of Site from ID. (For example, C-3PO worked only in a desert, R2-D2 worked only near sea, and BB-8 worked only inside a comfortable building, we cannot separate the ID effect from the place effect.)
Although I must still misunderstand your situation, the following is an example of an analysis for your last example. I calculate the nonparametric cumulative costs for each ID=001 and 002 separately by including the ID to Grouping column. I exclude data for ID=003 from my analysis because there is only one failure. I fit the parametric Loglinear Poisson process model for each ID. Based on this model, the cumulative cost at Time=300 for ID=001 is estimated to 13300.37, and the one at Time=300 for 002 is done to 550.007.
I attach the data table, your last example, which I used for the above analysis.
Thanks for the fast response. I understand you point on including 0 cost for each site change. I should provide more details.
I think the concern now is how JMP handle 0 cost. It seems that JMP will just exclude the bots earlier than it should, if the bot have 0 cost at early time. With less bots considered effective by JMP, the mcf value will be increased. Following is what I see. Top one is data with one 0 cost per bot. Bottom is data with multiple 0 cost (one per bot per site). The bottom mcf value is greater because jmp exclude the 0 cost value bot too early. That is my understanding, which might be wrong.
I ask the same question to ChatGPT and following is the answer. I felt that 0 zero cost per bot for the last event seen is what I should do. Let me know what you think.
Option A — Simple & Robust (recommended first)
Keep one row per event (Cost=1) with the Site value active at that event, and one final Cost=0 row per bot at the bot’s last observed transaction.
This approach uses the event rows to carry the time-varying Site value. It’s simple, avoids multiple right-censor rows per bot, and JMP will correctly use the Site value that was in effect at each event.
When to use: most common; sufficient if you only need the covariate at event times (which is usually the case).
Pros: easy, avoids JMP misinterpreting multiple 0s.
Cons: doesn’t explicitly model intervals with no events where the covariate changed — but that’s rarely necessary for NHPP estimation.
Data shape
Each row is either:
-
Event row:
BotID,AccumulatedTransactions(event time),Cost = 1,Site = site_at_event -
Final censor row (one per bot):
BotID,AccumulatedTransactions(last observed),Cost = 0,Site = <last site or NA>
How JMP uses this
-
When you add
Siteas a column affecting Scale/Shape, JMP uses theSitevalue on each event row to estimate howSiteshifts the log-rate and/or shape. Because each event row carries the site at that time, you have effectively encoded a time-varying covariate.
Hi, Thank for your fast reply. Could you explain why option 2 not option 1? In your sample data, it looks that both way(a column for cost and individual cost for two cause) work and generate the same results. I guess If I want to show one cause in figure 1 and the other cause in figure 2, I need to make new columns for Cost for different cause so the result are consistent. Is that what you are suggesting? How about a similar situation for Grouping then? For instance If I group by site. Is there a way to show single site result and figure which is the same as that for results generated from data include multiple sites?
I check the sample data you sent. It looks that you use Mode as cause, site as scale effect in the first saved analysis. The model you used is proportional NHPP. Is there a reason for the model pick? My understanding is that proportional NHPP model assumes a common baseline MCF curve for all causes, scaled up or down by multiplicative factors. In my case, the different cause effects are not assumed to be proportional, so I used the Log linear model. Let me know if that is the model I should use.
I have trouble understanding the fit curve generated. Is the red fit curve for Fail 1? The fit curve is really far away from the red MCF curve. Why is that happening? There are two blue fit curves. Which one is the fit curve for Fail2? Why are there two fit curves generated? What is the green fit curve?
Or the fit curves are for different sites. But the red one only has one curve instead of two. I don't understand why that happened.
Thanks.
Names Default To Here(1);
Random Reset(111111);
n = 30;
nid = 100;
data = J(2*n*nid, 4, .);
b1 = 3;
theta1 = 5;
b2 = 8;
theta2 = 8;
k = 0;
For( id = 1, id <= nid, id++,
x = 0;
For( i = 1, i <= n - 1, i++,
x = (x ^ b1 + Random Exp() * theta1 ^ b1) ^ (1 / b1);
k++;
data[k, 1] = id;
data[k, 2] = 1;
data[k, 3] = x;
data[k, 4] = 1;
);
k++;
data[k, 1] = id;
data[k, 2] = 1;
data[k, 3] = x;
data[k, 4] = 0;
For( i = 1, i <= n - 1, i++,
x = (x ^ b2 + Random Exp() * theta2 ^ b2) ^ (1 / b2);
k++;
data[k, 1] = id;
data[k, 2] = 2;
data[k, 3] = x;
data[k, 4] = 1;
);
k++;
data[k, 1] = id;
data[k, 2] = 2;
data[k, 3] = x;
data[k, 4] = 0;
);
dt = As Table(data,<<Column Names({"ID","Site", "Time", "Cost"}));
Column(dt,1) << Modeling Type("Nominal");
Column(dt,2) << Modeling Type("Nominal");
dt << Recurrence Analysis(
Y( :Time ), Label( :ID ), Cost( :Cost ),
Event Plot( 1 ),
Fit Model(
Scale Effects( :Site ),
Shape Effects( :Site ),
Run Model,
Model Type( "Power Nonhomogeneous Poisson Process" )
)
);
Hi,
Thanks for you reply, this is really helpful. Somehow I missed the email form JMP community to remind me to look at your response. Sorry for the late reply.
I will NOT use site as GROUPING role.
I have performed the analysis and presented some of the results. My manager is happy. So thanks a lot.
The next step is to see the COST (actual money) in the MCF to see the average money per bot repair.
So I am planning to put the money amount instead of the 1(indicating repair) in the cost role column. The 0 will still be kept to indicated censor status.
It that the right way to study average money per bot repair? Following is the data sample with actual money in Cost role column.
I am using JMP 18 standard.
Thanks.
Thank you again for your reply, @Caozheng0115 -san
You can specify any positive costs. In non-parametric estimates, the cumulative costs are calculated. In parametric estimations, costs are used as weights for log likelihood function. (If you would like to know the mathematical details, I would like to explain it more, so please reply so.)
I am very afraid that I misunderstood your situation and that I might have failed to explain "time-varying effect". In your last example, the "Site" column is not "time-varying effect". "Time-varying" effects are effects whose values changes within each ID. In the following data, the Site column is a time-varying effect.
I am also afraid that I misunderstand the difference in robots. I assumed that all robots are the same version, type and grade, so I did not set the "ID" as a grouping effect or a model effect. (For example, if ID=001, ID=002 and ID=003 are C-3PO, R2-D2 and BB-8 in Star Wars, respectively, these three robots are completely different kinds. So, I think we should set the ID column into Grouping column and also include it to a model effect.)
In your last example, the "Site" is completely confounded with the "ID". So, we cannot separate the effect of Site from ID. (For example, C-3PO worked only in a desert, R2-D2 worked only near sea, and BB-8 worked only inside a comfortable building, we cannot separate the ID effect from the place effect.)
Although I must still misunderstand your situation, the following is an example of an analysis for your last example. I calculate the nonparametric cumulative costs for each ID=001 and 002 separately by including the ID to Grouping column. I exclude data for ID=003 from my analysis because there is only one failure. I fit the parametric Loglinear Poisson process model for each ID. Based on this model, the cumulative cost at Time=300 for ID=001 is estimated to 13300.37, and the one at Time=300 for 002 is done to 550.007.
I attach the data table, your last example, which I used for the above analysis.